AVR7: Sensor Feld Orented Control for Brushless DC motors wth ATUCB056 Fetures Stndlone Spce Vector Modulton lbrry for AVR UC mcrocontroller. Prk nd Clrke mthemtcl trnsformton lbrry for AVR UC mcrocontroller. Theory of Feld Orented Control. PC pplcton for rel tme motor remote control nd dsply of regulted vrbles. -bt Mcrocontrollers Applcton Note 1 Introducton Ths pplcton note delvers n mplementton of Sensor Feld Orented Control lgorthm for brushless DC motor on Atmel AVR UCB mcrocontrollers. Ths softwre ncludes stndlone lbrres for ll mthemtcl trnsformtons requred by the lgorthm. For more nformton bout the AVR rchtecture, plese refer to the pproprte documents vlble from http://www.tmel.com/vr. Requrements The softwre provded wth ths pplcton note requres severl components: A computer runnng Mcrosoft Wndows 000/XP/Vst or Lnux AVRStudo nd the GNU toolchn (GCC) or IAR Embedded Workbench for AVR compler. A JTAGICE mkii or AVROne! debugger Rev. 16A-AVR-06/09
Theory of Operton.1 Overvew. Block Dgrm As contnuty n the energy effcency process, the ncrese of cpblty of mcrocontrollers llows to mplement complex lgorthm s Feld Orented Control methodology whch llows to: Reduce power consumpton (less power loss) of electrcl motor drvng. Provde smoother nd more ccurte motor control thn snusodl commnd wth hll feedbck. Optmze motor choce (torque): fnd the best lterntve between dmenson nd power. But ths lgorthm requres more complex computton nd requres more CPU bndwdth thn stndrd lgorthms. Moreover, ths commnd strtegy fts wth some brushless DC motors wth dynmcl lod chnges due to reducton of response tme. It llows regultng torque nd speed t the sme tme. The followng block dgrm descrbes the prncple of the lgorthm. Indeed, t s bsed on: A vectorl commnd for -phses Brushless DC Motors. A perodc current smplng of the shunts locted on these -phses. encpsulted regulton loops: one for the current (torque nd power loss) nd nother for the speed. Fgure -1. Block Dgrm -phses current (I,Ib,Ic) Feld Orented Control Block Current Regulton loop Vectorl Commnd Speed Trget Speed Regulton loop Speed nd Poston AVR7 16A-AVR-06/09
AVR7. System Overvew As shown Fgure -, the -phses current re mesured nd one Hll Effect feedbck s used to compute feld orented control lgorthm. Fgure -. System Overvew PWM -phses Inverