THESIS Roland Tóth 2004

Transcription

1 THESIS Roland Tóth 2004

2 Univeity of Vezpém, Hungay Depatment of Automation Faculty of Infomation Technology THESIS Implementation of a Speed Senole Induction Moto Contol on TMS320F243 Roland Tóth Supevio: Déne Fodo D. 2004

3 UNIVERSITY OF VESZPRÉM Depatment of Automation Faculty of Infomation Technology H-8200 Vezpém, 10 Egyetem St., Hungay Tel.: +36(88) Fax: +36(88) th Mach 2004, Vezpém DIPLOMA TOPIC Fo Roland Tóth 3 d yea Electical Engineeing tudent Title of the thei: Implementation of a Speed Senole Induction Moto Contol on TMS320F243 Induction moto ae widely ued in the induty due to thei imple tuctue, low cot, and high eliability. Although they ae the hoepowe of induty, thei contol i ignificantly moe challenging than of dc moto. Nowaday, theefoe, thee i a geat inteet in developing high pefomance contol device to enhance the opeation of induction dive in all field of application. Epecially, thee effot concentate on contolle that do not need peed eno to opeate, which geatly educe cot and maintenance. The goal of thi diploma thei i to implement a peed enole contolle on a TMS320F243 DSP baed VSI-fed induction moto dive. Thei wok aignment: tudy the exiting peed enole technique (obeve baed, MRAC, DTC, Sliding mode) and the moden invete elated contol technologie (pace vecto PWM, ync. PWM, ) peent the elected peed enole algoithm and the mathematical and phyical conideation of it deign develop the implementation of the algoithm on a TMS320F243 EVM and ealize the cloed loop dive with the diect contol of a DigitalSpectum invete fed induction moto.

4 Subject goup of the final examination: Analóg áamköök: (Analog Cicuit) Iányítátechnika (Contol Technique) Digitáli áamköök (Digital Cicuit) Szabályozott villamo hajtáok (Contol of Electical Dive). Déne Fodo D. Supevio..... Józef Va D. Head of the Depatment

5 Nyilatkozat Alulíott Tóth Roland, diplomázó hallgató, kijelentem, hogy a zakdolgozatot a Vezpémi Egyetem Automatizálá Tanzékén kézítettem el főikolai villamoménök diploma (Bachelo of Electical Engineeing) megzezée édekében. Kijelentem, hogy a zakdolgozatban foglaltak aját munkám eedményeit, é cak a megadott foáokat (zakiodalom, ezközök, tb.) haználtam fel. Tudomául vezem azt, hogy a zakdolgozatban foglalt eedményeket a Vezpémi Egyetem, valamint a feladatot kiíó zevezeti egyég aját céljaia zabadon felhaználhatja. Vezpém, máju Tóth Roland

6 Közönetnyilvánítá Mindenekelőtt zeetném megközönni Szüleimnek, hogy lehetővé tették zámoma egyetemi tanulmányaimat. Szeetnék továbbá közönetet mondani témavezetőmnek, D. Fodo Dénenek, valamint a Vezpémi Egyetem Automatizálá Tanzékének, amiét munkámat maga zintű technikai feltételek mellett végezhettem, továbbá D. Szedekényi Gábonak é Bogná Endének a zakmai egítégét. Külön közönöm Salekovic Ádámnak a nyelvi nehézégek leküzdéében nyújtott kitató egítéget. Hálá vagyok még kedveemnek é baátaimnak, akik biztatáukkal é tüelmükkel nagyon okat egítettek.

7 TARTALMI ÖSSZEFOGLALÓ A zakdolgozat az azinkonmoto obuztu fodulatzám-ézékelő nélküli zabályozáát megvalóító endze implementációját mutatja be egy TMS320F243 pocezo vezélet fezültég betápláláú invete (VSI) által üzemeltett laboatóiumi hajtáon. A zabályozá é endze elmélet ezen teületén fellelhető moden elméletek (mint a politopiku endze epezentáción töténő LPV H -zabályozó é -megfigyelő zintézi, a úlyozott ézékenyégű tuktúák, a ki eőítéek tétele é a kitejeztett Kálmán zűők (EKF) teóiája) alapján megtevezett é bemutatáa keülő zabályozó a moto diekt fluxu é fodulatzám zabályozáát tezi lehetővé a telje 4/4-e elméleti hajtái tatományon zajo ipai könyezet hatáit i figyelembe véve. Az eedményül kapott hajtá képe alkalmazkodni a moto tengelyén fellépő nyomatékváltozáokhoz é teljeíti a manapág egye növekvő villamo hajtáokkal zemben támaztott ipai elvááokat, mint a fodulatzám ézékelő nélküliég (cak a fázi áamok méée), obuztu tabilitá é a zaj ézéketlenég. A fenti elméleti imeetek alapján tevezett zát zabályozó kö Matlab/Simulink könyezetében kézült implementációját i imetetjük melyen elvégzett zimulációk eedményei alapján a tuktúa az elvááoknak megfelelően működött. A dolgozatban bemutatáa keülnek a jelenleg ipailag haznált fodulatzám ézékelő nélküli zabályozát biztoító megoldáok, mint a efeencia motomodellek, adaptív megfigyelők, MRAS, DTC, é vekto alapú technikák, melyek özehaonlítáa keülnek az általunk adott zabályzái tuktúával. Ezenkívül, a mai azinkonmotoo hajtáok elvi é gyakolati felépítéét i megvizgáljuk a gejezté előállítááa zolgáló impulzu zéleég moduláció (PWM) technikák bemutatáa mellet. Az implementáció alapjául zolgáló mikokontolle vezéelt tévekto (SV)-PWM VSI betápláláú hajtáláncot ézleteen elemezzük az általunk tevezett zabályzó megvalóítái lehetőégeinek függvényében, é az implementáció által a Code Compoe fejleztői könyezetben létehozott ANSI C pogamot valamint a hajtában felhaznált azinkonmoto paaméte identifikációját i imetetjük. A dolgozatot a mééek é a zimulációk alapján kapott eedmények vizgálata zája a hajtá jóágáa, hatékonyágáa, obuztuágának é tabilitááa vonatkozó következtetéek é a továbbfejleztéi lehetőégek imetetée mellett. Kulczavak: azinkonmoto, H, LPV, EKF, úlyozott ézékenyég, fodulatzám-ézékelő nélküli zabályozá, TMS320F243 EVM, DTC, MRAS, SV-PWM

8 ABSTRACT The thei how the implementation of a obut contol tuctue fo the peed enole vecto contol of the induction moto (IM) on a TMS320F243 poceo contolled voltage ouce invete (VSI) diven laboatoy induction moto dive. The deigned obut contolle whoe deign i baed on the moden achievement of Contol and Sytem theoy (uch a the politopic ytem epeentation baed H contolle and obeve ynthei, the mixed enitivity tuctue, mall gain theoem, and the theoy of extended Kalman filte (EKF)) i peented which make poible the diect contol of the flux and peed on the full 4/4 opeation ange of the moto with toque adaptation in highly noiy indutial envionment. In thi way the poduced tuctue fulfill the ecently gowing expectation fo indutial dive a the contol without peed eno (with the meauement only of the phae cuent), obut tability, and noie attenuation. The deigned cloed loop contol ytem i teted by intenive Matlab/Simulink imulation that ae peented in the thei to pove the goodne of the olution, which accoding to the eult how good dynamic and obut pefomance. In thi pape the ecently ued peed enole technique in the induty, uch a the diect efeence model, adaptive obeve, MRAS, DTC, and vecto contol baed method ae hown and compaed to the deigned contolle tuctue. Moeove, the theoetical and pactical concept of the moden IM dive and the pule width modulation (PWM) baed the powe feed geneation method of thee device ae alo peented. The micocontolle diven pace vecto (SV)-PWM VSI fed dive, which i ued fo the implementation of the contolle, i analyzed in detail with epect to the concept of the contolle ealization. The implementation eulted ANSI C pogam in the Code Compoe development envionment i alo explained with the paamete identification of the applied moto of the laboatoy dive. The expeienced meauement and imulation outcome of the implementation ae evaluated in tem of effectivene, obutne, and tability and the obtained concluion ae dawn. Finally, poible impovement of the contol tuctue and futue application ae pointed out a well. Key wod: induction moto, H, LPV,EKF, mixed enitivity, peed enole contol, TMS320F243 EVM, DTC, MRAS, vecto contol, SV-PWM

9 Table of content Table of content Abbeviation...vi 1. Intoduction The mathematical model of the induction moto Baic concept of opeation Modeling condition Geneal mathematical deciption Voltage and flux equation The dynamical motion equation Appoximation of oto eitance vaiation Model epeentation in otating efeence fame Geneal efeence oientation Roto flux oiented epeentation The linea paamete vaiant moto model Geneal dynamic popetie of the model Exiting peed enole technique Contant Volt pe Hetz contol Machine model Diect efeence model Adaptive obeve & filte Full ode nonlinea obeve Sliding mode obeve Extended Kalman Filte H baed LPV obeve Model efeence adaptive ytem Diect toque contol Vecto contol Fuzzy contol Opeation of induction moto dive Claical powe feed geneation concept Rectifie DC link Invete Invete contol cicuity The micocontolle The PWM invete The inulated-gate bipola tanito i

10 Table of content The mechanim of PWM-VSI invete Diffeent technique of the 3-phae PWM geneation on VSI-PWM invete Synchonou ymmetic PWM Synchonou aymmetic PWM Aynchonou PWM Space vecto PWM Ovemodulated PWM The expeimental laboatoy dive The induction moto The Spectum Digital invete Specification of the invete module Capabilitie of the invete module Seno Built in potection The Invete Inteface Cad Specification of the inteface module I/O ignal conditioning Invete Digital Inteface Shield of the dive The TMS320F243 Evaluation Module Specification of the EVM Conideation of contolle implementation Chip of many thing Speed and memoy Inteupt and peipheal Digital I/O pin Event manage (EVM2) Time PWM geneation Deadband unit Captue unit Quadatue Encode Pule (QEP) Cicuit Analog to digital convete (ADC) Communication inteface Seial Communication Inteface (SCI) Seial Peipheal Inteface (SPI) Contolle ae netwok inteface (CAN) Watchdog ii

11 Table of content Heat and oul of the dive The PC The XMS510P Plu JTAG dive The Code Compoe envionment The opeato inteface Implementation of the contolle The theoetical tuctue of contol The H contolle module I/O lineaization baed efeence tanfomation Roto flux oientation and flux angle tacking The tuctue of etimation The H obeve The EKF Etimation of the load toque Tuning paamete Simulation eult The identification of the moto Method of identification Meauement Reult of the identification Validation of the model The pogam of the DSP Flow chat of the pogam The hadwae boot up Sytem initialization and hadwied contant Contol loop Poce of ADC Pocee of etimation Poce of contol Poce of PWM geneation Additional featue Speed conideation Concluion Refeence iii

12 Table of notation Table of notation n(t) oto peed [evolution/ec] R x tato ide eitance of phae x [Ω] n 0 ynchonou fequency [Hz] R f 0 input ynchonou fequency [Hz] R tato ide 3 phae eitance [Ω] oto ide 3 phae eitance [Ω] p numbe of pole pai R initial value of R [Ω] 0 ω(t) angula peed of the oto [ad/ec] L ω 0 ync. angula peed [ad/ec] L ω (t) angula peed of otating efeence k fame [ad/ec] ω (t) ang. peed of oto flux [ad/ec] l flux L m lumped tato 3 phae induc. [H] lumped oto 3 phae induc. [H] lumped mutual 3 phae induc. [H] tato winding phae inductivity [H] ω (t) ef. ignal of oto peed [ad/ec] l ef oto winding phae inductivity [H] (t) lip l f field inductivity [H] cuent denity ditibution in phae F ( α,t) x m x [A/ad] l mutual inductivity [H] i (t) tato cuent in phae x [A] C capacity [F] x u (t) x tato voltage in phae x [V] ρ (t) angle between the tato fixed and the oto fixed efeence fame [ad] Ψ magnetic flux [Wb] ρ (t) angle between the tato fixed and k the otating efeence fame [ad] ϕ i init. ang. of tat. cuent vec. [ad] P (t) mech mechanical powe [W] ϕ u init. ang. of tat. voltage vec. [ad] W (t) mech mechanical enegy [J] a thee-phae unity vecto W(t) e electical input powe [J] x pace vecto in tat. fixed ep. W(t) v eitive powe lo [J] x pace vecto in oto fixed ep. W (t) field ai gap powe of magnetic field [J] f x pace vect. in oto field oient. ep. T (t) e electomagnetic toque [Nm] k x pace vect. in otating ef. fame T (t) load load toque [Nm] eal pat of pace vecto x in x τ d mech otating efeence fame mechanical time contant [Nm] x imaginay pat of pace vecto x in q τ e otating efeence fame electical time contant [Nm] eal pat of pace vecto x in tato x α τ fixed efeence fame tato time contant (contant) x imaginay pat of pace vecto x in β τ tato fixed efence fame oto time contant (contant) x nominal value of ignal x τ m. coupling time contant (contant) nominal x ef efeence ignal of x σ leakage facto (contant) x eo eo ignal of x λ notation, def. pp. (contant) i x pace vecto decibing cuent a denity ditibution of phae x [A] J moment of inetia [Nm] i x pace vecto decibing the oveall tato ide cu. denity ditib. [A] T(t) oto tempeatue [K] i x pace vecto decibing the oveall T 0 oto ide cu. denity ditib. [A] initial oto tempeatue [K] iv

13 Table of notation Ψ x (t) pace vec. decibing the oveall tato ide flux linkage ditib. [Wb] x pace vec. decibing the oveall Ψ (t) Ψ x (t) σ oto ide flux linkage ditib. [Wb] pace vec. decibing the oveall leakage flux ditib. [Wb] u x (t) pace vecto decibing the oveall tato ide volt. denity ditib. [V] Q(t) c m K k heat [kcal] pecific heat ct. Al [J/kgK] weight of the oto winding [kg] linea heat convection (contant) u x pace vecto decibing the oveall oto ide volt. denity ditib. [V] F faction (contant) i (t) eff m value of the oto phae cu. [A] h dicete time tep [ec] i (t) eff m value of the tato p. cu. [A] t time [ec] u (t) eff m value of the tato p. volt. [V] ν, α angle [ad] i (t) p active tato cuent [A] K cont. of geneal poblem definition U bu invete bu voltage P conideed ytem (plant) of the geneal poblem definition u x x th witching tate of the invete p paamete vecto u xox± 60 voltage vect. of ecto x (SV-PWM) x tate vecto of the ytem u (t) in contol voltage of the PWM G() fequency tanition func. of the y. u (t) x,y x o y ef. voltage of the PWM x( kk) etimated tate vecto baed on k peviou etimation u (t) out output voltage of the PWM P (k k) covaiance of the eo poce out U 0 amplitude of the fundamental fequency component x eo of the etimation m FM fequency modulation value y output vecto of the ytem m AM amplitude modulation value u contol/geneal ytem input V p peak voltage value v vecto of meaued output ignal V pp peak to peak voltage value z ytem output vecto (optimization) S ( ωˆ ) x complex gain facto w input ditubance of the ytem f(x,u) tate function (non linea tate pace y. deciption ) e eo ignal of the ytem f(x) tate func. of an input-affine model R covaiance of meauement noie f d (x) dicetied tate function Q covaiance of ytem noie h(x) output function (non linea tate pace y. deciption ) γ optimal H gain h d (x) dicetied output function v 1, v 2 vitual input g(u) input func. of an input-affine model ˆx pedicted / nomalized value g d (u) dicetied input function δ caling tep ize/re. of comp. feq. Ξ equence of meaued value T 1, T 2 Modulation time in the SV-PWM θ paamete value α u angle of tato voltage vec. [ad] G (.) fit ode gadient vecto change / eo of a given vaiable 2 econd ode gadient vecto λ filte gain of the exponential filte (A, B, C, D, E) (Φ, Γ, C, D) matice of the continuou tate pace epeentation of the ytem matice of the dicete tate pace epeentation of the ytem v

14 Abbeviation Abbeviation AC Analog Cuent/Voltage MIPS Million Intuction Pe Second ACG Automated Code Geneation MOSFET Metal Oxide Semiconducto Field Effect Tanito AI Atificial Intelligence MRAS Model Refeence Adaptive Contol AS Aymmetic Synchonou NL Nonlinea (ytem) CAN Contolle Aea Netwok NMI Non Makable Inteupt CPU Cental Poceing Unit NRZ Non Retun to Zeo DC Diect Cuent/Voltage PC Peonal Compute DSP Digital Signal Poceo PIC Pogammable Integated Cicuit DTC Diect Toque Contol PID Popotional, Integational, Deivational (contol) EC Extenal Commutation PWM Pule Width Modulation EKF Extended Kalman Filte QEP Quadatue Encode Pule EVM Evaluation Module RAM Random-Acce Memoy EVM2 Event Manage ROM Read-Only Memoy FIFO Fit In Fit Out (data toage) RTDX Real-Time Data Exchange FLC Fuzzy Logic Contol SC Self Commutation GEL Geneal Extenion Language SCI Seial Communication Inteface GP Geneal Pupoe SPI Seial Peipheal Inteface IDE Integated Development SS Symmetic Synchonou Envionment IGBT Iolated Gate Bipola Tanito SV-PWM Space Vecto baed Pule Width Modulation JTAG Joint Tet Action Goup TI Texa Intument (IEEE ) LPV Linea Paamete Vaiant (ytem) UART Univeal Aynchonou Receive/Tanmitte LQG Linea Quadatic Gauian UML Unified Modeling Language Contol LTI Linea Time Invaiant (ytem) VSI Voltage Souce Invete LTV Linea Time Vaiant (ytem) WD Watch Dog emf. mmf. electomagnetic foce magnetomotoic foce vi

15 1. Intoduction 1. Intoduction Induction moto ae widely ued in the induty due to thei imple tuctue, low cot, and high eliability. Although they have become dominant only in the pat decade on the field of vaiable peed electical dive, thei economical impotance i notewothy with moe than 12 billion US$ wold maket volume, of which the annual gowth ate i 15%. [18] The contuction of the fit induction moto (IM) wa a ignificant beakthough in the field of electical machine. In 1888, Tela eceived half a million dolla fom the Wetinghoue fo the patent of hi invention. Unfotunately, thi wa followed by 60 yea of banihment, becaue it quickly tuned out that the contol of thi electical machine i a challenging tak [31]. Difficultie had ien becaue of it highly nonlinea natue and the low technology level of Powe Electonic. The nonlinea dynamic behavio of thi ytem, which i even effected by paamete ditubance, pevented the effective ue of the analog contol method. Moeove, the extemely impotant tength and oientation of the magnetic field, decibed by the magnetic flux (Ψ), can be only expenively and inaccuately meaued, o it contol need mathematical etimation. Futhemoe, ome of the paamete of the IM, like the vaiation of the oto eitance (R ), intoduce lage uncetaintie into the ytem behavio. Thee wee the eaon fo the golden age of DC moto which povide eay contollability and powe management with a moe complicated contuction [19]. By the impovement of technology, like the evolution of contol and ytem theoie and the impotant eult in Powe Electonic, a the iolated gate bibola tanito (IGBT) and the cheap, eliable, and high fequency invete, the induction dive have lowly ovetaken thi field and become the hoepowe of the induty, poviding moe than 90% of today indutial dive. The ucce of the IM can be explained by thei imple tuctue and the need of le maintenance becaue of the abence of gaphite buhe. Only in thoe field which need imple contol and high peciion peeved the DC moto thei leading ole. Nowaday, theefoe, thee i a geat inteet in 1

16 1. Intoduction developing high pefomance and obut contolle to make induction dive unbeatable in all field of application. Epecially, thee effot concentate on contolle that do not need peed eno to opeate, which geatly educe cot and maintenance. Moden indutial dive alo need to be inenitive fo the heavy noie of the indutial envionment and be able to adapt to paamete uncetaintie elated to manufactuing. Motivated by thi goal and baed on moden mathematical method and phyical conideation, we how the implementation of a obut, peed enole contolle on a TMS320F243 digital ignal poceo (DSP) contolled induction moto dive that give the oppotunity of fat contol of the moto peed and the magnetic field aociated with the oto flux (Ψ = [Ψ α, Ψ β ] T ) on the full 4/4 opeation ange of the moto. The voltage feed of the IM i geneated by a voltage ouce invete (VSI), which i connected with an inteface cad to the DSP. The full opeation of the dive i hown with the tep of the implementation of the obtained contolle. Moeove, a the eult of the implementation, the poduced DSP pogam with it unique method i peented in C a well. Accoding to the theoetical and pactical eult, thi ealization hold the poibility of good pefomance and fulfill the need of the moden indutial expectation. To be able to explain the olution of the conideed contol poblem, fitly the dynamic mathematical model of the IM i intoduced with the elf contucted linea paamete vaiant (LPV) ytem model of the moto. Then, the main dynamic popetie of the given model ae analyzed. In the next ection the exiting peed enole technique ae peented biefly to povide good look out to the mot up-to-date technique ued in enole IM dive. The uage and effectivene of the howed method ae analyzed and thei diadvantage and applicabilitie ae pointed out. In the thid ection the poblem i invetigated fom the point of view of powe ytem. The exiting technique to povide the powe feed of the dive ae peented with the mechanim of the invete. Then the elf-aembled laboatoy dive i focued on, with the deciption of the phyical layout and by the intoduction of each hadwae element of the dive. 2

17 1. Intoduction Seveal iue of implementation ae analyzed and the pecification of an applicable contol tuctue i given. In the ixth ection the implemented contol algoithm i intoduced and invetigated fom both theoetical and pactical apect. The eult of the numeically imulated pefomance ae peented in the cae of intenive and dynamic change of the opeation envionment to pove the effectivene of the algoithm. The nonlinea paamete identification of the moto model i alo analyzed, baed on the eult of meauement and on the theoy of the gadient method. Futhemoe, the elf-witten DSP pogam, which make poible the implementation of the peented algoithm in C i alo given and analyzed in the point of view of optimality. Finally, the eult of the implemented dive ae given and compaed with othe publihed eult in thi field. Futhemoe, at the end, the futhe poibilitie of impovement of the ytem ae conideed with the ongoing eeach effot. 3

18 2. The mathematical model of the induction moto 2. The mathematical model of the induction moto 2.1. Baic concept of opeation In the the following ection, the tuctue of the induction moto and thei main featue of functioning ae intoduced baed on [6, 12, 20, 21, 26, 32]. The tuctue of the IM can be divided into two pat, namely the tato and the oto, a it can be een in Figue 2.1. The tato, which i built up fom good flux conducting plate, i held togethe by a cat-ion hull. In the othe pat, the voltage poweed tato winding i ituated in the haft-oiented abbet on the inne ide cylinde of the plated moto hull. Thi tato winding i uually mathematically modeled by an infinitely fine coil continuouly wapped aound the inne ide cylinde of the tato. The thee-phae AC voltage, which i applied to thi winding, eve a the powe ouce of electical toque that poduce the mechanical motion. The othe pat, which i called the oto, ha mechanical connection only though beaing with the tato and it i cafted fom ion plate. The thee-phae winding of the oto i ituated in imila abbet aound the uface like the tato winding. In thoe moto of which the ated powe i le then 10kW, thee oto coil ae uually built fom aluminum ba, which ae connected by conducting ing on the font ide of the plated body. Thi type of deign i called quiel-cage moto and it i vey typical in mot of the application of the IM. In the following ection, thi type of the IM i conideed. Figue 2.1. Schematic of the induction moto 4

19 2. The mathematical model of the induction moto In Figue 2.1, the chematic of the moto can be een, whee an ai gap epaate the peviouly mentioned tato and oto pat. The exitence of thi ai gap i impotant, becaue though it, the oto i connected only magnetically to the tato. Baed on thi, the two pat can be modeled by the pime and ecunde ide of a otating tanfomato which i decibed by complex quantitie due to the otation. Similaly to the popetie of a tanfomato, the magnetic coupling though the ai gap povide the flow of enegy between the two electical ubytem, and theefoe ha a ignificant ole in the oveall efficiency of the IM. The mechanim of the moto i biefly the following: when thee-phae AC voltage i applied to the evenly ditibuted coil aound the cylinde of the tato, a otating magnetic field i built up inide the machine, which poduce inuoidal cuent inide the oto winding baed on the induction phenomena. Thi inducted cuent alo poduce a otating magnetic field aound the oto which tie to extinct the effect that bought it to exitence. Thu, it tie to line up to the magnetic field of the tato in tength and in oientation a well, but becaue of the field of the tato otate and the induction in the oto leen when the two magnetic field appoach cloe, the field of the oto can neve align with the field of the tato. Afte the tanient an equilibium tate i eached when the two field otate with the ame peed, which i called ynchonou fequency, but the field of the oto alway lag behind the field of the tato. Moeove, the inteaction between the two magnetic field poduce a electomagnetic foce (emf), whoe effect i othogonal to the haft and foce the oto to otate. The peed of the oto i noted by n(t), which i uually given in angula peed: ω (t) = 2π n(t), and the ynchonou peed of the magnetic field can be decibed a follow: = f input fequency p = numbe of pole pai (2.1) 0 n 0, which i uually given in angula fequency: ω 0 = 2π n 0. Futhemoe, the nomalized diffeence of the two peed i the lip () of the moto: n n = (2.2) 0. n0 5

20 2. The mathematical model of the induction moto The lip i diectly elated to the load toque and it decibe the equilibium tate of the electomagnetical inteaction. (t) ( 0,1] (in motoic opeation ange) Baed on the diection of the enegy flow, the IM can be opeated a a moto and a geneato a well, although it i baely ued a a geneato becaue of efficiency elated iue. In thi pape, only the motoic opeation of the IM i going to be decibed Modeling condition In the next ection, the quiel-cage type IM i conideed whoe phyical layout paamete ae aleady included in the ynchon fequency of the magnetic field and in the mechanical time contant of the machine. Beide thi, the following aumption ae made, which ae widely common in mathematical invetigation of thi phyical phenomena [32]: The pemeability of the ion body of the oto i aumed to be infinite with linea magnetic popetie, o the atuation phenomena do not affect the magnetic coupling. The ion coe i aumed to be homogeneou, thu cicula paaite cuent ae not poduced inide the coe which would leen the induction. Slotting effect, like deep ba and end effect ae alo neglected. The patial ditibution of the phae cuent in the tato winding i conideed to be inuoidal, which decibe two half moon hape denity ditibution otating along the cylinde of the tato. The thee-phae ta connection of the tato coil ha ymmetic electical paamete, and the input excitation i alo a pefectly ymmetic theephae voltage o cuent feed Geneal mathematical deciption By applying the above mentioned aumption and neglecting the decibed lo effect to the deciption of the moto, the intantaneou patial ditibution of one phae cuent can be given a Figue 2.2. In the following, the mathematical deciption of the moto i invetigated though the pace vecto 6

21 2. The mathematical model of the induction moto theoy intoduced in [26] to be able to ue the poibilitie povided by thi appoach. If it i aumed that the cuent of the tato i the input excitation of the machine, than the F x ( α,t) patial ditibution along the tato of the x phae cuent can be decibed by the i (t) x complex vecto whoe oientation i detemined by the diection of the epective phae axi and the cuent polaity [18]. In the peented cae the poitive phae cuent i (t) a in tato winding phae a ceate a inuoidal cuent denity ditibution that lead the winding axi a by 90, having theefoe it maximum in the diection of the imaginay axi. Figue 2.2. Cuent denity ditibution of phae a Figue 2.3. Stato ide cuent denity ditibution The total magnetomotoic foce (mmf.) inide the moto i obtained a the upepoition of the cuent denity ditibution of all thee phae. Thi poduce again a inuoidal ditibution of the oveall tato cuent denity wave indicated by Figue 2.3. The i (t) pace vecto, which decibe thi oveall cuent ditibution, can be given by the upepoition of the pace vecto of each phae a it can be een in Figue 2.3. Futhemoe, i (t) can be alo computed fom the poitive ucceive epeentation of the ymmetic phae cuent: j 0t 2 π ω + +ϕ 0 2 i 2 i(t) = a i a(t) + a i b(t) + a i c(t) = 2 i eff(t) e, (2.3) 3 ia (t) ib (t) ic (t) 2 { } { } { } i (t) = Re i (t), i (t) = Re a i (t), i (t) = Re a i (t), (2.4) a b c 7

22 2. The mathematical model of the induction moto whee 2 e j π 3 a = i the complex unity vecto that decibe the phae lag and the pace oientation of the cuent denity ditibution to each othe along the tato. Fo completene, equation (2.4) povide the invee tanfomation of (2.3). So i (t), the tato cuent pace vecto, epeent the inuoidal patial ditibution of the total mmf. wave ceated inide the machine by the thee phae cuent that flow fom the outide of the machine. The mmf. wave ha it maximum in an angula poition that lead i (t) by 90 a illutated in Figue 2.3. The amplitude of thi mmf. i popotional to i (t). Futhemoe, the caling facto 2/3 peented in the equation (2.3) eflect the fact that the total denity ditibution i obtained a the upepoition of the denity ditibution of the thee phae winding, while the contibution of only two phae winding, paced 90 apat, would have the ame patial effect with the phae cuent popely adjuted. Theefoe, it povide the caling facto fom thee-phae deciption to the two-phae baed complex epeentation. Thi appoach i called enegy invaiant epeentation and it i ued in the following to contuct the model of the IM. The excitation poduced flux denity ditibution in the ai gap i obtained by patial integation of the cuent denity wave along the cylinde of the tato. Theefoe, it i alo a inuoidal wave, and it lag the cuent denity wave by 90 a illutated in Figue 2.4. Figue 2.4. Stato ide oveall flux linkage ditibution It i convenient to chooe the flux linkage wave, a a ytem vaiable intead of the flux denity wave a the fome contain added infomation on the winding 8

23 2. The mathematical model of the induction moto geomety and the numbe of tun of the coil. By definition, a flux linkage ditibution ha the ame patial oientation a the petaining flux denity ditibution, theefoe the tato flux linkage ditibution peented in Figue 2.4 can be decibed by the pace vecto Ψ (t). Baed on ame eaon, the Ψ (t) pace vecto can be alo intoduced to epeent the oto flux linkage ditibution. In the individual tato winding, the otating flux denity wave induce voltage. Since the winding denitie ae inuoidal patial function, theefoe the induced voltage ae alo inuoidally ditibuted in pace. The ame i tue fo the eitive voltage dop in the winding. Thu, the oveall ditibuted voltage in all phae winding can be epeented by the u tato voltage pace vecto, which i a complex vaiable and can alo be computed fom the poitive ucceive epeentation of the tato phae voltage: (t) j 0t 2 π ω + +ϕ 0 2 u 2 u(t) = a u a(t) + a u b(t) + a u c(t) = 2 u eff(t) e, (2.5) 3 ua (t) ub (t) uc (t) 2 { } { } { } u (t) = Re u (t), u (t) = Re a u (t), u (t) = Re a u (t). (2.6) a b c Voltage and flux equation If we conide the pime ide of the complex tanfomato (Figue 2.5) a the tato of the IM, then equation (2.7) decibe the connection between the intoduced tato ide pace vecto: d Ψ (t) u(t) = i(t) R +, dt (2.7) whee = = = denote the i(t) R i the eitive voltage dop and R Ra Rb Rc eitance of the ymmetic tato phae winding. The induced voltage vecto, epeented by the lat tem of (2.7), i the back electomagnetic foce (emf.). 9

24 2. The mathematical model of the induction moto Figue 2.5. Complex tanfomato that decibe the model of the IM By conideing the ecunde ide of the complex tanfomato, it can be concluded that the ame elationhip i tue to the oto ide pace vecto, but becaue of the hot cicuited oto winding, in thi cae u (t) = 0, t, thu d (t) u(t) = i(t) R + Ψ = 0. dt (2.8) Equation (2.7) and (2.8) decibe the electomagnetic inteaction a the connection of fit ode dynamic ubytem. Becaue fou complex vaiable: i (t), i (t), Ψ (t), Ψ (t) ae peented in thee two equation, (2.9) and (2.10) flux equation ae needed to complete the elationhip between them. Ψ (t) = i (t) L + i (t) L e ρ, (2.9) j (t) m Ψ (t) = i (t) L e + i (t) L, (2.10) ρ j (t) m whee the peented ρ (t) angle decibe the poition of the oto compaed to the axi of the tato, while L = 3 l + 3 l, L = 3 l + 3 l ae the thee-phae 2 2 f 2 2 f inductance and l, l ae the inductance of a tato and a oto phae winding, l i the elf inductance, and L = 3 2 l i the mutual inductance between the tato f m m and the oto [32]. In ode to eliminate the ρ (t) angle fom the model equation tanfomation of oto ide vecto into the efeence fame of the tato i needed. Thu, by applying the following ubtitution: i (t) = i (t) e j ρ(t) and Ψ (t) = Ψ (t) e ρ, then j (t) 10

25 2. The mathematical model of the induction moto Ψ (t) = i (t) L + i (t) L (2.11) m Ψ (t) = i (t) L + i (t) L (2.12) m equation povide the flux connection in the model, while, becaue of the conitence of the tanfomation, (2.7) and (2.8) do not change The dynamical motion equation Baed on the concept of enegy conideation, the electomagnetic toque of the moto can be deived eaily [26]. Fo the mechanic powe P mech (t) of the ytem, the following i tue: whee the mechanical enegy dw (t) = (2.13) dt mech P mech (t), W mech (t) in cae of otating ytem can be given by dw mech (t) = T(t) e ω (t). (2.14) dt Howeve, it i alo tue that the mechanical enegy can be peented in the fom of whee W e(t) = W mech (t) + W v (t) + W field (t), (2.15) dw (t) 3 e = Re +, dt 2 * * { } u i u i i the input electic powe, { } 2 2 dw (t) 3 v = Re R + R, dt 2 i i i the eitive powe lo, dw field (t) 3 dψ * dψ Re * = i + i, dt 2 dt dt i the ai gap powe. Hee, the complex conjugation wa noted by *. By ubtituting the above equation into (2.14), it can be concluded that: 3 L P = T ω= ω Ψ (t) i (t). (2.16) m mech e 2L 11

26 2. The mathematical model of the induction moto Fom (2.16) the electomagnetic toque of the moto can be expeed in cae of a p polyphae machine: 3 L T (t) = p Ψ (t) i (t). (2.17) m e 2 L It mut be noted that (2.17) can alo be given a a poduct of any two of the i (t), i (t), Ψ (t), Ψ (t) tate vaiable by appopiate caling. Futhemoe, fo the mechanical ubytem of the moto, the dynamical motion equation i a follow: d ω(t) τ mech = Te Tload F ω (t), (2.18) dt whee τmech = J/p i the mechanical time contant, J i the moment of inetia, T load i the load toque, and F ω(t) i the enegy lo due to fiction. Baed on (2.18), the diffeential equation, decibing the change of ω, the angula peed of the oto, can be deived a follow: 2 ω 3p L = m load ( i ) τ d (t) dt 2JL 1/ τe T (t) + F ω(t) Ψ (t) (t). (2.19) mech Appoximation of oto eitance vaiation Becaue the paamete uncetaintie have geat impact on the oveall ytem dynamic, the mot ignificant oto eitance vaiation ha to be modeled omehow fo an accuate deciption of the ytem. Howeve, it i not ewading to give vey detailed deciption of thi change, becaue the value of R i unique fo evey IM and it dynamic popetie tongly depend on the layout and the built-in mateial of the moto and on othe uncetain paamete [40]. Thu, only an appoximation of the eal deciption i needed to model the mot impotant dynamic of the uncetain paamete vaiation. It i known that the eitance change to heat of a given aluminum body with linea heating chaacteitic i a follow: R(t) R0 R0 =, T(t) T 245+ T 0 0 (2.20) 12

27 2. The mathematical model of the induction moto whee R 0 i the oto eitance at T 0 nomal tempeatue, and 245 i the pecific contant of the aluminum. Futhemoe, the heat poduced by the electical enegy can be given by (2.21). t 2 ( eff ) (2.21) t0 Q(t) = 0.86 i (t) R (t)dt. By conideing the heating popetie of mateial: Q(t) = m c (T(t) T 0), (2.22) i alo tue, whee c i the pecific heat, m i the weight of the aluminum ba. Baed on equation (2.20), (2.21), and (2.22) it can be concluded that dr (t) 0.86 R dt 245 T m c 2 ( eff ) k ( 0 ) 0 = ( + 0 ) RT0 i (t) R(t) K R (t) R, (2.23) if it i aumed, that the heat diipation to the envionment depend only on the enegy leaking caued by convection, which i linea and it i decibed by the ate contant K k Model epeentation in otating efeence fame The epeentation of the moto model in a otating efeence fame, intoduced by Blachke, Hae, and Leonad moe than 20 yea ago, ha completely changed the field of contolle ynthetiation fo aynchonou moto [41]. They fomed the baic idea of the pace vecto baed diect toque contol, which ha been ecently the mot widely ued method fo IM dive. Thi baic idea i the following: intoduce uch a new coodinate ytem, which otate with angula peed againt the peviouly ued tato fixed efeence fame. On thi way, at any time intant, if the angle between the eal tato axi and the eal axi of the new efeence fame i ρ k, then the flux pace vecto in thi epeentation (ee Figue 2.6) can be given in the following fom: ω k 13

28 2. The mathematical model of the induction moto Figue 2.6. Rotating two-phae coodinate ytem k j ρk (t) ( Ψ (t) e ) d Ψ (t) d d Ψ (t) d ρ (t) dt dt dt dt k j ρk(t) k k j ρk(t) = = e + j (t) e k j ( ρk (t) ρ(t) ) ( Ψ (t) e ) d Ψ d (t) = = dt dt k d Ψ (t) d ρ (t) d ρ(t) = + dt dt dt Ψ (2.24) j ( ρ (t) ρ(t) ) k j ( ρ (t) ρ(t) ) k k e j Ψ (t) e k (2.25) whee the vecto peented with index k ae the tanfomed vecto of the d ρk (t) otating efeence fame, =ω k (t) i the angula peed of the efeence dt otation, and d ρ (t) =ω (t) i the angula peed of the oto. By applying the dt efeence tanfomation to all of the pace vecto, equation (2.7) and (2.8) ae efomed a follow: k ρ j k(t) ρ j k(t) d Ψ (t) ρ j k(t) u(t) = u(t) e = i(t) e R + e = dt k k d Ψ (t) k = i(t) R + + j ωkψ (t). dt (2.26) d Ψ (t) 0 = u (t) = u (t) e = i (t) e R + e dt k k d Ψ (t) k = i(t) R + + j ( ωk ω) Ψ (t). dt k ρk ρ ρk ρ ρk ρ j ( (t) (t)) j ( (t) (t)) j ( (t) (t)) (2.27) By the conitency of the tanfomation, (2.11) and (2.12) peeve thei oiginal fom. 14

29 2. The mathematical model of the induction moto Geneal efeence oientation Let equation (2.11), (2.12), (2.26), and (2.27) ae conideed in a geneal efeence fame otating with the angula peed of k k k k ω k. In thi cae, any two of the i (t), i (t), Ψ (t), Ψ (t) pace vecto can be choen to tate vaiable duing the fomulation of the model, but fo decoupled contol of the flux and peed, it i woth chooing i k (t) and k Ψ (t) fo the tate of the ytem. On thi way, fom (2.11) and (2.12): can be fomulated with fom (2.27) and LL L L Ψ (t) (t) Ψ (t), (2.28) 2 k m k m k = i + L L k d Ψ (t) LmR k R k = i(t) + j ( ωk ω) Ψ (t), (2.29) dt L L 2 k 2 2 LL Lm d i(t) k L m LL L m k = u(t) R 2 + R + j ωk i(t) L dt L L LmR L m k + j ω 2 Ψ (t), L L (2.30) fom (2.26). Alo, the exact tate equation can be deived fom (2.29) and (2.30). If we decompoe ou complex vaiable to thei eal (d) and imaginay (q) pat, and uppoe that the oto eitance vaie, then the following input-affine tate pace equation ytem, which i nonlinea in ω, ω k, and R, decibe the model. 1 Lm ( ωk ω(t) ) 0 τ(t) τ(t) 0 0 k k Ψ d (t) 1 Lm Ψ d (t) 0 0 k ( k (t)) 0 d q (t) ω ω (t) (t) k k Ψ τ τ Ψ q (t) 1 u d (t) = + 0 k dt i d (t) τ τ ( λτ (t) + τ) k k i d (t) Lσ ω(t) ω u q (t) k k k i q (t) σ τ (t) σ σ i q (t) 1 0 τ τ ( λτ (t) + τ) L ω(t) ωk σ σ σ τ (t) σ B A( ωω, k,r ) (2.31) 15

30 2. The mathematical model of the induction moto whee σ = 1 (L m ) 2 / (L L ), λ = (L m ) 2 / L, τ = L m / (L L ), τ (t) = L / R (t), τ = L / R. Beide (2.31) the motion and the k k k k d ω (t) Ψd (t) i q (t) Ψq (t) i d (t) T load (t) + F ω(t) =, dt τ τ e mech (2.32) 2 k k 2 k k dr (t) Ψd (t) Lmi d (t) Ψq (t) Lmi q (t) = RT0 + R(t) Kk( R (t) R 0), (2.33) dt L L oto eitance nonlinea diffeential equation complete the deciption of the ytem by defining the vaiance of the paamete of the tate matix ωω A (, k,r ), fom which ω and of the (2.31) moto model, while R ae epeentation independent paamete ω k define the epeentation of the model. If ω k = 0, then the eal pat of the tate vaiable i indexed with α and the imaginay pat i with β Roto flux oiented epeentation Nowaday, thee ae eveal epeentation of the moto model ued in the field of IM dive, baed on the value choen fo ω k. Fom thee poible epeentation, only the field oiented appoach i conideed in the following ection, becaue a it i going to be hown, thi oientation make poible the deign of an efficient contolle with eae. By thi appoach, a new efeence fame i intoduced, whee the eal axi i bounded to the otating Ψ k (t) vecto, thu ω k =ω flux. In thi cae, k Ψ ha no imaginay component, which fact (t) implie the educement of the tate vaiable by letting out k Ψ fom the model. q (t) Moeove, becaue at teady tate all of the tato ide electical quantitie (Figue 2.7) in the tato fixed efeence fame otate with the ame ynchonou fequency of the flux field, thee field-oientated vaiable ae contant. So in thi way, ω flux =ω 0, and (2.31) i tanfomed into the following fom: 16

31 2. The mathematical model of the induction moto Figue 2.7. Roto field oientation in two phae otating efeence fame 1 L 0 Ψ d 1 i (t) i (t) 0 dt (t) L i (t) m f τ(t) τ(t) f 0 0 d (t) Ψd (t) f f τ ( λτ u (t) + τ) f d d = ωflux d + f f σ τ σ f σ q i q (t) q τ ( λτ (t) + τ) 1 ω(t) ωflux 0 σ σ Lσ (t) u (t) (2.34) f Becaue Ψ (t) 0 q =, thu fom (2.31), it involve that: f Lm q flux (t) (t). f τ(t) Ψd ω =ω + i (2.35) Since (2.35) enue the coect oientation, the fom of (2.19) mut be alo modified. f f d ω (t) Ψd (t) i q (t) T load (t) + F ω(t) =. dt τ τ e mech (2.36) In thi way, the poblem i efomulated billiantly, becaue f Ψ can be d (t) diectly contolled by i f d (t), while ω (t) i contolled with i f (t), without any q co-effect. Thi idea, which povide the decoupling of the contol, i going to be ued in the contolle to be deigned The linea paamete vaiant moto model Today, becaue the LTI ytem theoy i well woked-out and uppot eveal efficient and obut contol method, geat potion of the nonlinea contol poblem ae olved, by attibuting them to a linea time invaiant (LTI) fom, even in the cae of highly ophiticated and eliability-needed aea, uch a the aviation [28],. In the implet cae, the tanfomation to LTI fom i uually 17

32 2. The mathematical model of the induction moto done though the lineaization of the ytem model, although the global lineaization fo mot of the nonlinea model poduce geat lo in the deciption of the eal dynamic of the ytem. Thu, fo thoe cae whee the ytem ha tong dynamical popetie, the eaiet way to olve thi dilemma i to locally lineaize ou ytem point by point on a paamete pace to poduce locally LTI ytem. If we chooe the lineaization point to be infinitely cloe to each othe, then the ytem deciption of the model can be imagined a a locally LTI ytem moving in a n dimenional ytem pace. Thee type of ytem ae called LPV ytem, whee the model i linea with epect to the tate, input, and output, and the tate pace matice A(.) D(.) ae dependent on a p(t) n dimenional bounded paamete vecto. If we uppoe that the paamete ae mooth and changing low enough, then it i poible to ue the LTI contol theoie to deign in evey point of the paamete pace an LTI contolle fo the locally linea LPV ytem. Thi method i called gain cheduling and it wa intoduced by Packad [30] and Apkaian & Gahinet [2] baed on the mall gain theoy. Recently, moe and moe of uch nonlinea contol poblem, which can be tanfomed to an LPV fom, have been olved by the help of thi method [7, 16, 22, 28, 31]. Howeve, thi appoach doe not alway give bette eult than the common ad-hoc method. Becaue the model of the IM i highly nonlinea with tong dynamical popetie, thi method ha to be conideed at the fit place. Thu, let the field oiented ytem deciption of the IM tanfomed into an LPV fom baed on the peviouly mentioned idea. The eult of thi tanfomation i a paamete-affine LPV model dependent on the ω, ω flux, and R paamete: x = A( p(t)) x+ B u+ B ε (t) (2.37) inv whee y = C x+c ε (2.38) me (t) f Ψ d (t) f x = i d (t), f i q (t) f i d (t) y = f, i q (t) p(t) 1 ω(t) 3 p(t): + + = p 2(t) = R (t) p(t) ω (t) 3 flux 18

33 2. The mathematical model of the induction moto u (t) u = = f a u d (t) 1 3co ρ(t) 3 in ρ(t) 2 3 in ρ(t) u f b(t) u q (t) 3 3in (t) 3 co (t) 2 3 co (t) ρ ρ ρ u c(t) Pak & Clak tanfomation Ap p(t) 2 Lp(t) m 2 0 L L τ p(t) λ p(t) τ = + τ λ p(t) 2 τ p 1(t) p 3(t) + L σ σ σ 2 2 ( (t)) p 3(t), L σ L σ σ B = 0, Lσ 1 0 Lσ C = It can be een that the tate matix can be given in the fom Ap ( (t)) = A + A(p (t)) + A(p (t)) + A (p (t)), which popety i called of paamete affinity. Futhemoe, the input affinity of the oiginal model i alo peeved in the LPV tate equation ytem. In thi way, the tongly nonlinea (2.34) diffeential equation ytem can be handled a a puely LTI deciption. New element ae intoduced to the model a well, like ε inv (t), the pule width modulation (PWM) eulted eo of the invete which poduce the input voltage feed of the moto and ε (t), the meauement noie of the eno. While ε (t) me inv can be modeled a a band limited white noie effect, the ε me (t) i pefectly decibed by a high fequency dominant filteed white noie. The tanfomation of the thee phae quantitie to a two-phae coodinate ytem and the field oientation i calculated though the Clak and Pak tanfomation, whoe detail will be explained in the late ection. 19

34 2. The mathematical model of the induction moto 2.6. Geneal dynamic popetie of the model The dynamical analyi of the moto model need lage pectum of invetigation which hould cove anothe full pape in thi topic. Howeve, thee invetigation mut be done befoe the tue deigning of the contolle begin. Fo thi eaon, the full nonlinea analyi of the model ha been completed in [38], but hee only the main eult and concluion ae mentioned. Fom equation (2.31), it i clea that the model i built up fom fit ode ubytem. Thu, by conideing each of thee ubytem epaately, the tate vaiable tend to thei equilibium point without any ovehoot and fluctuation, a well a thei tanition function have puely exponential deceae. Howeve, the inne co effect caued by the multiplication between the tate vaiable intoduce high nonlineaitie into the ytem, which caue ocillation in the dynamic behavio of the model. Moeove, the whole ytem dynamic can be epaated into two opeation inteval: uch a the tatup and the teady tate, in which the behavio of the model i diffeent in tem of tability. Duing tatup, the ytem how intability till the electomagnetic toque ( Te ) ha not eached a pecific value called the pullout toque. Thi phenomenon exit, becaue a magnetic field ha to be built up inide the moto to povide an adequate enegy flow between the oto and the tato ubytem. Thu, a high cuent impule ha to be povided to the moto, which quickly build up the needed magnetic field and ha enough enegy to ovecome the moment of inetia of the oto. The diffeence in dynamic behavio of the two inteval can be een in Figue 2.8 [18], whee the inteaction between the nomalized T e and ω i plotted. It i clealy hown that duing the diect tatup, the function of toque / peed ha lage ocillation at fit, which ae dumped lowly till the ytem aymptotically eache the equilibium point ( ω,t ) nom e nom a in the cae of the teady tate change. Thi plotted function alo decibe the tep epone of the tanition function between the toque and peed. It i anothe impotant fact that the elative degee between any input and any output of the ytem i not geate than 3. Baed on thi eaon, the I/O 20

35 2. The mathematical model of the induction moto lineaization of the model can be given eaily in mot of the cae, but fo the load toque a vey complicated vitual input and output function have to be choen fo the lineaization, which caue the accumulation of numeical eo in pactice. The effect of thi popety i analyzed in late ection. The zeo dynamic of the ytem in contat of the peviou fact i table fo ω that make poible to hold T load with the moto at 0 peed and contol the full 4/4 opeation ange of the IM dive. Figue 2.8. Toque / fequency tanient of the moto in each dynamic inteval 21

36 3. Exiting peed enole technique 3. Exiting peed enole technique Today, eveal method ae known fo the peed enole contol of the induction dive, but each of thee olution ha it own diadvantage beide it tong ide. In the pat, thee wee aduou attempt to extact the peed o the poition ignal and to etimate the tength and the oientation of the flux field of an induction machine [18]. Howeve, the fit attempt have been eticted to technique which ae only valid in the teady tate. Thee can be ued in low-cot dive application, not equiing high dynamic pefomance. But a the aging competition of the dive manufactuing companie ha haken thi field up, a lot of new method have been intoduced which ae applicable fo high-pefomance application in vecto and diect toque contolled dive. It i a common featue of the enole technique that they depend on machine paamete, like the tempeatue of the moto, oto eitance vaiation, fequency, etc. To compenate the paamete vaiation, vaiou paamete adaptation cheme have been popoed in the liteatue. Unfotunately, conventional technique ae not uitable to achieve table, vey low peed opeation in peed enole dive becaue the oto peed diectly baed on the applied toque and the etimation of thi fine balance i vey poblematic in thi cae, due to the paamete mimatch and noie. Thi tak can only be olved by vey difficult model that utilize vaiou effect like the oto lot hamonic, aliency, etc.[18]. Thi i the eaon why beide the exiting technique thee i a geat each fo new method, like the contolle whoe implementation i the topic of thi pape, which make poible the contol with a imple model that ha malle computational load than the ecently ued olution in high pefomance dive. In the following pat, the mot popula method will be dicued biefly to have an outlook on the field of applied contol of induction dive Contant Volt pe Hetz contol One way of dealing with the complex and nonlinea (NL) dynamic of the IM in adjutable peed dive i avoiding excitation at the eigenfequency of the model. To thi aim, a gadient limite educe the bandwidth of the tato voltage 22

37 3. Exiting peed enole technique fequency command a hown in Figue 3.1. The band limited tato fequency command ignal then geneate the tato voltage efeence magnitude u. it integal detemine the phae angle ( ) ef u while ef Figue 3.1. Contant volt pe hetz contol By examining the eal voltage / oto peed (given in fequency) chaacteitic of the moto peented in Figue 3.2, it can be clealy een that duing a lage inteval of the opeation ange, the elationhip between ω and the applied voltage i linea in the cae of contant load [20]. Figue 3.2. Voltage / fequency chaacteitic of the IM It i alo poible to effect the mmf. of the moto by changing the ynchonou fequency of the voltage feed tough the PWM modulation of the invete. Moeove, the T/ω e chaacteitic of the moto can be diectly hifted along the fequency axi with the changing of the ynchonou fequency, of coue thi i 23

38 3. Exiting peed enole technique only tue theoetically, becaue the layout effect defom thi elationhip if the input fequency i too lage o too low [5]. Thi i hown by Figue 3.3. Figue 3.3. Toque / peed chaacteitic of the IM at diffeent ynchonou fequencie The above mentioned popetie can be deived mathematically a well. Fom (2.7), equation (3.1) i deived, by neglecting the eitive voltage dop R i and, in view of band limited excitation, by auming teady tate opeation with d Ψ /dt 0. Thi yield u (t) = j ω (t) Ψ (t), (3.1) o u / ω = cont. (o v/f = cont.) when the tato flux i maintained at it ef nominal value in the bae peed ange. Field weakening i obtained by maintaining u ef = u = cont., while inceaing the tato fequency beyond it max nominal value. At vey low tato fequency, a peet minimum value of the tato voltage i pogammed to account fo the eitive voltage dop, which can be een in Figue 3.1 and 3.2. ef The ignal u and ( u ) ef ae obtained to contitute the efeence vecto ef u of the tato voltage, which in tun contol a PWM modulato to geneate the witching equence of the invete. Since v/f dive opeate puely a feed fowad ytem, the poduced dive i abolutely obut, howeve, the mechanical peed ω diffe fom the efeence 24

39 3. Exiting peed enole technique peed ω ef when the machine i loaded. The diffeence i the lip fequency equal to the electical fequency of the oto cuent. The maximum peed eo i detemined by the nominal lip, which i mot commonly 3-5% fo low powe machine and le fo high powe. To compenate thi, a load cuent dependent cheme can be employed to educe the peed eo [1]. If the ytem equation ae deived in the tato fixed efeence fame, letting ω k = 0. The eult i d Ψ (t) 1 Lm = u(t) Ψ(t) Ψ (t), (3.2) dt στ L d Ψ (t) L στ +Ψ (t) = j ω(t) στ Ψ (t) + Ψ (t). (3.3) m dt L Fom the (2.11) and (2.12) flux equation it can be clealy een that 1 Lm i(t) = Ψ(t) Ψ (t), (3.4) σl L and the tato flux vecto i diectly geneated by the integal of u R i. The key quantity of thi contol concept i the active tato cuent i p which i i (t) i (t) (t) i (t)co( ) i (t)in( ), whee ( (t)). (3.5) p = u = ef α α + β α α= uef u (t) ef ω nominal It can be deived that i p i popotional to the toque, thu if at the nominal lip the magnitude of the active i i known, which i the lip to be compenated can be etimated a: ip nominal then ω nominal ω(t) i p(t). i pnominal (3.6) Baed on thi, the contol tuctue demontated on Figue 3.4. povide favoable dynamic behavio by making the tajectoy of the tato flux independent fom of the tato cuent and the load. 25

40 3. Exiting peed enole technique Figue 3.4. v/f contolle with lip compenation Contant v/f contol enue obutne at expene of educed dynamic pefomance which i adequate fo application like pump and fan dive. Thei paticula attaction i thei extemely imple contol tuctue which favo an implementation by a few highly integated electonic component. Thee cot aving method ae pecially impotant fo application at powe below 5kW, but at high powe, when the powe component themelve dominate the cot, the implementation of moe ophiticated contol method become available Machine model In pactice, machine model ae uually ued to etimate the moto haft peed to avoid the need of encode o tacho geneato and, in high pefomance dive with field oiented contol, to identify the time vaying angula poition of the flux vecto. In addition to thi, the magnitude of the flux vecto i etimated a well to enue the effective opeation of the dive. Diffeent machine model ae employed fo thi pupoe, and they ae implemented in diffeent manne to compute the unknown depending on the poblem at hand. Sometime, by only the meaued ignal baed olution of the diffeential equation of the model, with implemented eal time numeical computation on a micopoceo, povide adequate pefomance, but in cae of high expectation in optimality, thee model ae omehow enhanced by ceating mathematical method, called obeve, which can impove the quality of the etimation of the deied value geatly. By applying thee method, the common 26

41 3. Exiting peed enole technique non peed enole contol appoache become available to povide peed enole opeation of the dive Diect efeence model Diect efeence model ae deived fom the diffeential equation of the moto model eithe in tato fixed o field oiented epeentation. The accuacy of thee model depend on the degee of coincidence which can be obtained between the model and the modeled ytem. Coincidence hould pevail both in tem of tuctue and paamete. While exiting analyi method pemit etablihing of appopiate model tuctue in cae of the IM, the paamete of uch model ae not alway in good ageement with the coeponding machine data. Paamete may ignificantly change with tempeatue, o with the opeating point of the machine. On the othe hand, the enitivity of a model to paamete mimatch may diffe, depending on the epective paamete, and the paticula vaiable etimated by the model, but it i alway tue that the light computational load and eay tuctue of the efeence machine model can guaantee only limited achievable pefomance. Roto model ae deived fom the elationhip of the oto winding eithe in tato (2.12) o in field coodinate (2.29). By example, in the tato fixed epeentation, the following equation give poibility to compute the oto flux: d Ψ (t) τ + Ψ (t) = j ω(t) τ Ψ (t) + L mi(t). (3.7) dt If the peviou diffeential equation i numeically olved, fo example by the Eule method, then the deied value of Ψ can be obtained to povide the oto flux oientation by computing the angle of the oto flux tough 0, if Ψ α (t) 0 Ψ β(t) ρ (t) = atan + π, if Ψ α(t) < 0 and Ψ β(t) > 0, Ψ α (t) π, if Ψ α(t) < 0 and Ψ β(t) < 0 (3.8) and the feedback ignal of the field tength with 27

42 3. Exiting peed enole technique ( α ) ( α ) 2 2 = Ψ + Ψ Ψ (t) (t) (t). (3.9) Anothe impotant example i the tato appoach, whee fom the (2.7) tato voltage equation (3.10) can be obtained. t u 0 ( i ) Ψ (t) = ( ν) R ( ν) dν (3.10) Equation (2.11) and (2.12) can be ued to detemine the oto flux linkage vecto Ψ and the leakage vecto Ψ fom which the penetating field angle, and σ the magnitude of the flux linkage can be obtained: t Ψ L L (t) = ( ( ) R ( )) d L (t) ( (t) σ(t) ). L u ν i ν ν σ i = m L Ψ Ψ (3.11) 0 m The tato model i difficult to apply in pactice, ince the eo in the equied ignal u and i, and the offet and dift effect in the integating hadwae will accumulate becaue thee i no feedback fom the integato output to it input. The eulting unaway of the etimated output ignal i a fundamental poblem of open integation, theefoe a negative low gain feedback i added to tabilize the integation and pevent the output to inceae without bound. The feedback ignal convet the integato into a fit ode delay having a low cone fequency 1/τ 1. In thi way, the tato model (3.10) and (3.11) become τ Ψ (t) + L Ψ (t) =τ (t) R (t), Ψ (t) = Ψ (t) σ L (t), (3.12) 1 1 dt Lm and ( u i ) ( i ) epectively. Ψ (t) τ1l i(t) τ 1 + Ψ (t) = u(t) R i(t) σl (3.13) dt Lm dt Othe model of coue can be alo deived fom the ytem equation, but it i impotant to tell that the accuacy of thee model geatly depend on the coect etting of the model paamete. Thu, a coect identification of thee paamete ha to be povided befoe any application of thee model, o in the othe cae, 28

43 3. Exiting peed enole technique becaue of thee incoect paamete value, the model loe the elationhip with eality Adaptive obeve & filte The accuacy of the open loop etimation model decibed in the peviou chapte educe a the mechanical peed of the IM lowe. The limit of acceptable pefomance depend on how peciely the model paamete can be matched to the coeponding paamete in the actual machine. Paticulaly at the lowe peed ange the paamete eo have ignificant influence on the teady-tate opeation and the dynamic pefomance of the dive ytem. In thi cae, the obutne againt paamete mimatch and ignal noie can be impoved by employing cloed loop obeve to etimate the tate vaiable, and the ytem paamete. Unfotunately, becaue of the high nonlineaitie of the IM model, uually the linea time invaiant (LTI) model-baed etimation method do not povide much bette eult than the feedfowad appoach mentioned befoe, becaue they need the lineaization of the ytem model, which cannot be accomplihed without geat lo of the decibed ytem dynamic. Theefoe, mainly nonlinea method povide that quality of pefomance, which i enough to implement thee much moe computation needed method intead of the imple one mentioned befoe Full ode nonlinea obeve Etimation method ae contucted in uch a way that they ae capable to compute the unknown tate of the ytem with the help of meaued input and efeence output of the ytem. The deviation fom thee efeence ignal povide the cloed loop efinement of the etimation. In the LTI cae, Luenbege obeve can be eaily contucted to the lineaized moto model, uch a it i decibed in [33], but thei pefomance i much woe than if the idea of thi method i applied diectly to the untouched nonlinea ytem. In thi way, uch a full ode nonlinea obeve can be contucted fom the (2.7), (2.8), (2.11), and (2.12) machine equation in the 29

44 3. Exiting peed enole technique tato fixed efeence fame, which ae viualized in the uppe potion of Figue 3.5. Figue 3.5. Full ode nonlinea obeve The model output ae the etimated value of î and ˆΨ epectively. Adding an eo compenato to the model etablihe the obeve. The eo i computed by the deviation of the model cuent fom machine cuent: i (t) = ˆi (t) i (t). Thi value i ued to geneate coecting input to the electomagnetic ubytem that epeent the tato and the oto in the machine model. The equation of the full ode obeve ae then etablihed in accodance with the machine equation. d ˆi (t) λτ + τ ˆ τ 1 ˆ 1 = i ˆ (t) + j ω Ψ (t) + u(t) S( ω) i(t), (3.14) dt σ σ τ Lσ d Ψˆ (t) 1 Lm = ˆ j ω Ψ ˆ ˆ (t) + i(t) S( ω) i(t), (3.15) dt τ τ whee the complex gain facto S ˆ ( ω) and S ˆ ( ω) ae elected in uch a way that the eulted two complex eigenvalue of the obeve ae the k > 1 eal contant multiplied eigenvalue of the machine. By Kubuta [27], thi calibation of the gain povide good pefomance, becaue k > 1 cale the obeve by pole 30

45 3. Exiting peed enole technique placement to be dynamically fate than the machine. The nonlineaity of the ytem i alo conideed, becaue the complex gain depend on the etimated mechanical peed. The ignal ˆω i equied to adapt the oto tuctue of the obeve to the mechanical peed of the machine. It i obtained though a PI-contolle fom the cuent eo i. In fact, the tem Ψ ˆ (t) i (t) epeent the toque eo Te, which can be veified fom (2.17). If a model toque eo exit, the modeled peed ignal ˆω i coected by the PI contolle in Figue 3.5, adjuting the input to the oto model in thi way. The phae angle of ˆΨ, which etimate the tue field angle of the moto, can be ued fo field oientation a well. The coect etimate i eached when each of the i and Te eo ignal educe to zeo Sliding mode obeve The effective gain of the eo compenato can be inceaed by uing a liding mode contolle to tune the obeve fo peed adaptation and fo oto flux etimation [4]. Thi method i popoed by Sangwongwanich and Doki [10]. Figue 3.6 how the dynamic tuctue of the eo compenato. Figue 3.6. Sliding mode compenato It i intefaced with the machine model the ame way a the eo compenato in Figue 3.5. In the liding mode compenato, the cuent eo vecto i i ued to define the liding hypeplane. The magnitude of i i then foced zeo by a high-fequency nonlinea witching contolle. The witched wavefom can be diectly ued to exet a compenating influence on the machine model, while it aveage value contol an algoithm fo peed identification. The obutne of the 31

46 3. Exiting peed enole technique liding mode appoach enue zeo eo of the etimated tato cuent and tough it the tacking of the oto peed. The H appoach, which theoy i dicued late, ued in [27] fo pole placement in the obeve deign even minimize the oto flux eo in the peence of paamete deviation, which povide a obut contol tuctue. But the implementation of thi method equie vey fat micopoceo Extended Kalman Filte Kalman filteing technique ae baed on the complete machine model, and ty to tatitically efine the quality of etimation. The machine i uually modeled a a 3 d o 4 th ode ytem like in [13, 41], intoducing the mechanical peed a an additional tate vaiable. The mechanim of the Kalman filte i epeented in Figue 3.7, which i conit of meely two tep in each contol cycle. It ue the ame appoach a the peviouly mentioned obeve, by taking the meaued input ignal and efeence output ignal of the ytem to olve the poblem at hand. The baic of the algoithm i a follow [3]: In the fit tep the meaued data i obtained, and with the new infomation, the diffeential equation of the complete model ae olved by numeical appoximation, which i uually done though the explicit Eule method. In thi way the new x(k k 1) etimated tate of the ytem ae pedicted baed on the peviou k 1 etimate and the input data. Then, the pedicted tate ae tatitically coected with epect to the expected covaiance of the pedicted tate P (k k 1) and the a pioi-obtained infomation about the covaiance of the exiting ytem and meauement noie decibed in the R and Q matice. The expected noie of the ytem ae white noie pocee with zeo mean value and contant covaiance. The method povide the coectne of the etimation only in thi cae, which might eem to be a vey tict aumption, but by conideing the eal life ytem, the exiting noie can be adequately modeled with uch effect. Thi i tue in cae of the IM a well, becaue the meauement noie of the tato cuent ignal and the ytem noie caued by the PWM modulation of the invete can be appoximated well by uch a deciption. In the coection phae of the algoithm, not only the tate ae coected to 32

47 3. Exiting peed enole technique povide x (k k), but the efined value of P (k k) i alo obtained. Afte thi tep the new etimated ytem tate can be ued by the contol algoithm, which can be implemented in eveal way like in [39] The baic mechanim of the Kalman filte algoithm The above mentioned appoach i deived fom the minimization of a quadatic eo function, which i evaluated on the bai of the pedicted tate vaiable, noie, and paamete deviation. In thi way it educe eo enitivity and pemit alo the ue of model of lowe ode than the machine [15]. Since the model of the IM i highly nonlinea and the oiginal method [25] fo the Kalman filte i given fo the LTI cae, an extended Kalman algoithm mut be applied to olve the contol poblem of the machine. Thi algoithm conit of the imila tep a the oiginal one, but intead of uing contant matice in the pediction phae it ubtitute into the nonlinea equation ytem of the model. The numeical appoximation uually need much moe accuacy than the Eule method povide, theefoe highe ode method ae ued, like the Adam- Bafoth 3 d ode ecuive method [14] in [39]. Futhemoe, fo the pediction of the ytem covaiance matix, the full patial diffeential of the nonlinea equation mut be computed. In thi way, the extended algoithm baically lineaize the model in the actual opeating point in each contol cycle, which ha a huge computational load. Theefoe, the ealization of thee method can only be imagined on a floating point high peed hadwae which can handle thi load. 33

48 3. Exiting peed enole technique H baed LPV obeve In Contol Sytem Theoy, nowaday new method evolve to olve the inceaing need of accuate and obut contol, opening new way to handle poblem neve een befoe. The mot pomiing of thee method ae the H and H 2 nom baed contolle ynthetiation which have been ued in eveal application [9, 11, 28, 31, 39]. Thee theoie wee intoduced by Zame [42] in hi fit pape tying to impove the bad obut popetie of the linea quadant Gauian (LQG) contol. To eolve thi poblem, he intoduced an integation containt which ued the nom of the ytem tanfe function. Baed on hi foundation, the H nom, which i the conetone of the theoy, i defined fo the G() tanfe function of a P(w(t),z(t)) ytem a follow: G z(t) = ( ) 2 () up, t 0,, w(t) 0 w(t) 2 2 (3.16) whee w(t) denote the input ditubance, efeence ignal, and noie effecting the ytem and z(t) efe to the output petubation like efeence tacking eo o othe contol aim. The eence of the H theoy can be biefly explained by Figue 3.8. By the epeented ytem, uch a K contolle i eached fo which tabilize the given P plant, and baed on the (3.16) nom it minimize the tanfe function between w(t) and z(t). Figue 3.8. Geneal poblem fomulation of H contol poblem Accoding to the mall-gain theoem the obut tability i dependent on the oveall gain between the ditubance and the output ignal of the cloed loop ytem [42]. Theefoe, the minimization of thi nom can be viewed a the maximization of the tability and goodne of the contol. The H nom give the wot cae gain of the ytem theefoe povide a good match to engineeing 34

49 3. Exiting peed enole technique pecification and a ueful deciption of the eo and input ignal of the cloed loop contol, becaue it alo epeent an uppe and lowe bound on thee ignal on the whole fequency ange. Intead of the diect minimization of the mentioned tanfe function, which i an enomou tak, of coue, mot commonly only a uboptimal contolle i obtained, which can be computed though a ecuive gamma-iteation baed on the olution of Ricatti equation o linea matix inequalitie (LMI). The obtained contolle i pecified by it γ wot cae gain which i equal to the cloed loop H nom of the contolled ytem. Thi theoy povide both contolle cheme and obeve olution fo the poblem, depending on how the P ytem i defined. By cleve appoach, the ynthetied etimato can povide vey accuate eult with a mall computational load. With the ue of fequency ange decibing filte in the definition of the P poblem even the popetie of the poduced algoithm can be tuned. Thi appoach i called mixed enitivity [34]. Unfotunately, thi vey ueful theoy i only given fo LTI ytem, but fo uch NL model a the IM, an extenion of the theoy i needed. By the ue of the linea paamete vaiant LPV epeentation of the machine given in Section 2.5 the NL fom of the equation can be handled a LTI paamete dependent ytem defined on a paamete pace, on which a H contolle can be ynthetied. In thi way, the NL poblem can be handled a an LTI one but with the cot of the deciption of the paamete-dependent exact location of the model in a ytem pace, which epeentation i called polytopical deciption. Thi equie highe and highe computational load baed on the difficulty of the model, which can lowe the economical value of thi billiant method. Today, thee ae eveal example of expeimenting with thi method to olve the contol poblem of the IM, uing thi theoy fo obeve o contolle ynthetiation like in [9, 11, 31, 39]. Although the obtained pomiing eult, the indutial uage of thi appoach i not ignificant, which can be explained by the fat micopoceo need and the fehne of thi olution. 35

50 3. Exiting peed enole technique Model efeence adaptive ytem The model efeence adaptive ytem appoach (MRAS) make ue of the edundancy of two machine model of diffeent tuctue that etimate the ame tate vaiable on the bai of diffeent et of input ignal [35]. One of thee MRAS model i called the efeence model and the othe one i efeed a the adaptive model. The geneal mechanim of thee method i baed on compaing the output of thee model to etimate the deied unknown by continuou efinement of the adaptive tuctue. In the following example, both model ae epeented in the tato fixed efeence fame. The (3.12) tato model in the uppe potion of Figue 3.9 eve a the efeence model. It output i the etimated oto flux vecto ˆ Ψ, whee upecipt indicate that the vecto oiginate fom the tato model. Figue 3.9. Model efeence adaptive ytem fo peed etimation, efeence vaiable: Ψ Additionally, the oto model (2.29) with ω k = 0, which i the adaptive model, etimate the oto flux ˆ Ψ fom the meaued tato cuent and fom the tuning ignal ˆω, like it peented in Figue 3.9. Then, the tuning ignal i obtained though a popotional-integal (PI) contolle fom a cala eo ignal e = Ψˆ (t) Ψ ˆ (t). A the eo ignal e get minimized by the PI contolle, the tuning ignal ˆω appoache the actual peed of the moto. The oto model, a 36

51 3. Exiting peed enole technique the adjutable model, then align it output vecto vecto of the efeence model. ˆ Ψ with the ˆ Ψ output The accuacy and dift poblem at low peed, inheent to the open integation in the efeence model, ae alleviated by uing the ame 1/τ 1 delay element mentioned befoe. Although thi appoach eliminate the accumulation of the dift eo, it alo make the integation ineffective in the fequency ange and below of 1/τ 1. Even with a mall cut off fequency, the peed etimation become highly inaccuate aound 1-3Hz, theefoe a eveal of peed i nevethele poible with thi method [18]. Figue Speed and cuent contol ytem fo MRAS etimato In an application, the peed contol ytem upeimpoed to the peed etimato a hown in Figue 3.10 with a cuent ouce (CS) invete. In thi way, the etimated peed ignal ˆω i upplied by the model efeence adaptive ytem of Figue 3.9. The peed contolle in Figue 3.10 geneate a oto fequency ignal ˆω, which contol the tato cuent magnitude Ψˆ (t) 2 i (t) 1 (t), f = + τω L ( ˆ ) (3.17) and the cuent phae angle t ( i ) = ωˆ ν ν+ ( τ ˆ ω ) (t) ( )d atan (t). (3.18) 0 37

52 3. Exiting peed enole technique Equation (3.17) and (3.18) ae deived fom (2.35) with the teady tate olution of the oto field oiented coodinate. It i a paticula aet of thi appoach, that the accuate oientation of the injected cuent vecto i maintained even if the model value of τ diffe fom the actual oto time contant of the IM. The eaon i that the ame, even eoneou value of τ i ued both in the oto model and in the contol algoithm (3.17) and (3.18) of the peed contol cheme in Figue 3.10, then if the tuning contolle (Figue 3.9) maintain zeo eo, the contol cheme exactly eplicate the ame dynamic elationhip between i and Ψ that exit in the actual moto, even in the peence of a oto time contant eo [35]. Howeve, the accuacy of peed etimation, eflected in the feedback ignal ˆω to the peed contolle, doe depend on the eo in τ. The peed eo may be even highe than with thoe method that etimate ω and ue ω ˆ(t) =ω ˆ (t) ω (t) to compute the peed. The eaon why thi appoach i moe obut conideing the peed than the MRAS, i that the ynchonou fequency of the powe feed i a contol input and theefoe accuately known, and even if ˆω i eoneou, it nominal contibution to ˆω i mall, thu it doe not effect the peed etimation, unle the eal peed i vey low. A it could be een MRAS offe a poweful method to ealize low pefomance peed enole contol even with it obutne poblem Diect toque contol Diect toque contolled (DTC) induction dive wee developed appoximately 20 yea ago by Dependbock [8] and Takahahi [36], howeve at peent, ABB i the only indutial company who have intoduced a commecially available DTC dive. In a DTC-IM dive, upplied by a voltage ouce invete (VSI), it i poible to contol diectly the tato flux linkage (o the oto/magnetizing flux linkage) and T e by the election of optimum invete witching mode. The election i made to etict the flux and toque eo within epective flux and toque hyteei band to obtain fat toque epone, low invete witching fequency and low hamonic loe. In the following ection, uch a DTC dive will be biefly hown which in addition to contolling 38

53 3. Exiting peed enole technique T e, it alo contol the tato flux linkage. Howeve, it i alo poible to have othe implementation in which the oto o the magnetizing flux linkage i contolled. Geneally, DTC dive allow vey fat toque epone and flexible contol of the IM, although the peed contol of the haft i not povided by thi appoach, thu uually extenal contol i needed to complete the dive with the ue of peed etimation baed on the peviouly mentioned obeve. By conideing the (2.19) dynamic motion equation of the IM it i clea that T e i popotional to the co-vectoial poduct of the flux linkage pace vecto Ψ and the tato cuent i pace vecto. In thi way, (2.19) tanfomed into the following fom: 3 L T = p Ψ (t) i (t) in ( α (t) αψ (t)), (3.19) m e i 2 L whee α i(t) = ( i(t) ) and Ψ (t) ( (t)) α(t) α = Ψ. It can be hown, that by uing the voltage equation of the IM, fo a given value of the oto peed, if the modulu of the Ψ i kept contant and the angle α Ψ i changed quickly, then T e can be apidly changed. In othe wod if uch u i impoed on the moto, which keep the magnitude of tato flux contant at the demanded efeence value, but which quickly otate Ψ into the poition equied by the toque command, then fat toque contol i pefomed. It follow that in the DTC dive, if the developed actual T e i malle than the efeence value, then it inceae hould be achieved a fat a poible by uing the geatet d α Ψ /dt. Howeve, when T e i equal to it efeence, the otation i topped. If the tato flux linkage vecto i acceleated in fowad diection, then poitive T e i poduced, and when it i deceleated backwad, negative T e i poduced. Howeve, the appopiate voltage feed of the IM. Ψ can be adjuted by uing u, which i geneated though the invete, which poduce the The time contant of a tandad quiel cage IM i lage in compaion to the powe electonic element of the invete, thu Ψ change lowly compaed to 39

54 3. Exiting peed enole technique Ψ. Theefoe, it magnitude can be aumed to be contant. Thi follow fom the (2.8) oto voltage equation, if the magnitude of Ψ i aumed to be contant a well. Howeve, if both of the magnitude of thee vecto ae aumed to be contant, then the electomagnetic toque equation in fom of (3.20) yield that T e can be apidly changed by changing the lip angle α lip(t) = ( Ψ (t)) ( Ψ (t)) in the equied diection detemined by the toque command. 3 L T = p Ψ (t) Ψ (t) in α (t), (3.20) ( ) m e lip 2 L In cae of field weakening, which cae i not decibed hee, the magnitude of Ψ i not contant, theefoe the contol of the magnitude and lip angle ha to be povided, which i alo poible by the witching of appopiate invete voltage. In contat to a vecto contolled IM dive, which i going to be mentioned late, whee the tato cuent ae ued a contol quantitie, in the DTC, the tato flux linkage ae contolled. In both method thi i done though the u vecto. If, fo implicity hake, it i aumed, that the tato ohmic dop can be neglected, then d Ψ (t)/dt = u (t), o the invete-povided voltage diectly impee the tato flux, and thu the equied tato-flux locu will be obtained by uing appopiate witching tate of the invete. It follow fom the peviou concept that fo a hot t time, when the tato voltage i applied Ψ = u t hold. Thu, Ψ move by Ψ into the diection of u at a peed which i popotional to u, whee the magnitude of the tato voltage i popotional to the DC voltage of the invete bu. By electing tep by tep the appopiate tato voltage vecto, it i poible to change the tato flux in the equied way. By conideing the layout of a ix-pule VSI hown in Figue 3.11, it can be noticed, that thee ae ix poible non-zeo active voltage-witching pace vecto ( u,..., u ) and two zeo pace vecto (, ) 1 6 u u. Thee ae hown in Figue 3.12, which alo peent the coeponding eight invete tate. The ix invete-witching vecto can be expeed a

55 3. Exiting peed enole technique j(k 1) π 2 U 3 bu e, k 1,2,...,6 u k = = (3.21) 3 whee U bu i the DC bu voltage. Howeve, in cae of k 7,8, k = u = 0 hold fo the two zeo witching tate whee the tato winding ae hot cicuited. Figue Schematic epeentation of a voltage ouce invete Figue Poible witching vecto and the coeponding tate of PWM-VSI invete 41

56 3. Exiting peed enole technique Since Ψ = u, and a wee peviouly mentioned t Ψ move fat into the diection of the applied u, which i one of the ix invete-witching vecto, and top in cae of the two zeo witching tate, theefoe it can be een, that Ψ move along a hexagonal path with contant linea peed if the applied voltage vecto i continuouly ciculated in the ode of the given witching vecto. In the DTC dive, at evey ampling peiod, the witching vecto ae elected on the bai of keeping the tato flux-linkage eo and the toque eo in a given toleance band. It i aumed that the width of thee toleance band ae and 2 Ψ. If the 2 Te Ψ lie in the k th ecto (ee Figue 3.13) it magnitude can be inceaed by uing witching vecto u k, k+ 1 u, u k 1, and deceaed with u k+ 2, k 2 u, u k+ 3 well. The peed of the. Obviouly, the elected voltage witching vecto affect T e a Ψ i zeo in cae of u 7 and u 8 and it i poible to change it peed by changing the output ation between the zeo and non-zeo voltage vecto. A hown above, Figue Flux linkage contol by DTC Ψ i baically the integal of u and it will move into the diection of the elected uk a long a it i applied. Thu, if a educed Ψ modulu i equied, then it can be achieved by applying uch witching voltage vecto which ae diected towad the cente of the oto, and if an inceaed modulu i equied, then it i contolled by applying voltage vecto which ae diect out 42

57 3. Exiting peed enole technique fom the cente of the oto. Thi i illutated in Figue Theefoe, by thi method, the magnitude of Ψ can be kept in a 2 Ψ hyteei band. It i alo tue that in geneal, if an inceae of the toque i equied, then the toque i contolled by applying voltage vecto that advance Ψ in the diection of the otation, and if deceae i equied, then uch vecto ae elected which oppoe the diection of the toque. If zeo toque i equied, then u 7 and u 8 ae applied, by which the ate of toque change can be alo contolled. Baed on thi, uch an optimal voltage witching vecto look-up table can be obtained that tell which vecto hould be applied to each the deied tate. Seveal othe conideation alo have to be applied of coue, fo example the length of witch on of each vecto in the witching patten to contol the peed of toque and flux ie. It i alo impotant to tell that fo the functioning of uch a dive an etimation of the tato flux i needed which can be done in eveal way mentioned befoe, but the optimality of the contol tongly depend on the accuacy of the etimation. Figue 3.14 how the chematic of one imple fom of the DTC IM dive, employing a VSI invete. In thi cheme the tato flux i the contolled flux, thu it i efeed to be tato-flux baed DTC dive. Figue Stuctue of a imple tato-flux baed DTC-IM dive with VSI The main mechanim of thi tuctue i clea fom the point of view of the peviou concept and only the etimation method ha to be yntheized in uch a way that it can povide the accuate tate of the moto. Fo a imple cheme, the 43

58 3. Exiting peed enole technique peviouly mentioned tato flux etimato can be ued with the following equation to obtain T e : 3 L T = p Ψ (t) i (t) Ψ (t) i (t). (3.22) ( α β α β ) m e 2 L In thi way, the main advantage of the poduced DTC dive i the abence of coodinate tanfomation and voltage modulato block, which ae equied in pace vecto dive. Moeove, much malle accuacy of the flux vecto i needed in the etimation becaue only the 60 long ecto ha to be detemined fo thi method and it ha alo minimal toque epone time. Howeve, it ha diadvantage a well, like poible poblem duing tat up and low peed opeation and the quickly changing witching fequency, which poduce high ipple toque Vecto contol The baic of vecto contol have been aleady dicued in Section 2.4. The main advantage of vecto contol i that it make poible the epeentation of the ytem model in uch way that the contol and etimation of the whole model become elatively imple. Fo example, with the intoduced field oiented epeentation of the moto model the decoupled contol of peed and flux can be achieved with optimal pefomance of the contol, becaue thi appoach tanfom the IM into a DC moto like epeentation. Howeve, eveal othe epeentation ae known, fo example the tato flux oientation, magnetizing cuent oientation, etc., with the known advantage and diadvantage of each of them, but mot commonly the oto field oientation i ued. Unfotunately, it i geneally tue, that the good contol abilitie of the oiented model epeentation have to be paid in inceaed computational load. The main tuctue of peed enole vecto-contolled dive with VSI invete can be een in Figue In evey cae, if the high need of the induty have to be fulfilled, the vecto contol algoithm mut conit of a peed and flux etimation method, which can be implemented in the peviouly mentioned way. 44

59 3. Exiting peed enole technique Figue Geneal tuctue of VSI diven peed enole, vecto contolled IM dive Howeve, fo faultle opeation, vey accuate etimation of peed and flux mut be implemented, becaue in othe cae, the field oientation will be mied and the dive become intable. Afte thi meaued tato cuent baed etimation, the obtained pace vecto of electical and magnetical quantitie ae aligned with the otating efeence fame. Thi oientation i uually computed though the Pak tanfomation: k x d (t) coρ k(t) inρ k(t) x α (t). k = x q (t) in ρ k(t) coρ k(t) x β (t) (3.23) whee ρ k i the angle between the tato fixed efeence fame and the intant poition of the oiented efeence fame. The pace vecto x peented in (3.23) i computed fom it thee-phae quantitie by the Clak tanfomation method: x(t) x(t), a x (t) α = b x(t) 1 1 β 0 x(t) c 3 3 (3.24) Thee tanfomation ae uually applied fo the meaued tato cuent in cae of VSI feed. A it can be een, only the etimation and the accuate oientation ae ignificant tak to be accomplihed in vecto contolled dive, howeve, thee tak i woth the effot, becaue in thi way, decoupled toque and peed contol of the IM can be obtained, which i fee fom the ipple toque effect of the DTC. 45

60 3. Exiting peed enole technique The contol loop i uually ynthetied baed on the full infomation obtained fom the peviou tep. Moeove, in cae of the field oientation, the teady tate value of the machine tate ae contant, theefoe even PID-baed contolle can be ued fo good pefomance contol. Of coue, to fully ue the oppotunitie of thi appoach, moe ophiticated contol algoithm ae developed, uch a the H theoy-baed olution of [11, 30, 39], which povide pefomance that can only be hadly achieved in othe way. Fo contol ignal, mot commonly the tato voltage i ued, which i tanfomed back into the tationay efeence fame and then ealized though the PWM-modulated voltage povided by the VSI. The exact way of thi ealization will be dicued in the next ection. Nowaday, high pefomance vecto contol baed IM dive ae poduced by Siemen, which have moe computational load on the built in micocontolle than othe method. Theefoe, thee dive cot moe than conventional technique baed olution, but above 5kW the elative value of thi exta cot i inignificant to the pice of powe electonic device fo thi magnitude of ated powe Fuzzy contol The atificial intelligence-baed vecto contol appeaed almot 20 yea ago and it wa thought of the poible futue contol olution fo IM. In the liteatue, thee ae many pape which dicu vaiou vecto dive with fuzzy-logic baed peed contolle, but only a few pape dicu implementation, and the othe mainly concentate on imulation. Moeove, the commecial implementation of thi type of contol i non-detectable. The eaon i vey imple. In the cae of the peviouly mentioned non-ai appoache, the tability of the ytem and it anwe to any envionmental effect i pedictable, while in the cae of the AI method, any peculation to pove the oveall tability ae only divination. In pite of the main advantage of the fuzzy contol eult in the efeence tacking without ovehoot, thi ha not hown enough impotance to be ued in eal life application. Thee ae many type of fuzzy-logic contolle (FLC), but a good example i the Mamdani [29] type, hown in Figue

61 3. Exiting peed enole technique Figue Geneal tuctue of Mamdani type Fuzzy-logic contolle In geneal, the fuzzy logic contolle contain fou main pat, two of which pefom tanfomation. Thee ae the following: Fuzzifie (tanfomation 1) The fuzzifie pefom meauement of the input vaiable and cale mapping of the obtained value into fuzzy quantitie uing membehip function which tell that the quantity belong to which pecific fuzzy et detemined by the deigne. A membehip function ha a value between 0 and 1, and it indicate the degee of belongingne of a quantity to a fuzzy et. Fo example 0.5 mean that thee i only 50% chance fo the coect belongingne. Knowledge bae It conit of a data bae and a linguitic-contol ule bae. The data bae povide the infomation which i ued to define the linguitic contol ule and the fuzzy data manipulation in the FLC. The ule bae pecifie the contol goal action by mean of a et of linguitic contol ule povided by the deigne. The FLC look at the input ignal and by uing thee expet ule detemine the appopiate output ignal a a contol action. Theefoe, the ule bae contain a et of if-then ule which povide the contol cheme. 47

62 3. Exiting peed enole technique Infeence engine It i the kenel of the FLC and ha the ability both of imulating human deciion-making baed on fuzzy concept and of infeing fuzzy contol action by uing fuzzy implication and fuzzy-logic ule of infeence. In othe wod, once all the monitoed input vaiable ae tanfomed into thei epective linguitic vaiable the infeence engine evaluate the et of if-then ule and the eult i obtained which i again a linguitic vaiable. Defuzzifie (tanfomation 2) The defuzzifie yield a non-fuzzy, eal contol action fom the infeed fuzzy contol action by uing membehip function. Phyically thi coepond to taking a weighted aveage of the contol action contibution fom each of the fuzzy ule and then obtain the final deciion. Uually the whole FLC i deigned puely on a neual ytem appoach and ha the popety of elf leaning if duing the deign tage it i taught that whethe good o bad action wa pefomed. A a olution, thi type of contol i vey unique and povide obut pefomance with good dynamic behavio, but a it wa tated, if any event occu which ae not thought to the contolle o not conideed duing the deign of the ule et, the ytem behavio become unpedictable [41]. 48

63 4. Opeation of induction moto dive 4. Opeation of induction moto dive Ove the lat 45 yea, a evolution ha occued in the application of electic moto. The development of olid-tate moto dive package ha pogeed to the point whee pactically any powe contol poblem can be olved by uing them. With uch olid tate dive, it i poible to un DC moto fom AC powe upplie o AC moto fom DC powe upplie. It i even poible to change AC powe at one fequency to AC powe at anothe fequency, which i cucial fo the ealization of command ignal in IM contol poblem. Futhemoe, the cot of olid-tate dive ytem ha deceaed damatically, while thei eliability ha inceaed. The veatility and the elatively low cot of olid tate contol and dive have eulted in many new application fo the AC moto, uch a the IM, in which they ae doing job fomely done by DC machine [6]. In the following ection the geneal powe electonic olution of IM dive will be hown with pactical concept that tongly connected to the conideed ealization, detailed in Chapte 5 and Claical powe feed geneation concept A it wa theoetically intoduced in the peviou chapte, the contol of the magnitude and fequency of the powe feed of the IM povide the ability to continuouly guaantee the deied peed and toque of the machine. While the contol of the magnitude i an eay tak with the help of tanfomato, the fequency conveion of AC powe to AC powe at anothe fequency need the ue of complicated olid-tate electonic. Taditionally, thee have been two appoache to AC fequency conveion: the cycloconvete and the ectifieinvete. The cycloconvete i a device fo diectly conveting the fequency of AC powe to AC powe, while the ectifie-invete, fit convet the AC powe to DC powe and then convet the DC powe to AC again at a diffeent fequency. Howeve, today the ectifie-invete appoach i ued mot commonly becaue cycloconvete need moe olid-tate component and thei digital contol i much moe complicated. 49

64 4. Opeation of induction moto dive Figue 4.1. Geneal tuctue of ectifie-invete poweed IM dive In Figue 4.1 the mot geneal tuctue of a ectifie-invete poweed IM dive i peented. A it can be een, the powe poceo element convet the thee-phae o one-phae AC powe to the deied 3-phae AC voltage defined by the micocontolle. The powe poceo, hotly called the invete, conit of the following thee main element: Rectifie The baic concept of ectifying i to contol the flow of enegy with the help of diode o ilicon contolled ectifie (SCR) in uch a way that the eulted voltage will conit of only poitive voltage component poducing nealy a DC ignal. Thee ae many diffeent ectifie cicuit but the mot common full-wave bidge ectifie ae hown in Figue 4.2(a) fo one-phae input, and in Figue 4.2(b) fo thee-phae input. Figue 4.2(a). One-phae full-wave ectifie cicuit Figue 4.2(b). Thee-phae full-wave ectifie cicuit 50

65 4. Opeation of induction moto dive The poduced voltage can be een in cae in Figue 4.3(a) and 4.3(b). Thee cicuit have one poblem fom a moto-contol point of view; thei output voltage i fixed fo a given input voltage. Figue 4.3(a). Output wavefom of the one-phae full-wave ectifie bidge Figue 4.3(b). Output wavefom of the thee-phae full-wave ectifie bidge Thi poblem can be ovecome by eplacing the diode with TRIAC o SCR a it can be een in Figue 4.4. Figue 4.4. Rectifie bidge with SCR The aveage DC output voltage fom thi cicuit depend on when the SCR ae tiggeed duing thei poitive half-cycle. If they ae tiggeed at the beginning of the half-cycle, thi cicuit will do the ame a the thee-phae fullwave ectifie. If the SCR ae neve tiggeed, then the output voltage will be 0V. Fo any fiing angle between 0 and 180 on the wavefom, the DC output voltage will be omewhee between the maximum value and 0V. Unfotunately, by uing SCR the output voltage will have moe hamonic component than with diode, but in thi way the contol of the DC voltage output can be achieved and even back-feeding into the electical netwok i poible duing the eveal beaking of the IM. With diode, only dynamic beaking i poible by witching an extenal beaking eito to the input ide of the invete bidge with fo example a elay. 51

66 4. Opeation of induction moto dive The contol of the tiggeing ignal i povided by the invete contol cicuit peented in Figue DC link The DC link i a powe capacito cicuit which ha two vey elated pupoe. Fitly, it toe enegy to povide contant input of the invete bidge, and it i alo efeed to a to mooth the incoming ignal to filte out the unwanted hamonic. By conideing thee tak, it can be een that they mean the ame. A low pa filte contucted fom an L inductance and a C capacito (a it i hown in Figue 4.1) fulfil the need mentioned above, and by a cleve choice of thei value a vey mooth DC powe can be poduced. In the cae of VSI invete the elative geatne of C i dominant to L, becaue the moothing of the voltage i needed, but fo CSI invete a elatively much lage L than C ha to be applied. Becaue ceation of lage inductance i a vey expenive tak, and the poduced coil ha a non-neglectable pace need, while lage capacitie can be cheaply poduced in mall cale, thu the VSI invete dominate the maket. Howeve, becaue of the cuent elated contol of the IM, CSI invete would hold much moe poibilitie Invete Invete ae claified into two baic type with epect to the ued commutation technique: extenal commutation (EC) and elf-commutation (SC). EC invete (Figue 4.5(a)) ae uch invete in which enegy, povided by an extenal powe upply, i equied to tun off the olid-tate witch device, while SC invete (Figue 4.5(b)) ae contucted in uch a way that they ae capable of elf-tuning off the olid-tate witch device by the ue of toed enegy in builtin capacito o coil. If the egulation of fequency i needed fo the output AC powe, a in the cae of the IM contol, both of the two baic type can be ued, howeve, the EC invete povide moe flexibility of AC powe poduction. In the following ection only the thee-phae SC-VSI will be conideed, becaue they povide the mot cot effective way to implement a IM dive. The VSI can alo be divided into two goup: the pule width modulation (PWM) 52

67 4. Opeation of induction moto dive baed invete and the quae wave invete. PWM invete equie moe complex contol cicuity and fate witching component, uually thei DC bu voltage i contant, and they ae capable of contolling the fequency and amplitude of the poduced thee-phae voltage ignal, while quae wave invete equie changeable DC bu voltage with contolled ectifie, becaue they ae only able to change the fequency of the poduced ignal which i imila to a quae wave fom (hence the name i coming fom). The mechanim of PWM invete will be decibed in the next ection. Figue 4.5(a). Extenal commutation needed invete with TRIAC Figue 4.5(b). Self-commutation needed invete with powe tanito The dive tuctue peented in Figue 4.1, alo conit of element which ae eponible fo the contol of the powe poceo. Thee ae the following: Invete contol cicuity The main pupoe of thi cicuity i to povide the tiggeing ignal of the invete and the ectifie bidge with guaanteeing the potection of the dive by mean of built in watchdog function, ove voltage and ove cuent potection, themal potection, and though hoot potection. Hee, the though hoot potection mean that the olid-tate witch device ae tiggeed in uch a way, that the tiggeing of thee device in the half bidge at once, which poduce hot cicuit, i avoided. The invete contolle device i uually i built up fom analog and digital component. By the complexity of thee potection and by the digital pogammability of thi cicuit uch powe ytem ae called intelligent powe dive. 53

68 4. Opeation of induction moto dive The micocontolle The micocontolle povide the computational mucle fo the contol algoithm implemented within the dive. It i alo capable of the poceing of the eno ignal coming fom the contolled IM, uch a the ignal conditioning and the A/D conveion of thi analog infomation. Thi device alo geneate the command ignal which i ealized by the powe poceo, and becaue of thi, it i the heat and oul of the whole dive. Mot commonly, fixed point DSP poceo o pogammable integated cicuit (PIC) ae ued fo thi pupoe depending on the pefomance expectation of the dive The PWM invete PWM invete ae vey popula becaue of thei low cot, high eliability and capability to poduce wide ange of inuoidal AC voltage ignal in fequency and in amplitude a well. Becaue, a it will be hown, they equie vey fat active element, theefoe mot commonly inulated-gate bipola tanito (IGBT) ae ued fo thi pupoe The inulated-gate bipola tanito The IGBT i a elatively ecent development of powe electonic. It mechanim i imila to the powe tanito [6], except that it i contolled by the voltage applied to a gate athe than the cuent flow into the bae, a in the cae of the powe tanito. The impedance of the contol gate i vey high in an IGBT, o the amount of cuent flowing in the gate i extemely mall. The device i eentially equivalent to the combination of a metal-oxide-emiconducto fieldeffect tanito (MOSFET) (voltage type, low powe demand witching) and a powe tanito (low gate-emitte voltage, low powe lo). The ymbol of an IGBT i hown in Figue 4.6(a). The chaacteitic of the IGBT i given in Figue 4.6(b), fom which it can be een that imilaly to the BJT it ha a voltage dop in tuned out mode, which i 2-3V fo a 1000V-ated device. It alo need a deadband time to tun out, imilaly to the thyito, duing which it need to have negative voltage applied between the gate and the emitte till the flow of cuent dop to zeo. If thi phenomenon 54

69 4. Opeation of induction moto dive i not conideed, then the device doe not tun out, and fo example in the invete bidge it caue a though hoot, which detoy the whole powe upply. Figue 4.6(a). Symbol of the IGBT Figue 4.6(b) chaacteitic of the IGBT Since the IGBT i contolled by a gate voltage with vey little cuent flow, it can witch much moe apidly than a conventional powe tanito can. IGBT ae theefoe being ued in high-powe high-fequency application, but of coue in vey high powe ange, the thee-wie thyito (alo efeed to SCR) i dominant till thi day becaue only thi family i capable to conduct 3000A The mechanim of PWM-VSI invete Figue 4.7 how a thee-phae PWM-VSI uing IGBT a the active element. Thi layout i vey common, and ince the IGBT ae elf-commutating, no pecial commutation component ae included in thi cicuit. Hee, the IGBT, which can be conideed a witche, ae made to conduct in the following ode: IGBT 1, IGBT 6, IGBT 2, IGBT 4, IGBT 3, IGBT 5. The tak i theoetically vey imple, tun on the witche in uch an ode that the poduced a, b, c indexed voltage become a ymmetical thee-phae voltage. Thi tak can be done in the peviouly mentioned conduct ode which poduce the output phae and line voltage hown by Figue 4.8. Additionally, in eality, deadband effect and othe cicuity pecific fact mut be conideed a well, but the baic idea i the ame a it i in Figue

70 4. Opeation of induction moto dive Figue 4.7. Geneal tuctue of SC PWM-VSI with IGBT Figue 4.8. Output voltage of the 3-phae PWM-VSI The PWM i the poce of modifying the width of pule in a pule tain in diect popotion to a mall contol ignal; the geate the contol voltage, the wide the eulting pule become. By uing a inuoid of the deied ynchonou fequency of the feed a contol voltage fo the PWM cicuit, it i poible to 56

71 4. Opeation of induction moto dive poduce high-powe wavefom whoe aveage voltage vaie inuoidally in a manne uitable fo IM. The baic concept of the PWM ae illutated by Figue 4.8. Baically the functionality can be decibed eaily by a ingle-phae PWM invete cicuit peented in Figue 4.9(a) with IGBT. The tate of IGBT 1 though IGBT 4 in thi cicuit ae contolled by the two compaato hown in Figue 4.9(b). Figue 4.9(a). One-phae PWM-VSI Figue 4.9 (b). Mechanim of PWM geneation A compaato i a device that compae the input voltage u in (t) to a efeence ignal and tun the IGBT witche on o off depending on the eult of the tet. Compaato A compae u in (t) to the efeence voltage u x (t) and contol IGBT 1 and IGBT 2 baed on the eult of the compaion. Compaato B compae u in (t) to the efeence voltage u(t) y and contol IGBT 3 and IGBT 4 baed on the eult of the compaion. If u in (t) i geate than u x (t) at any given time t, then Compaato A will tun on IGBT 1 and tun off IGBT 2. Othewie it will tun on IGBT 2 and tun off IGBT 1. Similaly, if u in (t) i geate than u(t) y at any given time t, then Compaato A will tun on IGBT 3 and tun off IGBT 4. Othewie it will tun on IGBT 4 and tun off IGBT 3. The efeence voltage ae hown in Figue Mot commonly the amplitude and fequency of efeence voltage ae contant and equal, o thei V = V = V and fm = fx = fy. ppx ppy ppm 57

72 4. Opeation of induction moto dive Figue Refeence ignal and Figue Refeence ignal and the output of the compaion in one-phae the output of the compaion in one-phae PWM geneation, when u in = 0 PWM geneation, when u in = ½V pp of efeence To undetand the oveall opeation of thi PWM invete cicuit, ee what happen when diffeent contol voltage ae applied. Fit, let aume that the contol voltage i zeo. Then u x (t) and u(t)ae y identical, and the load voltage out of the cicuit u out (t)i zeo (ee Figue 4.10). Next aume that a contant poitive voltage with 1 2 V of the efeence ignal i applied to the cicuit. The pp eulting output voltage i a tain of pule with a 50 pecent duty cycle, hown in Figue Finally, aume that a inuoidal contol voltage i applied to the cicuit with Vpp in and f 1 fequency a hown in Figue The width of the eulting pule tain vaie inuoidally with the contol voltage. The eult i a high-powe output wavefom whoe aveage voltage ove any mall egion i diectly popotional to the aveage voltage of the contol ignal in that egion. 58

73 4. Opeation of induction moto dive Figue Refeence ignal and the output of the compaion, when u in i inuoidal Moeove, the fundamental fequency of the output wave fom i the ame a the f 1 fequency of the input contol voltage. It i alo tue, that thee ae hamonic component in the output voltage, but they ae not uually a concen in moto-contol application. To be able to decibe the popetie of the modulation, the following ating value ae intoduced: Amplitude modulation value: m AM V = V ppin ppm Fequency modulation value: m FM f = f m 1 With thee ating value, the elationhip between the command and efeence ignal can be invetigated fom the point of view of poduced hamonic. In cae of mam = 0.8 and mfm = 15 the nomalized pectum of poduced output voltage of the modulation can be een in Figue By conideing thi figue the following can be concluded: The amplitude of the fundamental fequency component i out U 0 peak out mam Ubu U 0 =, if Vpp V in pp (4.1) m 2 59

74 4. Opeation of induction moto dive Equation (4.1) alo yield, that 0 m 1 if m AM mut be in the ange of AM inuoidal output ignal i needed to be geneated, becaue of the contant U bu. Figue Fequency pectum of a PWM ignal with m AM = 0.8 and m FM = 15 In the poduced voltage ignal, the uppe hamonic clute in ide band aound the 2m FM,3m FM,, and the h th hamonic component on the j th m FM fequency in the k th ide band ha the fequency of Baed on thi, if f h = (j mfm ± k) f1 (4.2) m FM i choen to be an odd natual numbe, then the poduced voltage will be oddly ymmetic and the even hamonic component ae eliminated fom the pectum. In pactice, howeve, the hamonic component may caue additional heating in the moto being diven by the invete, but thi exta heating can be compenated fo eithe by buying a pecially deigned moto o deating an odinay moto, like unning it at le than it full ated powe. So in the above mentioned way it can be clealy een that with the peak-topeak magnitude and fequency of the contol voltage ignal, which only theoetically exit fo the digitally computed compaato, the deied voltage ignal can be applied to the moto. The quality of the ealization i tongly depend on the fequency of the efeence ignal which i mot commonly 20 khz to povide vey fine modulation which i above the human heaing pectum. 60

75 4. Opeation of induction moto dive Figue 4.14(a). PWM output wave fom of 60Hz, 120V p inuoid contol ignal Figue 4.14(b). PWM output wave fom of 30Hz, 120V p inuoid contol ignal Figue 4.14(c). PWM output wave fom of 60Hz, 60V p inuoid contol ignal A complete thee-phae invete would conit of thee of the ingle-phae invete decibed above with contol voltage coniting of inuoid hifted by 120 between phae. Of coue in pactice, a moe economical olution of theephae compact invete i ued a it i hown in Figue 4.7. Fequency contol in a PWM invete of thi ot i accomplihed by changing the fequency of the input voltage imilaly to the peviou cae. Figue 4.14(a) and 4.14(b) illutate the manne in which the PWM dive can contol the output fequency while maintaining a contant m voltage level while Figue 4.14(a) and 4.14(c) illutate how the contol of the m voltage level can be achieved while maintaining a contant fequency. 61

76 4. Opeation of induction moto dive Diffeent technique of the 3-phae PWM geneation on VSI- PWM invete Baed on the peviouly mentioned concept eveal utilization of the PWM technique exit [17, 37]: In thi cae, Synchonou ymmetic PWM m FM i an odd intege numbe, thu the efeence ignal mut be ynchonized with the contol ignal. Moeove, the ynchonou ymmetic (SS) PWM ha the advantage ove it aymmetic couin a it ha two inactive zone of the ame duation: at the beginning, and at the end of each peiod. Thi ymmety and the cleve choice of m FM have hown to caue fewe hamonic than in the following cae. Fo thi type of modulation, the effective value of the line voltage ae 3/8 mam Ubu Synchonou aymmetic PWM The aymmetic (AS) geneation of ynchonou PWM i vey cloely elated to it SS couin except that the efeence ignal ae aw-tooth like, o the active peiod i tiggeed only at the end of each PWM cycle [37]. Although in thi cae, it i much eaie to poduce the tiggeing ignal of the IGBT, the pefomed output will be heavily loaded with hamonic Aynchonou PWM Fo aynchonou PWM, the value of m FM i not an intege numbe, theefoe the poduced voltage ignal will have much moe additive fequency component than in the peviou cae. Thi technique doe not need the ynchonization of the command and efeence ignal, thu it i ued in analog logic-diven invete, which ae employed aely today. In thi cae, if vey lage mfm 21 i ued, then the hamonic component become ignificant, poducing uch lage cuent cuff which can eaily damage the moto o the powe ytem and oveload the electic netwok in an indutial application. 62

77 4. Opeation of induction moto dive Space vecto PWM Space vecto (SV) PWM geneation i vey cloely elated to the concept mentioned in DTC and it geneate the minimum hamonic ditibution in voltage and cuent fo the IM [43]. A it wa mentioned in Section 3.2.4, fo PWM-VSI eight poible combination of the eulted voltage can be obtained by the on and off witching of the IGBT peented in Figue The deived eight combination of the witching tate and the coeponding moto line-to-line and phae voltage in tem of U bu ae hown in Table 4.1, whee 0 = off, 1 = on. a b c U a (U bu ) U b (U bu ) U c (U bu ) U ab (U bu ) U bc (U bu ) U bd (U bu ) /3-1/3 2/ /3 2/3-1/ /3 1/3 1/ /3-1/3-1/ /3-2/3 1/ /3 1/3-2/ Table 4.1. Poible witching tate of PWM-VSI invete Figue Six poible non-zeo voltage vecto tate of SV-PWM VSI Mapping thee voltage on the d-q complex vecto plane, by pefoming the (3.23) Pak tanfomation, eult in the ix non-zeo vecto and two zeo vecto (ee Figue 4.15) in conitence with Section Howeve, thi appoach ue diffeent ecto location, a it i peented in the figue. 63

78 4. Opeation of induction moto dive The objective of the SV-PWM i to appoximate the contol voltage epeented by the u in pace vecto with a combination of the eight poible witching patten of the ix IGBT. One way to achieve thi, equie that fo any mall inteval of the T PWM PWM peiod, the aveage invete output be the ame a the aveage efeence voltage a hown in (4.3). whee PWM (n+ 1) TPWM 1 1 u (t) = ( T u + T u ), n T (4.3) nt PWM out 1 x 2 x± 60 TPWM u x and u x ± 60coepond to the voltage level of the u x and u x± 60tate which ae the baic pace vecto of the ecto containing u in. Note that T 1 and T 2, ae the epective duation fo which witching tate coeponding to u x and u x± 60 ae applied. Howeve, if we aume that the change in the command ignal i tiny within T PWM, then equation (4.3) can be appoximated with (4.4). 1 u (t) = T u + T u, T + T T. (4.4) ( ) out 1 x 2 x± PWM TPWM Theefoe, it i citical that T PWM be mall with epect to the peed of change of u out. In pactice, thi i guaanteed by the 20 khz modulation fequency whoe peiod time i 50 µec. Equation (4.4) mean that fo evey PWM peiod u out can be appoximated by applying the witching tate u x and u x± 60fo the T 1 and the T 2 time duation epectively. Since T 1 T 2 T PWM +, the invete need to be in the u 7 o u 8 zeo ate fo the et of the peiod, theefoe fo the complete pace deciption T u = T u + T u + T u, T + T + T = T, (4.5) PWM in 1 x 2 x± o PWM applie, which guaantee that uin (t) u out (t). Fom (4.5) the coeponding time can be computed by vecto inveion like in (4.6) o by tigonometic bae like in (4.8) if the angle between u in and u x i α. [ T T ] T [ ] T = PWM x x± 60 in u u u (4.6) 64

79 4. Opeation of induction moto dive 1 PWM in ( ) T = 2 T u co α+ 30 (4.7) 2 PWM in ( ) T = 2 T u co α (4.8) Depending on the pecific application, the SW-PWM can be done eithe with (4.6) o (4.7) and (4.8). Method (4.6) i ecto dependent, howeve the matix invee can be calculated off-line fo each ecto and obtained via a look-up table duing on-line calculation, which need le pace and give moe accuate pefomance than the look-up table baed co and ine calculation. Thi modulation technique alo povide a moe efficient ue of the upply voltage in compaion with the othe technique and it make poible a m U / 2 AM bu amplitude fo out u with a m phae voltage of mam U bu / 6 which i 2/ 3 time geate than any type of inuoidal PWM can achieve. Becaue of it eay digital computation and mot optimal pefomance thi SV- PWM method i ued in mot cae of vecto contol. In cae of Ovemodulated PWM mam 1, the amplitude of the fundamental hamonic component can be inceaed above the elative value of 1, but with the cot of moe uppe hamonic a it i hown in Figue It i alo impotant to tate, than if mam 1 then out U 0 i no moe changing linealy in epect to m AM a it i hown in Figue Becaue of the lo effect of high hamonic, thi technique i only ued fo IM dive, and jut only in that cae, whee the ated voltage of the moto i much moe than 1 2 U. bu 65

80 4. Opeation of induction moto dive Figue Fequency pectum of an ovemodulated PWM ignal with m AM = 0.8 and m FM = 15 Figue Amplitude change of the fundamental hamonic component via m AM 66

81 5. The expeimental laboatoy dive 5. The expeimental laboatoy dive Baed on the peviouly intoduced theoie of contol method and on the phyical chaacteitic of the invete uch contolle algoithm wa deigned which, by a ucceful implementation, would fulfill the ecent expectation, fo moden indutial IM dive. But befoe any deign of an algoithm can be tated, at fit, the available technical equipment mut be examined to know the phyical envionment of the implementation. Thu, in the following ection, the Digital Spectum motion contol development kit poweed expeimental laboatoy IM dive, whoe heat i a TMS320F243 evaluation module (EVM), i going to be peented. Thi dive wa elf-aembled and upplemented to be able to povide peed enole contol of an IM. In Figue 5.1 the above mentioned dive i peented whoe mechanim i explained by Figue 5.2. Figue 5.1. The aembled laboatoy dive Figue 5.2. The mechanim of the conideed IM dive 67

82 5. The expeimental laboatoy dive The dive conit of 4 main pat: A 3 phae, 4 pole induction moto whoe contol i needed to be achieved fo flux and peed. A PWM-VSI invete, which i the powe element of the ytem and povide meauement on the cuent and on the invete bu voltage. An invete inteface cad and a TMS320F243 EVM, which ae connected to each othe in a andwich like deign and make poible the unning of implemented algoithm and though them the digital contol of the whole dive baed on the meaued data. A peonal compute (PC) which make poible the debugging and monitoing of the pogam and alo povide a ue inteface fo opeating the dive. Each of thee ytem pat ae going to be explained in the next ection: 5.1. The induction moto The conideed 4 pole induction moto, een in Figue 5.2, i a low powe and low peed contuction mainly ued fo expeiment and laboatoy wok. It ated powe i 90W with 230/300 V and 0.59/0.49 A ated input in Y/ connection. It nominal feeding fequency i 50Hz, with 5.3% nominal lip, but of coue, it can be excited on lowe fequencie a well. Becaue of it mall capabilitie and it lage tato winding eitance which i 38,1Ω / half winding, it i only a hadow of tue indutial IM. Although, it povide a good tet ubject fo contol algoithm implementation becaue if fat and dynamic contol of thi moto can be achieved than fo moe poweful IM the ame algoithm with light modification will povide ueful contol olution. The whole wiing between the moto and the invete wa elf-contucted to povide a connection with 230V/5A m capability by uing 1.5 type cable. In ode to uccefully deign a high pefomance contolle, the paamete of thi moto have been identified though meauement and tet ignal povided by a pecial pogam witten fo thi tak and implemented on the conideed 68

83 5. The expeimental laboatoy dive Ladive ytem. The exact pocedue of thi identification i going to be hown late with the obtained paamete value and with thei veification a well. To be able to complete the identification pocedue and to veify the functioning of the contolle a connectable encode wa built on the haft with a DC moto (ee Figue 4.1) to povide peed meauement with a capability of load toque contol. The opto-encode which, ha a 60 lot dic fixed to the haft of the IM, ue two pai of 5V-poweed phototanito and LED to geneate impule duing the otation of the dic. Impule ae geneated baed on that whethe thee i a lot between the tanito and the LED, if it i, then the tanito i tiggeed by the photon team povided enegy of the LED, o in the othe cae, it i witched off by the abence of the light. The time bae of thee impule i the 1/60 of the time peiod of each otation, thu the 1/60 of the fequency of the impule tain i equal to the fequency of the oto peed. Uing two pai of LED and phototanito not only the peed but the diection of otation can be obtained by calibating them to geneate impule tain which diffe in phae. Thi can be een in Figue 5.3. If the leading ignal i fom Seno A then, when the diection of otation change and the peviouly lagging B will have a phae hift. The 90 phae diffeence of thee ignal can be eaily obtained by the ue of edge enitive cicuit uch a the Schmitt tigge connection. In pactice, uually a thid pai i ued in the encode which obeve a lowe egion of the dic with only one lot. Thi i called the index lot and it i impotant when the incoming ignal ae ued to obtain the poition of the haft. In high peciion application, thi index ignal i ued fo calibation, becaue it mean the 0 angle poition, and by ening it the fit time, the contolle can be ue than fom thi point pecie tacking of the angle poition can be achieved. Figue 5.3. Encode ignal fo peed and diection ening 69

84 5. The expeimental laboatoy dive The connected DC moto, whoe ole i to povide load on the haft i a 24V and 15.6W contuction. It main pupoe i to tet the tability and pefomance of the contolle duing the opeation of the dive with applying load toque change on the haft. The impotance of thee tet will be decibed in the late ection The Spectum Digital invete The diect thee-phae voltage feed of the moto i geneated though a Spectum Digital PWM-VSI. Thi invete i a vey intelligent powe ytem with the ability of diect digital contol of the tiggeing ignal of each built in IGBT, dynamic beaking, and eveal built in eno to povide a good olution fo the powe element of any enole IM dive [24]. The invete module i pat of the Spectum Digital Moto Development Sytem and it i deigned to be ued with the TMS320F243 EVM and the Labdive Inteface cad. The Labdive inteface module piggyback the EVM and ue cable to connect to the Invete module, o the diect contol of the invete i povided via thi inteface module. Becaue the invete ha the logic to dive 3- phae AC induction and 3-phae DC buhle moto a well, theefoe the tiggeing ignal of the built in 10A capable IGBT, can be epaately povided. Moeove, becaue of the hybid deign, no built in potection ae available to avoid hoot though effect. Thi potection i povided by the inteface module. Thi device alo contain inteface cicuity which i common to mot moto contol ytem. Thi mean that the moto pecific electonic can be iolated to one boad, the invete module Specification of the invete module The boad outline of the invete i hown below in Figue 5.4. The device conit of two main pat, the contol logic and the powe cicuity, which have epaated powe input on P1 and on P5. The powe cicuity ha a common deign with a diode ectifie-bidge which i ated to 230/110V AC input. The output of the ectifie bidge i moothed by a RC-low pa filte with 2 paallel connected 400V, 470µF electolyte condenato. Thi 70

85 5. The expeimental laboatoy dive povide a ated bu voltage of 350VDC & 10A and though a elay, it alo able to input extenally povided DC voltage on P5 fo the invete bu by diconnecting the ectifie bidge. Becaue of the non-contolled ectifie, only dynamic baking can be achieved by witching a beaking eito to the invete bu to diipate the backfed enegy coming fom the moto. Thi i done tough an optically iolated tanito. Figue 5.4. Boad outline of the Digital Spectum PWM-VSI The dead time of the ued IGBT ae 2 µec but becaue the high and the low ide dive ae optically iolated, thu with the 1 µec tanient time of the optoiolation, the tiggeing ignal mut be inteleaved with a 3 µec deadband Capabilitie of the invete module The contol logic of the invete, which ha an onboad epaated powe upply, povide intelligent contol of thi powe element. It i connected though the P2 and P3 connection to the inteface module on which communication i povided on analog ignal. Thi logic make up eveal impotant featue of the invete: A it wa mentioned, the invete i capable of dynamic beaking though an extenally povided eito on the P5 connecto. Thi eito i witched on the 71

86 5. The expeimental laboatoy dive bu with a 30A IGBT, tiggeed by an optically iolated dive. Becaue in the cae of thi type of beaking thee i a apid voltage ie on bu with high cuent, a lage powe capable conume i needed. Fo thi pupoe a 100W bulb i connected to the appopiate pin with a eial connected high powe eito. The IGBT bidge ide of the invete bu i epaated though a elay, which i contolled though a digital logic implemented a a tate machine. Thi logic enable the bu voltage fo the IGBT in cae of faultle opeation, and if the appopiate ignal i povided fom the invete cad. If thi ignal beak, the logic aume that the micocontolle mied it opeation and theefoe it diable the bu, peventing the damage of the dive. The ame functionality i povided if any kind of built in potection i activated. The PWM ignal contol i made poible though digital connection with the invete inteface cad. On thi connection, the 6 tiggeing ignal fo the IGBT, which ae 0-4V digital ignal, ae given by the inteface module. Unfotunately, the invete logic povide no potection on the PWM ignal, o by incautiou uage hot cicuit can be eaily geneated. To avoid thi, the powe connection wee fued by me. The contol logic can alo be poweed tough the inteface connection. Moeove, in cae of any ened fault, by aiing the Fault ignal on the connection line, the micocontolle can be notified about the eo in the opeation. The dive ha eveal tet point to make the meauement eay and it alo ha onboad LED to ignal that the contol powe and the bu voltage i on o the event of baking o invete fault ha occued Seno The invete ha 3 Hall effect cuent eno with ±10 A ening ange on each of the a, b, c phae of the moto feed. The output of thee eno ae ±4V analog ignal which ae filteed by ignal pole filte with a cutoff fequency of 33.8Khz. 72

87 5. The expeimental laboatoy dive It alo contain an optically iolated bu voltage ene whoe ignal i divided by eito with 1766 diviion ate. Thi divided voltage i then applied to the input of an optically iolated amplifie which ha a nominal gain of 8. The maximum input voltage of the iolation amplifie i 200mV, which give a maximum bu voltage of 353V DC. The amplifie tage alo convet the diffeential output of the iolated amplifie to ingle ended. Thi amplifie tage ha a gain of 1 and incopoate a ingle pole filte with a cutoff fequency of 33.8 Khz. A econd amplifie i alo povided with an adjutable gain though a potentiomete, to pecify the deied enitivity ange of the voltage ene Built in potection The module contain intenal dive and potection cicuity. Potection i povided fo unde voltage, lockout, ove cuent, ove tempeatue, and hootthough. The fault pin in the inteface cad connection i ued to detect the type of fault. In cae of ove cuent and hoot though fault, the fault ignal i pulled low fo a hot time and fo ove tempeatue, the fault line i low until the unit cool. Beide the ignaling of the fault, the logic doe nothing to avoid futhe faulty opeation. Thi i done by the inteface cad The Invete Inteface Cad The next component in the contol chain (Figue 5.2) i the Labdive inteface cad which i the bidge between the micocontolle, the invete, and othe extenal eno and alo uppot the contol of AC induction, DC buhle, and witched eluctance moto [23]. The main pupoe of thi element i the ignal conditioning and potection, theefoe it contain inteface cicuity that i common in mot moto contol envionment uch a input fo optical encode, limit witche, and contol ignal. Thee ae alo two heade fo an optional piggy back boad fo additional ue cicuity, fo intance a eolve inteface. Two cable ae ued to inteface to the peviouly mentioned invete module. One cable dive the PWM and digital ignal, while the econd cable inteface to the analog eno of the invete. 73

88 5. The expeimental laboatoy dive Specification of the inteface module A boad outline of the Labdive inteface module i hown below in Figue 5.5. Figue 5.5. Boad outline of the Labdive inteface module Thi boad i diectly connected to the TMS320F243 EVM and a an extenion povide additional, 28 jumpe-defined capabilitie to the EVM to make it able to fulfill the contol of the dive. Moeove, each of the incoming ignal i limited by the cad and eveal of them ae conveted to make the EVM able to ue them fo futhe poceing. The following ignal conditioning and connection ae impotant to mention: I/O ignal conditioning The cad povide an optical encode inteface with diffeential A, B, and an Index channel. Additionally, it i alo able to eceive ingle ended ignal of the encode and thee ignal can be mapped to the appopiate input pin of the EVM. The cad alo contain a ingle-ended Tachomete input, which can be alo ued fo peed meauement. The 3 input of the Hall effect cuent eno and the bu voltage ene coming fom the invete can be conditioned though a potenciomete contolled offet and an adjutable gain to tanfom the eceived ±4V ignal into the 0-5V 74

89 5. The expeimental laboatoy dive input ange of the ADC of the EVM. Thi i done tough the peented imple connection with the ue of an opeational amplifie in Figue 5.6. The coect configuation of the potenciomete wa adjuted manually in expeiment to each the mot optimal cuent meauement. Becaue only 1.45 gain and 1.34 V offet could be achieved by the implemented cicuit, and becaue of the low powe capabilitie of the moto, theefoe the ened 0-5 A (±2V) ange wa calibated to the 0-5V input ange of the ADC. Thee i alo a built in filte on each channel with a cut off fequency of 32 khz. Figue 5.6. Logical tuctue of the ignal calibation cicuity in the inteface module Moeove, the cad povide 2 extenal limit-witche input, 1 diffeential/ingle-ended input fo contol voltage, and 1 dive enable input to make poible the contol by extenal efeence ignal geneated though fo example potentiomete-divided voltage o limite. In thi way, with a imple cicuit, the efeence fo peed ignal can be extenally geneated. Thee connection ae potected and have jumpe defined temination polaitie a well. The boad alo ha unipola analog output in 0-5V ange fo futhe pupoe Invete Digital Inteface Thi inteface diectly communicate with the invete and it main pupoe i to povide the coect and faultle contol flow between the EVM and the VSI, with alo paying attention to the potection of the dive. To be able to fulfill thi, the boad povide the EVM geneated 9 PWM dive output to the 6 tiggeing channel of the invete. Each of thee incoming ignal can alo be manually 75

90 5. The expeimental laboatoy dive diabled by jumpe and even emapped. The 9 ignal ae geneated by the EVM becaue not only IM contol but alo DC moto contol capability i povided, thu the appopiate channel ha to mapped to the 6 invete connection. The polaity of thee channel can be alo pecified by jumpe, which ae needed to be oppoitely configued fo the high and low ide of the invete bidge. In any cae of phae fault, the cad can be configued to diable the PWM input of the invete to avoid hoot-though. The cad i alo able to povide the beak, dive enable, and dive eet ignal fo the invete and though them the contol of the built-in logic. It alo eceive the fault ignal of the invete which i pulled down if any kind of potection i activated. If thi happen, the cad diable all the PWM output and the dive enable ignal, which diconnect the invete bu fom the powe ouce. In thi way, it enue that in cae of faulty opeation the dive will not be damaged. Additionally, the connection with the EVM i povided though fou 32bit wide channel a I/O, adde, data, and contol expanion bue Shield of the dive A it wa peviouly mentioned, the inteface cad i vey impotant in the contol chain, becaue it conit of thoe watchdog and potective cicuit that make poible the potection of the EVM and the invete ide a well. In any cae of ove voltage on any I/O channel o fault detection fom the invete, the two element ae totally epaated and potected until the had eet of the EVM The TMS320F243 Evaluation Module Thi micocontolle-containing boad i the heat and oul of the whole ytem with lot of dedicated hadwae poviding a vey effective way of motion contol. It peed pefomance make poible the implementation of an algoithm with a lage computational load and it i alo capable of geneating the tiggeing ignal of the IGBT of the invete diectly by the ue of SV-PWM. In the following ection, the main capabilitie of thi cad ae going to be peented. 76

91 5. The expeimental laboatoy dive Specification of the EVM The family of 24x DSP fixed point contolle i deigned to meet the need of contol-baed application. By integating the high pefomance of a DSP coe and the on-chip peipheal of a micocontolle into a ingle-chip olution, the 24x eie yield a device that i an affodable altenative to taditional micocontolle unit like the PIC and expenive multichip deign [37]. With 20 million intuction pe econd (MIPS), the F243 DSP contolle offe ignificant pefomance ove taditional 16-bit micocontolle and micopoceo. The 16-bit fixed-point DSP coe povide deigne a digital olution that doe not acifice the peciion and pefomance of thei ytem. In fact, ytem pefomance can even be enhanced though the ue of advanced contol algoithm uch a adaptive contol, Kalman filteing, and vecto contol. To achieve thi, the given 24x achitectue i uited fo poceing contol algoithm. It ue a 16-bit wod length along with 32-bit egite fo toing intemediate eult, and it ha two hadwae hifte available to cale numbe independently of the CPU. Thi combination minimize quantization and tuncation eo, and inceae poceing powe. Theefoe, The F243 offe eliability and pogammability, and a a digital micocontolle, in contat to analog contol ytem, i not effected by pefomance degadation due to aging, component toleance, and dift. Figue 5.7. Boad layout of the TMS320F243EVM 77

92 5. The expeimental laboatoy dive The intuction et of thee DSP contolle, which incopoate both ignal poceing intuction and geneal-pupoe contol function, coupled with the extenive development uppot and pogamming envionment available fo the 24x device by Texa Intument (TI), which geatly educe development time. The ingle DSP chip i upplemented by a peipheal boad, and the hadwied connection of thee element poduce the TMS320F243 EVM, which boad layout i peented in Figue Conideation of contolle implementation It can be een fom the pecification of thi device, that it offe a geat poibility to ealize algoithm with even high computational load. Fo peed enole opeation, the incoming inteface cad conditioned cuent and bu voltage ignal fom the invete mut be digitized and thei value obtained fo the contol algoithm. Thi tak can be handled with ome caefulne by a built in ADC convete. It i an alo impotant tak to ealize the contol voltage ignal, which can be done though an event manage (EVM2) module. Fo communication with the monitoing PC, a wide ange of poibilitie ae alo peented (SPI, SCI, CAN). Of coue all of thee featue have thei pecific way of ue and the advantage of each of them ae alway followed by ome talking dawback. Theefoe, the above mentioned impotant tak and thei way of implementation on the TMS320F243 i going to be biefly explained in the point of view of thei applicability fo the peed enole motion contol poblem at hand. The deciption of the hadwae i alo needed to claify the implemented algoithm and to make the poduced pogam moe undetandable Chip of many thing The logical tuctue of the EVM i peented in Figue 5.8, which element and the integated device of DSP ae going to be decibed in the following pat. 78

93 5. The expeimental laboatoy dive Figue 5.8. Logical tuctue of the TMS320F243EVM Speed and memoy A it wa mentioned, the F243 i a 16 bit adde and data wide fixed point micocontolle which i alo able to opeate in micocompute mode if the builtin 8K flah ROM of the chip i activated. Becaue fo motion contol, puely a fat algoithm unning i needed which conit of a linea contol cycle, thu only the micocontolle opeation i conideed. The deign of the DSP poceo i baed on the Havad achitectue, which in contat with the Neumann achitectue of commecial PC, ha epaated pogam, data, and I/O pace memoy. Thi tuctue i impotant, becaue mainly vey imple pogam ae unning on thee device, which pefe fat execution intead of eay pogamming capability. With thi deign, the fetching of intuction fom the pogam pace and the manipulation of the data can be done epaately and paallel, which allow making vey ophiticated pipeline tuctue with a poibility of 8 paallel multiplication, like in the cae of ome highly advanced DSP. The F243 alo pofit fom thi tuctue and even if it peed only 20Mhz, which eem to be vey mall in compaion to today 2-3Ghz poceo of the PC, it can totally ue fully thi peed fo computation. Thi i alo uppoted by the RISC intuction et of the DSP, which in contat with the CISC appoach of the PC, make poible the 1 intuction / 1 machine cycle fo any kind of opeation. Thi make the whole algoithm moe pedictable and fate, of coue with a lightly moe complicated pogamming. 79

94 5. The expeimental laboatoy dive In the cae of the F243, 64K wod of pogam, data, and I/O memoy i peented whoe configuation can be een in Figue 5.9. A it i hown, the egite of the poceo ae available fom the data pace, while the input and output communication i eticted to I/O pace with the contol of pecific data pace egite. Pogam pace i inhabited by the ue code with the inteupt vecto table which decibe the code egment of the event pecific evice outine. Thi tuctue povide enough computational powe to ealize complicated algoithm. Figue 5.9. Memoy achitectue of the TMS320F243 DSP Inteupt and peipheal The 24x CPU uppot one nonmakable inteupt (NMI) and ix makable pioitized inteupt equet. The 24x device have many peipheal, and each peipheal i capable of geneating one o moe inteupt in epone to many event. Becaue the C24x CPU doe not have ufficient capacity to handle all peipheal inteupt equet, a centalized inteupt contolle (PIE) een in Figue 5.10 i equied to abitate the inteupt equet fom all the diffeent ouce. 80

95 5. The expeimental laboatoy dive Figue Peipheal inteupt contolle of the TMS320F243 DSP A it can be een, the numbe of available inteupt equet i expanded by having two level of hieachy in both the inteupt equet/acknowledge hadwae and in the inteupt evice outine oftwae. In any cae of inteupt event, the pecific low goup ignal to the main inteupt handling logic, that a INTx level inteupt i pending. In epone, the highe level logic decide which INTx inteupt i going to be eviced, and if the poceo coe acknowledge thi, the cuent unning code i inteupted and fom the vecto table defined pecific pogam adde, the fit intuction i fetched. In thi way, the inteupt handling outine only know that a INTx goup inteupt geneated a call. To be able to obtain which of the inteupt in thi goup i active, the PIE egite of the logic mut be ead. Afte finding out which pending inteupt in thi goup ha the highet pioity, the appopiate evice outine can be called fom the inteupt handling method. At each level, evey INT can be maked except ome global inteupt, which ae eponible fo the faultle opeation. In thi way, eveal event can be eviced though inteupt, which povide a vey good monitoing 81

96 5. The expeimental laboatoy dive featue of the device. Thi i cucial fo motion contol, becaue in the cae of fault event o efeence change, the dive ha to eact intantly Digital I/O pin The device ha multiplexable I/O pin to witch between the main function and the channel povided by the extenion bue. Though thee pin the inteface conditioned ignal can be eceived and output function, uch a the contol of the invete enable ignal, can be povided. By the ue of data pace egite, the functionalitie of the poceo pin ae defined with the data diection a well. Thi featue make poible the ue of the inteface module and theefoe it i cucial to povide the implementation of the IM dive. I/O capabilitie alo enhanced with a MP7680 fou channel digital-toanalog convete Event manage (EVM2) The EVM2 module povide a boad ange of function and featue that ae paticulaly ueful in motion contol and moto contol application. The block main functionalitie ae decibed a follow: Time The module conit of two geneal pupoe (GP) time which can be ued a independent time bae in application uch a: The geneation of ampling peiod in a contol ytem. Poviding a time bae fo the opeation of the integated quadatue encode pule cicuit (QEP) and the captue unit. Alo poviding a time bae fo the opeation of the integated compae unit and the aociated PWM cicuit to geneate PWM output. Thee time ae 16-bit up- and up/down-counte with pogammable peiod and a vaiable counting peed which can be the caled CPU peed o extenal impulive ignal. The block diagam of the time i given on Figue

97 5. The expeimental laboatoy dive Figue Block diagam of the implemented GP time Each time alo ha a compae egite which geneate an inteupt if the counting value i equal to it and alo at each undeflow, oveflow o peiod hit event the ame inteupt geneating featue i povided. All the main contol egite can be hadowed, o in cae of any functionality change, the peviou opeation will be completed befoe the new one. The two counte can alo be ynchonized with each othe, and the tat of an A/D conveion can alo be geneated by the each of a pecific value. The time have the following opeation mode: Continuou up counting, whee a it i hown in Figue 5.12(a) the time i continuouly counting up till it eache the peiod egite value and then tating the counting fom zeo again. Diectional Up/Down-Counting Mode, whee a it i hown in Figue 5.12(b) the time counting baed on the diection flag to count up o down till it eache the peiod o 0, when the counting continue fom 0 o the peiod value. Continuou Up/Down-Counting Mode, whee a it i hown in Figue 5.12(c) the time i counting upwad fom 0 to the peiod value and then downwad till it eache zeo again. Thi i epeated continuouly. 83

98 5. The expeimental laboatoy dive Figue 5.12(a). Continuou up counting mode of the time Figue 5.12 (b). Diectional up-down counting mode of the time Figue 5.12 (c). Continuou up-down counting mode of the time While the continuou up counting can be ued fo eveal time bae meauement, the othe mode ae impotant mainly fo PWM geneation PWM geneation The hadwae-uppoted PWM geneation featue of thi device i extemely cucial fo the invete contol. It povide eveal way to ealize the peviouly mentioned PWM technique, even the SV-PWM with a dead time compenating ability, which make the implementation of vecto contol vey efficient. With the ue of the built in compae unit of the GP time 1, SA/SS type PWM tiggeing ignal can be obtained by eae. Becaue 3 egite ae aociated with the compae unit tuctue peented in Figue All the 6 PWM tiggeing ignal can be geneated. The compae unit ae diectly connected to the PWM cicuit, which geneate a tanition on the appopiate output towad the invete, when any counte-hit on the compae egite occu. Even inteupt can be connected to thee event. 84

99 5. The expeimental laboatoy dive Figue Compae unit tuctue of GP time 1 The block diagam of the PWM cicuit i hown in Figue The PWM cicuit aociated with the compae unit, make poible the geneation of ix PWM output channel with pogammable deadband and output polaity. The unit i capable of on-the-fly change of PWM caie fequency and pule width, howeve, becaue thee egite can be hadowed it alo uppot the peiod eticted change a well. Figue Block diagam of the PWM cicuit If the geneation of AS-PWM i needed then by configuing the GP1 time to continuou up counting with a peiod equal to the time peiod of the modulation and by etting up the compae unit to the oftwae detemined value, the AS PWM can be achieved though the PWM cicuity that et up the tiggeing ignal baed on the compae egite hit. Thi i peented in Figue

100 5. The expeimental laboatoy dive Figue Aymmetic ynchonou PWM geneation with the EVM2 In cae of SS PWM, the peviou hadwae element can be ued, but the time i calibated to continuou up-down counting which eult the tiggeing ignal een in Figue 5.16 to ealize the ymmetic PWM. Figue Symmetic ynchonou PWM geneation with the EVM2 SV-PWM can be alo geneated, but fo thi dedicated hadwae logic i implemented a een in Figue The GP1 time i calibated to continuou up-down counting with a peiod match equal to the PWM peiod. Thi povide the time bae. Two of the compae egite ae ued to obtain the tanition at T and ( T T ) , becaue the witching between the bae vecto i done ymmetically to educe the unwanted uppe hamonic (ee Figue 5.17). The hadwae alo need the index of one of the bae vecto, which ae defined by the ecto of the needed output tato voltage vecto. The calculation of T 1 and T 2 i done though one of the peented method of Section by a oftwae implemented algoithm. Becaue fo coect functionality, only the T 1 and T2 time bae have to be calculated, thi hadwae element povide a vey fat and eliable ealization of the deied output tiggeing ignal, not mentioning that the 86

101 5. The expeimental laboatoy dive SV-PWM i the mot efficient and low computation needed method to povide the voltage feed of the IM. Figue Space vecto PWM geneation with the EVM Deadband unit The deadband unit i vey impotant to povide the dead time in the tiggeing ignal to achieve faultle opeation of the IGBT. It i implemented with thee 4-bit down counting time which knock out the active tiggeing at the tanition in each PWM pai. The clock of thee time i the calable ignal of the CPU clock, theefoe the minimum dead-band duation i one device clock cycle, and the maximum can even be defined a 96µec Captue unit Captue unit enable logging of tanition on captue input pin. Thee ae thee captue unit in the F243 and they can be ued mainly in motion contol application to poce the ignal of encode. Thei mechanim, epeented by Figue 5.18, i the following: by chooing one of the time a a time bae, wheneve a tanition happen on the aociated input pin, the counte value of the time i toed in a 2 level deep 16 bit wide FIFO. In thi way if the output of an encode i connected to thee pin though the inteface cad and the aociated time i in continuou up-counting mode, then by the diffeence of the toed time tamp in the FIFO, the exact elaped time, fo example between two iing edge of the incoming ignal can be calculated, which will be popotional to the 87

102 5. The expeimental laboatoy dive fequency of the haft, baed on the eolution of the encode. The input pin ae Schmitt-tiggeed and they ae ynchonized with the CPU clock, theefoe in ode fo a tanition to be captued, the input mut hold at it cuent level to meet the two iing edge of the device clock. Moeove, the type of detected tanition can be defined to one of the following: iing edge, falling edge, o both edge. To the defined tanition, inteupt geneation can be alo connected. Figue Captue unit of the EVM2 With thee of thee captue unit, a bidiectional encode with index lot can be connected to the dive and in thi way, even poition-dependent contol of the oto can be achieved. Fo one, thi featue eem to be unneceay fo peed enole deign, although fo the well-functioning of uch a dive, fitly the identification of the moto mut be completed, which need peed meauement. Theefoe, duing any contolle deign poce, thi ability i heavily needed Quadatue Encode Pule (QEP) Cicuit The F243 EVM alo offe a diffeent way of poceing the ignal of a poition encode. Thi i povided by the built-in QEP cicuit peented in Figue When thi featue i enabled, it decode and count the input pule fom the 88

103 5. The expeimental laboatoy dive encode on the appopiate input pin. The time bae fo the QEP cicuit i povided by GP time 2, which mut be put in diectional up/down-count mode, with the QEP cicuit a the clock ouce, fo coect opeation. The diection detection logic of the QEP cicuit in the EV2 module detemine which one of the A o B equence lead in phae. It then geneate a diection ignal a the diection input to GP time 2. Thu, the time count up if ignal A i the leading equence, and count down if B lead in phae. Figue QEP cicuit of the EVM2 In thi way, the fat tacking of angle poition can be achieved, although the peed of the oto can not be obtained, becaue the elaped time between the count i not toed. Howeve, thi type of tacking i enough fo tep like opeation of the IM, which i needed in high peciion field Analog to digital convete (ADC) The F243 ha a built-in 600n, 10-bit convete with witched capacito ting poviding an inheent ample-and-hold function to digitally obtain the analog ignal, uch a the invete povided cuent and bu voltage meauement fo the ue of the implemented contol algoithm. Howeve, becaue of vaiou ynchonization delay, a ingle conveion take about 1µ, o fo the fou incoming ignal, minimum 4µ delay in the contol loop ha to be povided. The convete ha 8 analog input and it i alo capable to almot imultaneou conveion on paied input channel. The two conecutive conveion ae pefomed 850n apat, fo a total imultaneou dual-conveion time of 1700n. Thi opeation i called peudo-dual ADC. 89

104 5. The expeimental laboatoy dive The conveion can be tated by the oftwae, an intenal event, and/o an extenal event and the eult ae placed in two-level-deep FIFO that contain the digital value of completed conveion. The mechanim of the conveion i baed on ucceive appoximation which mean that the bit of the eult ae obtained in MSB-LSB diection with compaing the analog ignal to the epeented value of the bit to decide whethe it i le o geate than that. The eult of the conveion i appoximated by the following equation: U = U ADC_IN REF _ LOW Digital eult 1023, REF_ HIGH U U REF_ LOW (5.1) whee 0 UREF_ LOW UADC_IN UREF_ HIGH, and a it can be een, the efeence ignal can be abitaily changed to obtain the deied enitivity on the pecified amplitude egion. At the end of each conveion, inteupt notification can be equeted, but becaue it would equie much time, thee action ae eviced afte each othe. Thi type of fat conveion give the ability to quickly fetch the equied data in each contol cycle, which i vey impotant fo the deign of high pefomance application that need a mall contol loop time Communication inteface The communication poibilitie ae alo ignificant if the dive wanted to be contolled fom a PC o integated into a lage indutial contol chain, whee incoming efeence ignal and the outgoing tatu epot of the dive ae povided though thi inteface. The F243 EVM offe thee poibilitie to olve thee tak and make the dive able to function a an intelligent ytem Seial Communication Inteface (SCI) The SCI offe the univeal aynchonou eceive/tanmitte (UART) communication mode fo intefacing with many popula peipheal which ue the tandad NRZ (non-etun-to-zeo) fomat though the eial pot of the device. The aynchonou mode equie two line to inteface with many tandad device uch a teminal and pinte that ue RS-232-C fomat. The 90

105 5. The expeimental laboatoy dive SCI eceive and tanmitte ae double-buffeed, and each ha it own epaate enable and inteupt bit, thu both may be opeated independently o imultaneouly in full-duplex mode. To enue data integity, the SCI check eceived data fo beak detection, paity, oveun, and faming eo. The bit ate (baud) i pogammable to ove 65,000 diffeent peed though a 16-bit baudelect egite with a maximum of With the help of thi inteface the well known RS-232 potocol-baed communication with a PC can be achieved to povide the efeence ignal change and contol of the dive on-line, which i needed to povide the ability to integate the poduced IM dive into lage ytem Seial Peipheal Inteface (SPI) The SPI i anothe communication mode povided though the eial pot, but in contat with the peviouly mentioned SCI, it i a ynchonou type of eial I/O communication. It allow a eial bit team of pogammed length (one to ixteen bit) to be hifted into and out of the device at a pogammed bit-tanfe ate. The SPI i nomally ued fo communication between the DSP contolle and extenal peipheal o anothe contolle; theefoe it ha a mate-lave type of potocol. Typical application of it include extenal I/O o peipheal expanion via device uch a hift egite, diplay dive, and ADC. Theefoe, it i ueful if othe equipment have to be connected to the contolle to povide the opeation Contolle ae netwok inteface (CAN) Today, the CAN ha a gowing impotance not only a the potocol of ditibuted contol ytem in the induty but alo a a mot widely ued communication method between the ubytem of ca and aiplane. The CAN ue a eial multimate communication potocol that efficiently uppot ditibuted eal-time contol with a vey high level of data integity, and communication peed of up to 1 Mbp. The CAN bu i ideal fo application opeating in noiy and hah envionment, uch a in the automotive and othe indutial field that equie eliable communication. Pioitized meage of up to 91

106 5. The expeimental laboatoy dive eight byte in data length can be ent on a multimate eial bu uing an abitation potocol and an eo-detection mechanim fo a high level of data integity. Thu, in a eal life application thi type of communication hould be ued to inteface othe contol element fo example in an indutial contol chain. Howeve, fo a tand alone dive and fo implicity, intead of thi featue, only the ue of the SCI i atifying Watchdog The watchdog (WD) time peiphey monito oftwae and hadwae opeation, and implement ytem eet function upon CPU diuption. If the oftwae goe into an impope loop, o if the CPU become tempoaily diupted, the WD time oveflow to aet a ytem eet and in thi way pevent the continuing of the faulty opeation. Thi featue i povided though a 8-bit counte that geneate a ytem eet upon oveflow an it i fed by a 6-bit fee-unning counte to povide the appopiate pecaling. To avoid the oveflow of the counte, it need to be eeted with a pecific eet key egite that clea the WD counte when the coect combination of value ae witten in it, and it geneate a ytem eet in cae of an incoect value Heat and oul of the dive A it can be een, the TMS320F243 EVM povide a vey ueable hadwae olution to contol the opeation of the hadwae element by an implemented digital contol oftwae in it pogam pace. Fo the conideed peed enole poblem at hand, it i pefectly uitable, and additionally, even the identification poce of the moto can be diectly accomplihed with it help. Fom evey apect, it can be called the heat and oul of the dive, becaue evey main opeation i pefomed by itelf and the othe element in the contol chain ae only caying out it ode. Theefoe, by the conideation of it mentioned capabilitie the implementation of a pecie contol algoithm with high computational load can be completed on it. Thi algoithm will be hown in the next ection. 92

107 5. The expeimental laboatoy dive 5.5. The PC At lat, the dive conit of an opeato pogam unning on a PC that monito the opeation of the dive and povide the ue given efeence ignal, while it alo eceive the tatu epot of the contolle via eial RS232 connection baed on the SCI inteface. Thi PC i alo the developing platfom of the code and though a paallel connected JTAG dive the debugging and monitoing of the uploaded code execution can be pefomed The XMS510P Plu JTAG dive The main connection to the contolle i povided by the Spectum Digital XMS510P Plu JTAG dive, which allow the full egite can of the CPU though the JTAG tatu pin and the ead /modification of the memoy pace of the DSP cad. It i connected to the LPT pot of the PC by a paallel cable and it dive integate into the Code Compoe envionment of TI. In thi way, it i the bidge between the code developing oftwae and the eal life contolle, poviding uch a flexibility which i expeienced in code development fo PC The Code Compoe envionment Texa Intument ha a geat tadition with the Code Compoe Studio (CCS) which allow fat and dependable code geneation fo extemely wide ange of DSP. Thi gaphical integated development envionment (IDE) i alo povided fo the TMS320F243 EVM. Thi oftwae uppot Aembly and C baed development, with lot of ueful featue like the tightly integated edito, the viual poject management ytem, watch window on memoy location and egite, beak point and tep like debugging, pobe point fo vaiable tatitic and gaph, code pofiling, and ue fiendly inteface with eay pogammable econfiguation. It C/C++ compile alo include uppot fo UML and Matlab which could be ued fo automated code geneation (ACG). The eal-time debugging tool, including the gaphing tool (ee Figue 5.20), have had beneficial effect on the poce of development and teting. 93

108 5. The expeimental laboatoy dive Figue Built-in gaphing tool of the CCS CCS alo uppot RTDX (Real-Time Data Exchange) between the hot and the taget, inteactive pofiling and advanced gaphical ignal analyi, and GEL (Geneal Extenion Language) function uppot fo automation activitie uch a egeion teting, automated teting, and cutomization via cipting, and multipoceo debugging. Theefoe, thi IDE povide an ideal tool fo the implementation poce The opeato inteface The opeato inteface i a elf-witten pogam unning on the PC that i connected to the EVM via RS232 eial connection. The pogam main pupoe i to povide the peed and flux efeence ignal to the contolle and in cae of faulty opeation, it notifie the opeato about the malfunction. It alo povide the etimated peed of the oto a back up abut the tate of the dive. The pogam i going to be biefly hown in the late ection with the ynthetied code of the implemented contolle. 94

109 6. Implementation of the contolle 6. Implementation of the contolle A it wa clealy hown the implementation of a peed enole IM dive i not an eay tak. In Section 3 eveal appoache wee peented to how olution of the poblem at hand, but it wa tated that each of them ha it own dawback even if it i able to handle the contol. By invetigation of the peented claical powe feed geneation appoache and the available elf-aembled dive, eveal iue wee dicued that how thee hadwae element can and hould be ued to ealize uch a complicated device. Baed on thee, to be able to build a dive that fulfil the ecent indutial equiement that wee mentioned in the fit ection, and baed on the peented theoetical contol appoache, uch a unique peed enole contolle tuctue wa aimed to be deigned that make poible the independent contol of the flux and peed on the full 4 quadant of opeation ange of the moto. With the peviouly decibed dive, thi opeation i needed to be povided though the ue of the thee-phae tato voltage a the contol input and by the meauement of the tato cuent only. Moeove, the contolle to be deigned mut conide the vaiation of R to heat, in ode to deceae the effect of paamete uncetaintie which wee mentioned in Section Becaue the thee-phae voltage feed of the moto i povided by a PWM-VSI, thu duing the deign, it wa unavoidable to pay attention to the eo of the invete, caued by the finite modulation bandwidth. Thi invete noie can be modeled a a medium fequency ange dominant noie on the input of the IM. Beide thi, it i alo woth conideing the meauement eo of the tato cuent eno, which ae high fequency noie with mot commonly 0.5% elative amplitude in compaion to the meaued quantitie. In ode to pevent any efeence tacking eo in peed and in flux, the contolle wa alo made able to online adapt to the load toque iing on the haft. Uually, the needed efeence ignal of the flux i a contant value duing the opeation, which decibe the mot optimal point of the magnetic atuation cuve. By the et point contol of oto flux to thi a pioi infomation defined opeation point, the maximal effectivene of the IM can be guaanteed. 95

110 6. Implementation of the contolle In contat with thi, the efeence ignal fo peed i expected to be a it i pleaed, with the occuence of even uncontinuou tep change. Futhemoe, the contol ha to be povided on that way, which make poible the mot accuate efeence tacking with the leat poible time contant, but with the awaene that the voltage ignal ued a a contol input, hould neve caue the ie of uch a geat cuent that would damage the moto. The deigned contolle alo conide the pecific behavio and popetie of the available digital and analog hadwae that i going to be ued fo the implementation The theoetical tuctue of contol Afte caeful theoetical and pactical deign peented in [39], the contol tuctue hown in Figue 6.1 ha been ynthetied fo the peviouly defined poblem. Figue 6.1. The deigned contol tuctue Fo the functioning of the ytem peented in Figue 6.1, which fulfil the given tict equiement, only the meauement of two tato phae cuent ae needed, becaue of the ymmety of the phae, i ( i i ) = +, which i c a b appoximately tue even in eal life application. Thu, the oveall vecto can be accuately obtained only fom two meauement, which make poible to ave up one ADC pe contol cycle. Futhemoe, becaue the input voltage feed i geneated diectly by the ytem, thu the accuate u i known without 96

111 6. Implementation of the contolle meauement, howeve, fo accuate PWM modulation, the DC bu voltage alway ha to be monitoed, which pevent the aving of anothe ADC. Baed on theoetical examination peented in [38], the elative degee of the moto model yield, that in the cae of known i and u, each of the tate vaiable peented in equation (2.19), (2.23), and (2.31) can be expeed with them o taken into diect connection via input-output lineaization. Thu, thee vecto conit of all the infomation about the opeation of the moto, theefoe the peed enole contol of the conideed IM dive can be achieved. The mechanim of the contol ytem i biefly the following: With the help of the (3.24) Clak tanfomation and fom the two meaued tato phae cuent, the two phae epeentation baed i α and i β component ae calculated, which ae equal to the d and q component of the tato pace vecto epeented in a tato fixed, tationay ( ω k = 0) efeence fame. Then, by a complicated etimation method, which i the connection of an EKF and an H obeve, the unknown Ψ (t), α Ψ β, ω, and (t) R tate vaiable ae obtained with the filteing of the tato cuent. In thi complicated etimation tuctue, the H obeve, whoe deign i baed on the (2.34) LPV tato oiented flux ubytem of the model, povide the tato oiented etimation of the oto flux, while the EKF etimate the peed and oto eitance vaiation with the filteing of the cuent. The application of the EKF i tongly uppoted by the fact, that it computational load i much le than fo a input/output lineaized model baed full tate H obeve [16]. The tability of the above mentioned tuctue i guaanteed by the highly accuate computation and tuning of the EKF and by the extemely low γ gain of the H obeve. Thi etimation ytem i upplemented by a tivial calculation baed, howeve, a it i going to be hown, vey impotant toque etimation module, which povide the imilaly unknown value of the load toque. All the infomation which i povided by the etimation tuctue i tanfomed into the otating efeence fame fixed to the oto flux with the help of the field oientation module. It i impotant to mention that thi oientation can only be 97

112 6. Implementation of the contolle done effectively if the value of Ψ α and Ψ β i accuately known. Thi wa the eaon why the etimation method wee deigned in the tato fixed oientation. With the help of the fehly tanfomed quantitie and the flux and peed efeence ignal of the ytem, the i and f def i f qef cuent efeence ignal, which ae needed to achieve the tacking of the efeence, ae calculated, and the tacking eo of thee quantitie ae eceived by the H contolle. Thi tuctue i vey impotant, becaue only the (2.37) ytem model can be given in a ueful LPV fom, thu efficient H contolle can alo be deigned only fo thi cae. Moeove, the cuent egulation i the fatet way of the contol of the poduced T e and Ψ. The goodne of thi appoach i uppoted by [41] a well. The contolle given f u d and f u q ignal, ae ealized though the SV-PWM hadwae module of the TMS320F243, which povide the coect tiggeing equence of IGBT of the VSI. It i impotant to note, that becaue the SV-PWM ue tato fixed efeence fame, thu the field oiented contol voltage ignal povided by the contolle ha to be tanfomed back by the invee of (3.23) into thi efeence fame. Fo the coect computation of thi tanfomation, the angle of the oto flux mut be known, which i tacked by the peviouly mentioned field oientation module. In concluion, the above decibed ytem theoetically olve the given poblem with the ue of the peented hadwae, but befoe it diect implementation i decibed, each of it ubmodule ha to be explained and analyzed fom the point of view of how they can handle thei tak in tem of quality and eliability. Thi i hown tep by tep in the following ection The H contolle module The contolle module wa ealized though the (2.37) and (2.38) field oiented LPV model-defined ubytem with mixed enitivity, to povide obut and a accuate a poible efeence tacking of i f d and i f q with the ue of the vecto contol appoach. The exact mathematical deign of the poduced LPV contolle with ω, R, and ω flux cheduling paamete, fo a identified moto 98

113 6. Implementation of the contolle expeimental moto can be found in [39], whee full validation of the pefomance by imulation i hown. The contolle wa ynthetied to eliminate the tacking eo of the cuent and to povide a fat and dynamical contol of the moto in a noie filteed envionment. Thi filteing i guaanteed by the late dicued etimation method. In the deign, the extenal tuning ability of the contolle pefomance wa povided to make the eay adjutment and calibation poible. By a caeful tuning in Matlab, imulation povided 0.35% teady tate tacking eo fo 0 to 1 tep like change in efeence ignal, with a iing time of 45m, which i nealy the time contant of the identified moto. Thi eult wa obtained when Tload = 0.5Nmwa applied to the moto. By the mixed enitivity appoach, lage obut contol inteval wa povided fo the whole contolle which ha hown tability fo even 15% paamete vaiation with a le than 1% tacking eo in the 0-10% vaiation inteval. By diffeent tability check of [39] it wa poved that the peented contolle povide extemely apid and accuate contol of the cuent and though them, a it wa mentioned peviouly, the contol of the whole IM. Moeove, the poduced contolle i a 3 2 = 8 cone ytem decibed polytopical egulato, which ha 5 tate, 2 input, and 2 output. Thu, the contolle matice ae obtained though 8 time of 45 multiplication and addition in each contol phae, and the method need additional 45 multiplication and addition to obtain the new contolle tate and output. Fotunately, by the mathematical tuctue of the model, the polytopical input matice ae identical in each dimenion, o the oveall opeation need i 325 multiplication and addition in each contol cycle. Howeve, thi computational load might eem to be huge, the F243 DSP can handle it with eae I/O lineaization baed efeence tanfomation Becaue the deigned contolle ue the cuent ubytem fo egulation, the ue povided flux and peed efeence ignal have to be tanfomed omehow to cuent efeence ignal. Thi tak i olved by the I/O lineaization of the (6.1) flux and (6.2) dynamic motion equation. The exact poce of thi lineaization can be found in [39]. 99

114 6. Implementation of the contolle d Ψ (t) R(t) L R(t) f = Ψ + i d (t) (6.1) dt L L f d f d (t) m 2 ω 3p Lm p = Ψ + ω (6.2) d (t) dt 2JL J f f ( d (t) i q (t)) ( T load (t) F (t)) Fom thee equation the following imple method of efeence tanfomation can be obtained: L 1 i (t) = v (t) + Ψ (t), (6.3) f f def 1 d LmR (t) Lm 2JL v (t) 2L i (t) = + T (t) + F ω(t). f 2 qef 2 f 3p L m Ψ d(t) 3pLm ( ) load (6.4) In thi way the input of the contolle aie fom the eult of i (t) = i (t) i (t) and f f f dhiba def d i (t) = i (t) i (t). It i impotant to mention f f f qhiba qef q that becaue Ψ f (t) i alway equal to the value of x d Ψ (t) in any x efeence fame, the diviion by thi quantity can alway be accomplihed expect at t = 0. To avoid the diviion by zeo, in thi time moment, the flux amplitude i ubtituted by a mall, nealy zeo value which povide continuou efeence chaacteitic. Unfotunately, in pactice thi would caue a hoibly high at tat up, which mut be avoided in ode to pevent the contolle to ealize the coeponding lage input ignal fo thi efeence, thu in the fit time moment, till f Ψ doe not exceed 0.01, it i woth ubtituting it value with 1 in the d (t) diviion. In thi way, it can be achieved that (6.4) would foce the contolle fo mooth exponential ie till it eache the bode of it untable dynamical inteval, and finally the whole eo ignal can be eceived by the contolle. In pactice, the above mentioned tak can be eaily implemented with no moe than 1 diviion, 4 multiplication and 4 addition. Of coue the efeence change mut be alo limited to avoid aggeive epone of the contolle to tep like change. Thi i achieved by implemented fit ode filte with a cutting fequency of 15Hz that foce the contolle to a mooth exponential ie. i f qef (t) 100

115 6. Implementation of the contolle Roto flux oientation and flux angle tacking To ue the powe of field-oiented vecto contol fo the ytem mentioned in Section and 6.1.2, it i cucial that the tato cuent meaued on the moto and the late hown etimation method povided oto flux i tanfomed to the ω =ω defined efeence fame. Thi oientation i done though the k flux following, puely mathematical pocedue. Let it be aumed, that the accuate value of Ψ (t) and α Ψ β(t) ae known. Then, fo the complex Ψ (t) pace vecto the following equation hold: Ψ (t) Ψ (t) α β co ρ (t) =, in ρ (t) =. ( Ψ α(t) ) + ( Ψ β(t) ) ( Ψ α(t) ) + ( Ψ β(t) ) (6.5) In thi way, by uing the calculated tigonometical value of the flux angle the field oientation can done with eae with the peviouly mentioned (3.23) Pak tanfomation method. It i needle to calculate the exact value of ρ (t), becaue fo the back tanfomation of the u f d (t) and u f q (t) contol input, only the knowledge of coρ(t) and in ρ(t) i enough, theefoe the whole oientation can be computed without the calculation of any tigonometical function. Baed on thi, the tak at hand can be completed with elative few opeation if the Newton- Raphon method [14] i ued fo the calculation of the quae oot opeation. Thi yield to 14 multiplication and addition with 6 diviion fo the whole oientation method, becaue a it follow fom Section 2.4.2, ( α ) ( α ) f 2 2 d (t) (t) (t) Ψ = Ψ + Ψ and Pak tanfomation. f Ψ =, o only the cuent need the q (t) 0 It alo noteable, that in the fit time moment, when Ψ =, the (6.5) (t) 0 calculation method i not ueable, thu ρ (t) = 0 aumption i made fo thi cae. The oientation eo due to thi ubtitution apidly vanihe when the magnetic field i built up inide of the machine. Moeove, it i impotant to tell that the efeence ignal need limiting in change a well, to pevent the enitive contol tuctue to needlely oveeact 101

116 6. Implementation of the contolle the apid efeence change. Fo thi eaon, filte (6.6) wa intoduced on the efeence ignal (6.6) The tuctue of etimation The main tak of the deigned etimation method, peented in Figue 6.2, i to make poible the peed enole contol of the IM. Becaue the peviouly intoduced method ae found on the accuacy of the ytem infomation, thu the etimation method ha to be able to atify thee need, and even be able to attenuate the meauement and the invete caued ytem noie. Fo thee expectation, uch a method i pefectly uitable which conit of thee pat: Figue 6.2. Theoetical tuctue of the deigned etimation method Duing the deign of the etimato, it ha quickly tuned out that the equation which contain the ω, R, Ψ (t) and Ψ (t) tate vaiable cannot be α β tanfomed into a paamete-affine fom, which would enable the deign of only one obut LPV H obeve to olve the poblem. Howeve, it i alo tue, that the etimation of thi nonlinea poblem with a EKF doe not offe uch accuate eult than a obut H obeve poviding only the etimation of Ψ (t) and Ψ β(t). Thu, to enue the pecie etimation and the obutne of opeation, uch a unique cloed loop tuctue wa deigned, which i the inteconnection of α 102

117 6. Implementation of the contolle a LPV H obeve and an EKF. The ω and R(t) cheduled H obeve povide the tato oiented etimation of Ψ (t) and α Ψ β(t) with the help of the meaued i (t) α and i β (t), while the EKF calculate ω and R(t) with the filteing of i (t) α, i β (t) baed on the etimated value of Ψ α (t) and Ψ β(t) and on the meaued tato cuent. Thi tuctue i completed by the dynamical motion equation baed toque efeence model, which give the helping hand to guaantee the accuate ω etimation by the Kalman filte The H obeve The obeve method wa deigned baed on the (6.7) LPV tato-oiented flux ubytem of the model p(t) 2 Lp(t) m 2 p(t) 1 0 d Ψ (t) L α Ψ (t) L i (t) α α = + dt Ψβ(t) p(t) 2 Ψ β(t) Lp(t) m 2 i β(t) p(t) 1 0 L L (6.7) whee the p(t) 1 =ω (t) and p 2 (t) = R (t) paamete wee ued fo cheduling. Hee, alo mixed enitivity tuctue wa ued duing the deign to calibate the obeve fo accuate etimation of the flux with obutne. The whole mathematical pocedue of thi i explained in detail in [39]. The poduced 2 2 = 4 cone ytem decibed polytopical obeve wa teted in Matlab imulation a well, and it howed exteme pefomance with no moe than 0.33% etimation eo in cae of 100V, 50Hz voltage feed and 0.5Nm load toque, due to it low γ wot cae gain which i Duing the imulation, modeled invete and meauement noie effect wee applied to the ytem. Thee wee geneated with filteing of white noie effect in uch a way that fo the invete noie a 10Vpp medium fequency dominant noie peented in Figue 6.3, while fo the eno noie a high fequency dominant noie with a 0.5 A amplitude peented in Figue 6.4 wa intoduced. 103

118 6. Implementation of the contolle Figue 6.3. Modeled invete noie Figue 6.4. Modeled meauement noie Howeve, the cuent technologie, like the Labdive invete povided Hall eno of the LEN company, have mot commonly 0.5% eno accuacy, which intoduce much le noie effect into the ytem, the envionment wa intentionally choen to be highly noiy to make able the deigned contolle to adapt to cuent glitche caued by the PWM modulation in the tato winding. The obut pefomance wa alo invetigated fo 5% andom paamete vaiance, which gave a elative eo of 4.3% in the etimation. Thi can be explained baed on the peiodicity of the eo, by an inceaed phae delay of the obeve. Baed on thee, it can be concluded that a vey accuate etimation of the flux wa yntheied, whoe implementation due to the 2 inne tate, with 2 input and 2 output of the obeve, can be ealized though elative few opeation. Becaue of the popetie of the mathematical model, the output matix of the obeve i identical in each of it polytopical dimenion, theefoe the whole computational load i no moe than 44 multiplication and addition The EKF Baed on the peviouly hown EKF theoy, the etimation method wa deigned fo the 6 tate nonlinea ytem contucted fom equation (2.19), (2.23), and (2.31) in cae of ω k = 0 oientation. Becaue of the tong dynamical popetie of the ytem model, in evey pediction phae the numeical olution of the equation ytem i calculated tough the Adam-Bafoth 3-tep ecuive appoximation (fo moe detail ee [39]), while in the coection phae, it wa found enough to ue only the Eule method fo the dicetiation of the IM model, which povide the Jacobi matix fo thi tak. By conideing the chaacteitic 104

119 6. Implementation of the contolle of the model and afte ome ty and eo, the Q and R matice wee choen to be the following: h Qij = 0, except Q33 = Q 44 = ; i, j { 0,1,,6} (6.8) L σ ij { } R = 0, except R = R = , R = R = 13.85; i, j 0,1,,4 (6.9) The h/lσ tem in (6.8), wa povided to eliminate the effect of the invete noie on the fit dynamical ubytem. The meaued cuent ignal and the obeve povided fluxe wee choen to be the efeence tate vaiable of the EKF, while the output of the etimato wa contucted in the manne to povide the unknown value of ω, i (t) R, and the filteed value of i α (t) and β. The effectivene of the deigned EKF wa examined fo the pecific model and the eult of thee imulation in Matlab howed that the elative geatne of the eo wee 0.41% fo ω and 0.08% in cae of attenuation of 98% on the meaued i (t) α and R with an aveage noie i β (t) while the peviouly mentioned load and excitation condition wee applied to the model. Futhemoe, the obutne of the algoithm wa alo teted in cae of 5% vaiance in ytem paamete whee the elative eo wa 0.8% fo ω and 0.33% fo R. Unfotunately, beide of thee eult, it wa expeienced that the peviouly hown geat noie attenuation popety lot omewhat fom it optimality in an affodable manne. It i alo impotant to mention, that the deigned method ha a lage computational load becaue of the huge matix opeation with even matix invee calculation, thu it i the weak point of deigned contol tuctue. Howeve, fom eveal appoache, thi technique povide the fatet way to ealize uch an accuate etimation method fo the tongly NL equation of the IM. Thi i poved by [16] alo. Fotunately, with the lage peed capability of the F243 the deigned EKF i expected to be calculated fat if it implementation i caefully accomplihed. 105

120 6. Implementation of the contolle Etimation of the load toque Nowaday, eveal publihed pape [9, 11, 31] which decibe the deign of H contolle fo the IM, ignoe the etimation of the load toque, eithe by concealing thi o auming it to be known in the ytem. Thi can be accepted in uch application whee the toque eally doe not change, only lightly fluctuate aound a contant load duing the opeation. Howeve, in cae of the moe datic change in the load, thee method ae tuned out to be wothle. Unfotunately, the meauement of the load toque i highly expenive and if a peed enole contol ha to be achieved, then only the tato cuent and voltage can be ued fo it etimation. Although, fom the (2.19) dynamic motion equation the value of T load can be calculated, it cannot be fogotten, that ω and the flux peented alo in thi equation wee etimated by the known value of the load toque. Thu, if they would be ued fo the etimation of T load, then uch a looped etimato would be poduced, which amplifie it own eo intead of convegence in the etimation. Baed on thi, the value of Ψ and ω ef ae ued in the calculation f d ef intead of the etimated quantitie, and afte ome tanfomation the following imple equation can be ued fo gueing the load: 2L T = Ψ i (t) Fω (6.10) f ( ) load d ef q ef 3pLm It i impotant to mention that thee efeence ignal cannot be ued diectly jut only in that cae when thei evolution i limited by dynamical filte in a imila way to the expected behavio of the ytem tate, o on the othe hand, the etimation method peented in Section and loe thei connection with eality, becaue of the tep like eo of the toque calculation. Becaue of thi eaon, the weighting filte wee choen imilaly like the peed limiting filte of the efeence in Section In thi way, etimation of the load toque could be achieved in the imulation with a elatively low teady tate eo Tuning paamete Becaue of the exiting eo in each level of the inteconnected tuctue, the looped contol ytem i not able to pefectly olve the whole contol poblem, 106

121 6. Implementation of the contolle only in that cae when the module ae tuned to each othe by the caeful calibation of the tuning paamete. The contolle wa initially deigned to have pefect tuning ability to achieve thi goal. By eveal conideation mentioned in [39] the tuning wa ealized in the following way. Fitly, by the amplification of the tacking eo of ω ef and Ψ f def befoe and afte the efeence tanfomation, and by applying gain fo the deviation fom i, f def i f qef, the enitivity of contol can be calibated to achieve accuate efeence tacking. Howeve, it i not woth inceaing thee gain limitlely, becaue in thi way the contolle can achieve a tate, when becaue of the maximum 250V of the SV-PWM modulation limited contol ignal, it begin aggeively pulling aound the tato voltage to input moe enegy into the ytem. Thi phenomenon poduce uch ocillation in the tanient, which cannot be allowed. So it i bette to ue extenal offet compenation to influence the geatne of the etimated flux and load toque and making the efeence tacking optimal in thi way. The exact value of thee compenation can be mot pefectly calculated in the cae of lage toque and flux ignal becaue thei effect i inignificant fo mall value of thee quantitie. The exact value of thee compenation will be given with the imulation in the next ection Simulation eult Befoe any kind of implementation begin, it i woth invetigating the ytem pefomance by numeical imulation. Theefoe, the peviouly mentioned contol tuctue and the continuou model of the IM baed on the equation given i Section 2.3 wa modeled in the Simulink envionment of Matlab. Becaue the implementation of the complicated contol ytem at hand i going to be completed digitally, each of the contolle block, except the model of the IM, wee dicetied with a h = 10 4 time tep, which aume that the cycle time of the contol pogam i no moe than 100 µec. Howeve, thi kind of aumption might eem to be tict, with caeful implementation it can be fulfilled with the ecently intoduced DSP. In the cae of the conideed F243 poceo, thi aumption ha to be elaxed to h = 10 3 of coue, which can be achieved with a 107

122 6. Implementation of the contolle highly optimized ealization in Aembly. The meaued ignal of the contol tuctue ae alo aumed to be digitalized with the ame ampling time, to enue the coect functioning of the dicetied etimation method. Thi etiction can alo be accomplihed with the given dive, becaue the 1µec A/C conveion time of the incoming ignal i elatively mall to the cycle time of whole contol loop. Theefoe thee ADC can be aumed to be happening at once fom the view of the algoithm. Becaue the oveall dynamic of the cloed loop dive ae much lowe than the tep ize of the dicetiation, the dicetied continuou contolle and obeve mut appoximate well the continuou opeation. Moeove, fo the EKF uch dicetiation i not needed, becaue it povide the etimation in dicete time. The above mentioned dicetiation i done online inide of the pogammed S- function Simulink model, o fom the polytopical fom of the method the intant paamete value defined ( ) ( ) x (t) = A p(t) x (t) + B p(t) u (t), (6.11) K K K K K ( ) y (t) = C p(t) x (t), (6.12) K K k LTI ytem can be given in a dicete fom decibed by the ( p ) ( ) K( p ) ( ) ( ) x (k) = e x (k) + A p(k) e I B p(k) u (k), A K (k) h 1 A (k) h K K K K K Φk ( p(k)) Γk ( p(k)) (6.13) ( ) y (k) = C p(k) x (k), (6.14) K K k equation, which, due to the h mall tep ize, can be appoximated with the ( p(k) ) 2 2 h AK Φ K( p(k) ) I+ h AK( p(k) ) +, (6.15) 2 ( ) ( ) 2 h AK p(k) BK p(k) Γ K( p(k) ) h BK( p(k) ) +, (6.16) 2 matice. In thi way, the continuou contolle and obeve appoximated in econd ode opeate with the continuou dynamic popetie in dicete time. If the econd ode tem ae left out, then the dicetiation can be implemented in a 108

123 6. Implementation of the contolle eal life hadwae with eae, becaue the opeation of the dicetiation can be mathematically done befoe the obtaining of the A K and B K matice fom the cone ytem of the polytopical et defined LPV contolle and obeve. In thi way, only the element of the A and B matice have to be multiplied by the tep ize, and 1 added to the diagonal of A in each of thei dimenion befoe hadwiing thee value into the pogam. In uch way, the dicetiation intoduce no additional opeation into the ytem. In the imulation by ome ty and eo, the tuning paamete, decibed in Section 6.1.8, of the ytem wee calibated in the peviouly mentioned noiy envionment, whee the offet of the flux wa affimed to be 0.992, while the enitivity gain of the flux tacking eo wa adjuted to be 45. The offet of the load toque wa calibated to and the eo enitivity of the peed tacking wa defined to have a gain of 150. The contolle tate wee limited in the inteval of ± 500 in epect to the lage efeence ignal duing the tatup. The enitivity fo the tato cuent tacking deviation wa choen to be 35 in both of the cae. The oveall ytem poduced in thi way wa invetigated in a noiele envionment, with uch intenive efeence ignal which not only invetigate the ytem behavio on the full 4/4 opeation ange of the IM, but alo tet the ytem on the bound of it opeation. In thi way the imulation wee completed with the additive noie decibed in Section and the eult ae given in Figue 6.5(a-p). Figue 6.5(a). Refeence (ed) tacking (blue) fo ω Figue 6.5(b). Refeence (ed) tacking (blue) fo Ψ f d 109

124 6. Implementation of the contolle Figue 6.5(c). Change of load Figue 6.5(d). Change of R Figue 6.5(e). Etimation eo of ω Figue 6.5(f). Filteing eo of R Figue 6.5(g). Change of Ψ Figue 6.5(h). Etimation eo of Ψ α α Figue 6.5(i). Change of Ψ Figue 6.5(j). Etimation eo of Ψ β β 110

125 6. Implementation of the contolle Figue 6.5(k). Change of f i Figue 6.5(l). Filteing eo of d i α Figue 6.5(m). Change of f i Figue 6.5(n). Filteing eo of q i β Figue 6.5(o). Change of u α Figue 6.5(p). Change of u β Duing the imulation the load toque i given with a light clutching to the ytem in the fit time moment (Figue 6.5(c)) The clutching i needed to pevent the moto to lip too much backwad at tatup, becaue in the othe cae the contolle would ty to ie the peed in thi intable dynamical inteval with geat voltage cuff, which would poduce ocillation of ω fo almot 0.4 ec. It can be een, that at 0.5 ec, the toque ie to 200 time of it oiginal value, which i quickly compenated by the contolle in 5mec and the moto eache the given peed efeence ignal again. The efeence tacking i vey apid, the 111

126 6. Implementation of the contolle limited peed efeence ignal ae intantly followed by the eal peed of the moto (ee Figue 6.5(a)). The changing of the diection of otation i alo tacked down quickly, in no moe than 35mec, and the negative load change i alo compenated with the ame effectivene. Hee the IM opeate a a dynamic bake, feeding enegy back to the powe ytem. Even if thi popety cannot be ued with the peented dive becaue of the tuctue of the invete, it i good to know, that the tability and good pefomance i povided fo thi opeation ange a well. At the 6. ec, the contolle hold the given load with 0 peed, which i ignificant in the view that the mot common algoithm ae not capable fo thi becaue of the lack of uch accuate etimation a it peented in Figue 6.5(e-n). Duing the full opeation, the tacking of the oto flux ha no ignificant effect on the peed tacking, although Ψ f d i cucial in the poduction of the electomagnetical toque. By conideing the flux tacking, it can be concluded that even fo exteme and apid change in the opeation the flux emain table (ee Figue 6.5(b)). Fo the tacking of both efeence ignal, the elative teady tate offet eo did not exceed 1.5% duing thi dynamic teting, thu in thi way, it can be aid, that the tacking capability of the contolle i extemely good. Moeove, by Figue 6.5(o) and 6.5(p) the contolle only give out moe than the maximal 500Vpp, when the ated toque of the moto i eached. Duing tatup, the cuent load of the powe ytem i alo not ignificant, which povide economical opeation of the dive. The obutne of the imulated dive wa alo teted with 5% paamete uncetainty. The eult of efeence tacking ae given in Figue 6.6(a) and 6.6(b) fo thi cae. The wot eo of the tacking of peed wa nealy 25%, which mean that the inteval of obut tability i deceaed in cae of uch heavy noie and dynamic change, but the contolle emained table even fo thi lage uncetainty. It mut be mentioned, that by taking ome pefomance tet on the ytem, thi offet eo can be alo eliminated with eae with the help of the tuning paamete. The intability only occu fo vey lage, 15%-20% paamete vaiance, which eult in the ocillation of the contol ignal. 112

127 6. Implementation of the contolle Figue 6.6(a). Refeence (ed) tacking (blue) fo ω Figue 6.6(b). Refeence (ed) tacking (blue) fo Ψ f d The calculation of the load toque, a it wa tated many time in the liteatue, i a geat theoetical challenge in thi poblem, thu even the open loop toque etimato ytem opeate well, the efeence tacking of the cloed loop contol with the ue of toque etimation doe not povide uch good eult a in the peviou imulation. In thi cae, the imulation give the eult peented in Figue 6.7(a) and 6.7(b) fo the peviouly ued apid efeence ignal and load change. The bad tacking ability of thi cae can be mainly explained by the low iing time of the load calculation, which in cae of apid change milead the etimato method, and the cloed loop ytem can only tack down the eal life dynamic anwe of the ytem with limited ucce. Figue 6.7(a). Refeence (ed) tacking (blue) fo ω Figue 6.7(b). Refeence (ed) tacking (blue) fo Ψ f d In cae of clutched, contant toque, the contol tuctue peent nealy the effectivene that could be een in the peviou cae (ee Figue 6.8(a) and 6.8(b)). Although thi etimation method fo the load toque doe not povide uch feedom which could be expected, it i capable of making the dive adaptable to 113

128 6. Implementation of the contolle the load change, if thee change ae caefully applied to the ytem, which can be achieved duing the implementation. Thu, thi contol tuctue give moe than the [9, 31] pape, becaue it make poible the efeence tacking without knowing the load toque. The peent eeache ae concentating on the development of uch an etimation method which i capable of the accuate and independent etimation of the toque with the help of the phae diffeence between the tato cuent and voltage. In thi way the peented contolle diven IM dive could be even applied fo vey dynamic tak, fo example a a mechanical powe ouce of a vehicle. Figue 6.8(a). Refeence (ed) tacking (blue) fo ω Figue 6.8(b). Refeence (ed) tacking (blue) fo Ψ f d 6.3. The identification of the moto To be able to apply the peviouly peented contol tuctue fo the eal time contol of the given IM of the conideed dive, fitly the identification of the moto paamete ha to be completed. Since the model of the IM i highly nonlinea and eveal of the paamete ae not meauable uch a L and R, the ue of paamete identification method i unavoidable. Unfotunately, even if vey accuate and ophiticated method exit fo paamete identification in the LTI cae, uch a the linea egeion, leat quae, maximum Likelihood, and Baye pediction baed method, fo NL ytem, the olution of a global optimization poblem i the only exiting way, if the lineaization cannot be affoded. Thi optimization can be olved by the gadient method that ecuively tie to efine the etimated paamete value till the eal ytem behavio i achieved in an adequate manne. 114

129 6. Implementation of the contolle Method of identification The paamete etimation of a NL dynamical ytem, defined a an optimization poblem, i mot commonly given in the fom of the peented algoithmic method below [13]: Let the following be given: N A Ξ i a equence of meaued value, o ample, which conit of the meaued input-output pai till the ampling time moment N, thu Ξ N {( y u ) } = (k), (k) k = 1,, N. A pedictive model in the fom of whee yˆ ( k ) k 1 ( ) = g( ) yˆ k θ k, Ξ, θ, (6.17) θ i the pedicted value of the k th time tep and the etimated paamete value given in θ while g(.) i a NL vecto function. A pediction eo equence, which i computed fom the peviou value. A lo function whit an applicable ( ) ε(k θ ) = y(k) yˆ k θ. (6.18) N N 1 V N ( θξ, ) = ε(k θ ), (6.19) N k = 1. vecto nom. q q It i impotant to note, that the election of the mot uitable nom i method dependent, but mot commonly the Euclidian nom i ued. 1 ε = ε (6.20) 2 dim( ) ε 2 i = 1 2 i If thee exit, than uch a paamete identification method can be eached fo, N that poduce uch a method ( ) value, to which (6.21) hold: ˆθ Ξ etimated paamete vecto fom the meaued 115

130 6. Implementation of the contolle method ( ) N N ( ) = N ( ) θ ˆ Ξ ag min V θ, Ξ, (6.21) o the lo function i minimal at the etimated paamete value. If the peviouly mentioned Euclidian nom i ued to define (6.19) than thi equation will became: θ and then N N 1 k 1 V N ( θξ, ) = y(k) g(k, Ξ, θ ), (6.22) N 2 k= 1 N ˆ N 1 k 1 θmethod ( Ξ ) = ag min y(k) g(k, Ξ, θ ). N 2 (6.23) θ k= 1 Even if (6.23) eem to be quadatic, the peented nonlinea g Ξ θ k 1 (k,, ) uually pevent the analytical olution. Howeve, the quadatic fom geneally guaantie the exitence of minimum point and tough of it the olution of the poblem at hand, but in mot cae moe than one minimum point exit. By the abence of analytical olution, a global optimization poce i needed. One of the exiting olution i the gadient method, which i named about the G (.) gadient vecto of the f(.) function. The gadient vecto of f(.) in x i defined a follow: T fx (,t) fx (,t) T Gx ( ) =,,, x= [ x 1, x m]. (6.24) x1 x x m x Fo vecto function, G (.) i alo efeed a the Jacobi matix. Moeove, while G (.) how the tangential, the (6.25) defined G (.) 2 the convex o concave popety of the f(.) function in x. 2 ij i j give the cuvatue, o 2 fx (,t) G ( x) =, i,j { 1,,m}, (6.25) x x which i alo called the Hee matix. If f(.) ha a minimum in x than the following i tue: Gx ( ) = 0, and det G( x) > 0 poitive definit ( 2 ) ( ) (6.26) 116

131 6. Implementation of the contolle By the ue of thee popetie, a minimum point of the eo function can be eached with ε affodable eo, by a ecuive poce tated fom a given x 0 initial tate. Thi poce, called the gadient method, i the following: 1. Initially i= 0, whee i i the numbe of completed ecuive tep. Let x i= 0= 0 x which i the initial appoximation of the paamete value baed on a pioi infomation. 2. G (.) gadient vecto of the lo function in the x i point i computed fom the meaued value. 3. If the gadient vecto i mall enough, uch a aumed that the minimum i eached and the poce end. Gx ( ) <ε, than it i 4. In the othe cae, baed on the ign of the gadient, the etimated paamete ae efined by δ caling tep ize (6.27) and with i= i+ 1 the algoithm continue fom Step 2. x = x G + ( x ) δ (6.27) i 1 i i In thi way, the paamete identification of NL ytem can be completed. By examining thi mathematical appoach, it quickly tun out that the effectivene of the method tongly depend on the x 0 initial value of the paamete. Becaue if thee choen value ae fa away fom the eal one, the method can quickly bump into othe, even vey mall pothole given minimum point on the function cuve and fail the identification of the eal paamete. Moeove, evey iteation tep ha a polynomial time need, theefoe the initially lage tep ize i deceaed a the method appoache towad the minimum point to povide mall computational time with fine eult. Thi tep ize vaiation can be eaily olved by chooing it magnitude compaed to the nom of the gadient. The peviouly mentioned method wa implemented in Matlab by the help of the identification toolbox, to olve the paamete identification poblem of the peented IM. Fo thi pupoe, a cipt code wa witten which implement the gadient method with vaiable tep ize. The method ue the pecalculated fit 2 117

132 6. Implementation of the contolle ode deivative of the tato fixed educed IM model and it alo vaie the tep ize fo the paamete in a diffeent manne. The model of the IM decibed in Section 2.3 wa educed, becaue ome paamete like the tato eitance and inductance could be computed fom the eult of meauement, theefoe thei identification i not needed. To obtain thee paamete locked oto and no load tet wee completed. In thi way, the following equation ytem could be given fo the paamete identification method: Ψ (t) α Ψ (t) α k d Ψβ(t) Ψ (t) u d (t) β = A ( θ,r,l, ω) +B ( θ,l) k (6.28) dt i α(t) i α(t) u q (t) i β(t) i β(t) whee θ1 θ θ 1 3 ω 0 θ2 θ 2 θ1 θ θ 1 3 ω 0 θ2 θ 2 L A( θ,r,l, ω ) = θ2 θ 2 1+ R θ θ 1 3 θ θ 3 2 ω L θ2 θ2 θ3 L θ2 θ3 L θ2 θ 3 L θ2 θ 2 1+ R θ3 θ1 θ θ 3 2 ω L θ2 θ3 L θ2 θ2 θ3 L θ2 θ θ 2 B( θ,l ) = 0 2, and L θ2 θ3 θ L θ2 θ3 θ1 R 2 L θ θ 3 = L M. θ J 4 θ 5 F Meauement To ue the peviouly decibed identification algoithm eveal meauement wee done on the moto. Fitly, the tato eitance wa meaued, which tuned out to be 96.2 Ω,. Then by a no load tet, the tato inductance wa computed to 118

133 6. Implementation of the contolle be 352,4 mh fom the phae diffeence of the voltage and the cuent and fom the given ated paamete of the moto. Afte thi, by the help of a HP 5461B ocillocope, eveal meauement wee taken on the tato phae and line voltage and on the tato cuent, when diffeent feeding condition wee applied. In thee tet, the peed of the oto wa alo meaued with the peented encode on the haft by the help of the QEP hadwae of the DPS. The diffeent condition of the voltage feed wee choen to map the oveall fequency anwe function of the applied moto. Fo thi pupoe, a imple pogam wa witten on the TMS320F243 micocontolle, to ealize the PWM tato voltage of the moto on diffeent fequencie and amplitude, while it alo meaue the oto peed fom the encode given ignal. Some eult of thee meauement eult ae given in the following figue, with the meaued analog ignal of the encode fo completene. Figue 6.9(a). Meaued i a and i b Figue 6.9(b) Meaued u ab in cae of f 0 = 16,9Hz and V p = 100V in cae of f 0 = 16,9Hz and V p = 100V Figue 6.9(c). Meaued in cae of f 0 = 16,9Hz and V p = 100V u a Figue 6.9(d) Meauedω in cae of f 0 = 16,9Hz and V p = 100V 119

134 6. Implementation of the contolle Figue 6.9 (e). Meaued i a and i b Figue 6.9(f) Meaued u ab in cae of f 0 = 25Hz and V p = 150V in cae of f 0 = 25Hz and V p = 150V Figue 6.9(c). Meaued in cae of f 0 = 25Hz and V p = 150V u a Figue 6.9(d) Meauedω in cae of f 0 = 25Hz and V p = 150V Thee eult wee alo filteed befoe the identification begun to eliminate the noie effect which had ien becaue of the high voltage polluted envionment. Fo the identification, the integated ignal of the meaued PWM feed wa ued becaue the peviouly intoduced mathematical modeling of the IM conide no effect of the lot and hamonic loe theefoe thee i no need to conide the effect of thee tep like change Reult of the identification The identification algoithm wa applied fo each meaued ignal quatet (thee-phae cuent and the peed) of 6 diffeent excitation fequencie and amplitude. The computation time wa lage appoximately 6 hou on a 950Mhz PC, and it eulted in the following paamete et which had 0,072 aveage eo by the lo function computation. L L L m = 172,1 mh = 352,4 mh = 245,3 mh R = 96,2 Ω R = 30,1 Ω 0 = K p 2 J = 0.52 Nm F= 0.04 K = 3.5 c= J kgk m= 1,2 kg T =

135 6. Implementation of the contolle whee K k wa given baed on the cientific liteatue without identification, becaue the poce which involve the obtaining of thi value need vey fine tanient meauement of the cuent and voltage and fo uch meauement extemely ophiticated device mut be applied Validation of the model The validation of the model wa made in teady tate by the help of the Matlab ealized moto model with the obtained paamete. The invetigation wa pefomed to the cae when f 0 = 16,9Hz with Vp = 150V wa applied to the IM. By thi validation poce, the following eult in Figue 6.10(a-b) could be concluded fo the cuent, with an aveage elative eo of 9.09%, and a teady tate elative eo of 4,1% fo peed. If it i conideed, that the meaued ignal alway contain noie, than thee eult can be evaluated to be vey atifying. Figue 6.10(a). The eal (blue) and imulated cuent epone of the conideed moto Figue 6.10(b). Relative eo in cuent epone In thi way, it could be poved that the identified moto model decibe well it eal countepat. Thu, the deigned contolle, which howed it effectivene in imulation will contol the moto well by the ue of thi infomation, if a fat ealization of it algoithm can be given The pogam of the DSP The peviouly mentioned contolle tuctue wa applied to the identified moto paamete and the edeigned tuctue gave imila eult that wee een in Section 6.2. To ealize thi theoetical method eveal conideation wee aleady given, with the bief deciption of the taget dive. The lat tep that emained i to actually pogam the DSP of the dive to obtain un eult. 121

136 6. Implementation of the contolle Theefoe, the algoithm wa ealized in C and in the following ection the tep of thi ealization poce i peented Flow chat of the pogam The logical tuctue of the poduced pogam given in Figue Figue The flow chat of the implemented DSP pogam Thi logical tuctue i totally identical with the tuctue of the aleady peented theoetical contolle, except that it include ome initialization pocedue, which ae needed to enue the coect calibation of the hadwae to the tak at hand. The logic block ae ealized though pocee to make futhe modification of the pogam eay and to ue moe ophiticated memoy utilization by tempoally vaiable. The pogam wa alo initially implemented in 122

137 6. Implementation of the contolle uch a way, that it guaantee the fatet unning by aving of calculation time and uing the pecial featue of ANSI C. The finally poduced contolle pogam i given with each of it ued ouce file on an encloed CD. To claify the peented code, the functioning of the pogam i explained in the following pat in the viewpoint of it logical tuctue baed on the peviouly given flowchat The hadwae boot up The fit pogam block (Boot.am) i eponible fo the coect initialization of the hadwae at evey tat-up. It i the modified veion of the TI uggeted boot-up outine, which included eveal othe pat unneceay fo the poblem at hand, and ome additional code wa alo placed in it to ealize the whole hadwae et up in Aembly. The pogam tat with a ection defined by label _c_int0, which i the enty point of the code. In the vecto table, given in Vecto.am, thi label i defined a the evice outine of the eet tiggeed inteupt, theefoe in any cae of eet event the pogam tat again fom thi point. Theefoe, the dive i capable of continuou functioning, with etat handling ability. A the pogam poceed, it initialize the poceo flag and diable all inteupt fo the duation of the initialization poce. Then it give the coect equence to the watch dog hadwae to pevent thi device geneated hadwae eet. Afte thi, the poceo peed, memoy and I/O wait tate ae calibated to thei maximal affodable value to obtain the fatet machine cycle time. Then, all memoy i defined to be local, the ytem i placed into micocontolle mode, and alo evey inteupt i maked and the pending inteupt equet ae cleaed. Then the et up of the memoy tack poceed with the copying of the pogam included contant into the data memoy. Thi lat tep i cucial becaue duing the compiling, all the contant included in the pogam ae placed into the object file which i diectly loaded into the pogam memoy. Theefoe, to be able to ue thee value, fitly they have to be copied into the data pace. Afte thi memoy movement, the pogam call the main pocedue of the Stat.c file which i the enty point of the C ouce code. 123

138 6. Implementation of the contolle Sytem initialization and hadwied contant The C-implemented code begin with the main pocedue which conit of the contol cycle, o it mut neve etun. If thi eve happen, the abot function i called which hang up the ytem. Fo imila eaon, if uch an inteupt i acknowledged which i maked, then the evice outine of thee inteupt ae outed to the bad_tap pocedue which i imila to the peviouly mentioned one. Thee method wee vey ueful duing the debugging of the code, becaue at any time when poblem had ien, the unning of pogam could be caught by thee pocee. The main outine itelf begin with ome additional initialization pocee. The fit i init_pe which initialize all the key egite to zeo and in thi way it diable all output activity of the EVM. Then the init_comp i called which et up the main contant in of the ytem. A it could have been een in the peviou ection, the contolle i woking with eveal contant, like the huge matice of the H contolle, the obeve, etc., and of coue thee ae othe contant paamete which ae needed to be obtained befoe the eal calculation begin, to inceae the pefomance. Theefoe, thee contant ae defined in the fit ection of the pogam to fulfill thi tak and to alo eae futhe modification of the code. Unfotunately, thoe contant which ae calculated with the help of peviouly defined one mut be declaed a vaiable, becaue in contat with MS C++, the Code Compoe doe not uppot defining baed on peviouly defined value. Becaue of thi, all thee contant ae ecalculated duing the initialization poce. Thi include the tep ize baed dicetiation a well, o the calculation do not conit of any unneceay opeation. Moeove, the heade file All.h, Evm.h, and ADC.h contain the definition of the egite allocated on pecific memoy addee. The initialization continue with init_adc, which include the initialization of the analog-to-digital convete. The device i calibated to multi conveional mode o the needed phae cuent and the bu voltage ae obtained in two tep. Then the initialization of the PWM geneato hadwae i given with init_pwm. The PWM module i calibated to 2µec deadband and 10Mhz SV-PWM mode 124

139 6. Implementation of the contolle with poitive vecto otation and with GT1 a the aociated time. With init_sci, the communication inteface i alo initialized. Finally, the pogam i eady fo continuou opeation a a contolle o the invete i enabled though the dive_enable outine povided output equence. The fit conveion ae alo tated on the analog input channel and the LED of the EVM boad ae igned to infom about the end of the initialization phae Contol loop The contol loop of the pogam un continuouly, and becaue all the initialization wa aleady completed by the peviou phae, it jut epeat the ame intuction in each of it cycle peiod. Since the analog ignal wee aleady conveted in the initialization phae, the loop begin with tato_oiented_ cuent_vec_fom_3p outine which convet the 3-phae cuent ignal to the coeponding complex vecto with the help of the (3.24) Clak tanfomation, then the KalmanFilteZZ i called which calculate the EKF. To enue coect loop like functioning the eult of the peviouly tated ADC i ead fo i a and i b and the conveion fo i c and U bu i tated. Afte thi Flux_ob i called that poceed with the etimation poce by calculation of the H obeve, which i diectly followed by the DQ and efeence tanfomation that ae exactly implemented in the ame way mentioned in Section Thi i followed by the calculation of the H contolle with the H_inf_contol pocedue and afte thi, the eult of the peviouly tated conveion i ead. The conveion on the meaued ignal of i a and i b ae alo tated again. Finally, the contolle poduced new u f voltage contol ignal i tanfomed back to the tato-fixed efeence fame and it i diectly ent to the et_voltage_pwm poce which ealize the SV-PWM geneation. Thi i followed by the tep with light on the LED ow, which poduce a unning light pot that infom about coect functioning Poce of ADC A it wa mentioned, the ADC i completed a paied conveion of the meaued ignal. The coeponding pocedue ead_adc(int mode), which at 125

140 6. Implementation of the contolle fit check that whethe the conveion wa completed uccefully o not, then it obtain the eult fom the FIFO of the ADC module. The pocedue can be called in two mode, if mode 0 i elected than the ead value ae going to be aigned to i a and i b and the conveion of the othe two ignal ae tated. In cae of mode 1, the value ae aigned toi c and U bu with conveion tated on the othe two cuent ignal. Since the eult ae on the uppe 10 bit of the egite, theefoe hifting them by 6 bit to ight i equied. Duing the ealization all the thee phae cuent ignal wee ued fo obtaining infomation about the ytem to enue bette functioning and edundancy of data, which i impotant to eliminate ome potion of the noie effect. Howeve, the contolle ytem i able to functioning with two meaued cuent a well. The obtaining of the bu voltage i alo impotant, becaue a it i going to be howed thi value i needed fo the coect SV-PWM geneation. Then, baed on the peviouly mentioned offet and gain conditioning of the invete inteface cad in Section the eult ae caled back to get thei eal meaning. Becaue of ome hadwae uncetaintie, even at zeo voltage ignal on the coeponding input pin, the obtained eult do not had a zeo mean value. Theefoe, ome offet conditioning wa implemented in thi poce baed on ty and eo to enue coect functioning. The eult ae alo filteed by an exponential filte with λ filte = 0.6, whoe Bode diagam i given in Figue Figue Bode-diagam of the oftwae implemented filte of the ADC 126

141 6. Implementation of the contolle Thi filte enue the attenuation of meauement noie and othe uncetainty effect of the conveion. The ADC ae alo ditibuted to the beginning and to the end of the contol loop, to guaantee them enough time to happen and to tatitically povide moe accuate meauement becaue of the edundant infomation toed in the thee phae cuent which ae obtained at diffeent time intant Pocee of etimation The EKF wa implemented with geat cae to minimize the numbe of the needed opeation. To achieve thi, if a calculated value i ued moe than once duing the computation then it i toed in a tempoaily vaiable to ave calculation time when it i next bought into play. Memoy accee of matice wee alo educed by uing pointe, which poduce indiect addeing in the intepeted ASM code. Incementing of thi pointe type index ave much moe time compaed to the calculation of the memoy adde baed on the matix indexe. With the peviouly given optimization, the pocedue of the EKF fitly calculate the numeical appoximation of the tate baed on the Adam-Bafoth method then it poceed with the calculation of the Jacobbi matix fo thee new tate. Fom thi, the pedicted covaiance matix P (k k 1) i calculated. Then fo the tatitical coection a K matix i computed which need matix inveion, which i calculated though the Gau-Jodan elimination [14]. Thi elimination poce i highly optimized fom the view of calculation and memoy acce time a well. Afte thi, the tatitical coection of the pedicted tate and the P (k k) i completed with the obtaining of the new etimated value. Thi etimation i diectly followed by the calculation of the H obeve, whee at fit the polytopic coodinate of the ω and R cheduling vaiable ae computed. With the help of thee coodinate, the new obeve matice ae obtained and then the new obeve tate ae computed a well. Becaue in the deigned obeve, the tate coepond to the etimated value o, no output calculation i needed, theefoe thee value ae diectly povided. The calculation of thi pocedue i alo optimized fo peed. 127

142 6. Implementation of the contolle Poce of contol The contolle calculation i done in a vey imila manne a the calculation of the obeve. The polytopic coodinate of ω, ω flux, and R ae obtained, fom which the calculation of the contolle matice ae done with optimized numbe of opeation and memoy acceing. Becaue of the mathematical tuctue of the contolle, the input matix i identical in each of it dimenion, only the output and tate matice mut be calculated fom the cone ytem, povided by thei polytopical deciption. Thi ave a lot of calculation time. The magnitude of the tate i alo checked and limited to 500 to enue that the contol doe not become too aggeive. Finally, the new tato voltage i obtained, which i eady fo ealization. the Poce of PWM geneation The peviouly calculated and then tato oiented eal and imaginay pat of f u i eceived by the et_voltage_pwm method, which tak i to coectly adjut the egite of the SV-PWM hadwae to poduce the coeponding tiggeing ignal of the IGBT of the invete. To achieve thi, the calculation of T 1 and T 2 i needed, which i done with the vecto baed method that wa mentioned in Section Thi method alo need the calculation of the coect ecto, which i obtained fom the u α (t) co α (t) =, in α (t) = v u (t) v ( u α(t) ) + ( u β(t) ) ( u α(t) ) + ( u β(t) ) β (6.29) value by the following logical poce een in Figue With the help of the ecto code and the T 1 and T 2 value, the SV-PWM module can be coectly pogammed to do it tak. Howeve it can happen that the amplitude of u i moe than the U bu / 2 maximal voltage magnitude of SV- PWM method. In thi cae the poce cale back the magnitude of the voltage vecto to U / 2, theefoe it alo enue the limiting of the input voltage. bu 128

143 6. Implementation of the contolle Figue Poce of ecto calculation fo SV-PWM Additional featue The poduced pogam i alo able to communicate with the PC tough the peviouly mentioned R232-C capability. Thi i olved though an inteupt handling outine, which accept the eceived packet and update the new contol efeence. In evey 100 calculation cycle, it povide infomation about the etimated peed and flux with the meaued cuent and the ued contol voltage. The pogam which doe thi tak in the PC ide of the dive, i elatively imple. It only include a pot handling outine with a imple ue inteface to eceive the new efeence fom text window and to epeent the contolle given value a well. Becaue of it implicity, thi pogam i not decibed in thi pape Speed conideation Afte completing the implementation and by obtaining maximally optimized code with the caeful chooe of optimization paamete of the Code Compoe, ome tet wee taken to meaue the unning capabilitie of the contol loop. Unfotunately, it tuned out, that the oveall cycle time i 57.9 mec with all the poible optimization. Moeove, 84.2% of the computation time i pent on the EKF, and 14% on the H contolle pocedue a it can be een in Figue Sadly, thi lage cycle time pevent any tet to be taken on the functioning of the dive, becaue uch geat dicetiation tep will uly diupt the etimation 129

144 6. Implementation of the contolle pocee and make the whole contol to fail. Although, each of the block wee teted epaately to be coect mathematically and in functionality a well, finally it wa concluded, the whole algoithm cannot be implemented in C fo thi dive. Clack tanfomation EKF ADC H_inf flux obeve DQ tanfomation Refeence tanfomation H_inf contolle Invez DQ SV-PWM geneation Figue Time need of the implemented tak in the DSP pogam It i well known that, mot of the micocontolle pogam ae witten in Aembly, becaue obtaining the highet peed i eential fo pefomance eaon. It i alo widely accepted, that the automatic optimization of uch code in C cannot ovethown the manually given optimized Aembly code, which aveagely need 50% le computational time. Thi can be explained by that only the deigne know exactly when the whole matix calculation can be completed though one Aembly intuction povided memoy copying fo example, o which vaiable ae needed to be left in the multiplication egite fo the next 10 calculation. It alo woth to pay attention to that, with the caling of the vaiable, which i a vey laboiou tak and only woth the effot in Aembly, the whole calculation can be done with intege and not with fixed point value decibed floating point vaiable. Thi appoach would uly give a boot fo the whole poce. In uch way, the C-implemented contolle i expected to each a 6-8 mec contol loop time, o even le, which would be in the acceptable ange compaed to the time contant of the moto. Thi implementation in Aembly i an ongoing poce, but unfotunately till need time to be completed, thu the eal life pefomance of the whole contolle can only be invetigated when thi happen. 130

145 6. Implementation of the contolle TI ha aleady ealized that the 20Mhz peed i not enough fo contolle with heavy computational load, theefoe it intoduced the 150Mhz peed poviding TMS320F243, which i compatible in main apect with the F243. Thi hadwae, could even leen the execution time, and give enough peed fo the C implemented code a well. Unfotunately, it ue i pevented by the enomou cot of the EVM which cannot be affoded by the Univeity. Thee i alo an inceaing tendency in the micocontolle maket to each the pefomance of PC becaue of the gowing need of contol algoithm. Thu, TI ha aleady intoduced a micocontolle with 1,2Ghz peed and 8 paallel floating point multiplication/machine cycle, which give the poibility to ue extemely difficult method fo contol. The uage of thi poceo i only pevented by the fact that i only old to the US Amy which ue it mainly in it new caft, like advanced obot-aiplane. 131

146 7. Concluion 7. Concluion In thi thei, the phyical implementation of uch a complicated contol tuctue wa aimed, which fulfill the high equiement of indutial eeache on the field of induction moto dive contol. Not only the ceation of a peed enole opeation capable ytem wa tied to be achieved, but it wa alo guaanteed duing the deign, that thi tuctue povide pefect functioning in noiy indutial envionment a well. To ealize uch a eult, even in the fit ection, complicated mathematical epeentation wee intoduced to completely model the phyical and dynamical popetie of the induction moto. In thi way, uch an LPV model of the ytem wa ynthetied, which not only give the deciption of the ideal opeation of the machine, but it alo pay attention to the paamete uncetaintie of the phyical ytem by modeling the oto eitance vaiation to heat. To uppot ou deign conideation, the main dynamical popetie of the moto wa alo invetigated. Howeve, the difficultie of the decibed moto model and the aimed equiement in contol have eached that point, when the common olution of Contol Sytem Theoy could not be applied eve moe. Becaue of thi, eveal unique and common method wee peented which ae capable to olve the poblem at hand with vaying ucce. Thi wa followed by the thoough deciption of the common concept fo the powe feed ealization of IM, with the mechanim of the nowaday widely ued PWM invete. The PWM ealization wa peented in detail with eveal theoetical and pactical conideation and with the outlining of the geat poibilitie of the SV-PWM appoach. Afte thi, a elf aembled Labdive ytem, which heat i the TMS320F243 EVM, wa invetigated in both tem of functionality and concept of contolle ealization. The oppotunitie offeed by thi device, which uppot the achievement of peed enole contol, wee mentioned with the caeful analyzation of each of it ub module. 132

147 7. Concluion Then, a deigned contol tuctue wa intoduced, which wa ynthetied by the help of theoie peented in the peviou ection. Thi ytem wa invetigated fom eveal apect in Matlab imulation. It tuned out, that the elf deigned contol and etimato tuctue ha exceptional abilitie in apect of accuacy, obutne, and tability in noiele and in noiy envionment a well. In contat with thi, the etimation of the load toque could not be achieved in the given way with uch dynamim, that would be expected in a widely ued indutial application. Although, it wa alo howed that with contant applied toque, thi contol tuctue can be pefectly ued fo the implementation of an indutial dive. It i alo impotant to note, that the accuate load toque etimation of IM i till in the focu of ongoing eeache in the cientific wold. In the lat ection, the implementation of the deigned algoithm wa explained by outlining the ued featue of the Labdive ytem. The implementation wa analyzed in detail and it wa completed in uch a way which povide the mot optimal ealization of the deigned contolle. The moto paamete fo thi ealization wee alo obtained by the help of the gadient method. Howeve, with the help of the paamete identification of the moto of thi dive and by the witing of the code in C, the exact ealization of the contolle wa achieved, the peed capabilitie of the ued DSP wa not enough to obtain meaued eult of the pefomance. In thi way, the goodne of the deigned contol ytem could be confimed completely with thi Labdive device only in that cae, when the whole code would be implemented in Aembly with the caling of the vaiable. Thi type of implementation i an ongoing wok and it hold geat poibilitie to ealize the whole ytem pefectly. Baed on thi, ou futue eeach plan concentate on the achievement of thi ealization on the thooughly analyzed Labdive ytem with the ynthetiation of uch a apid and accuate toque etimation method, that olve the dynamical poblem of the peently ued efeence model and giving in thi way uch a enole contol method, that can be ued in wide vaiety of indutial application. 133

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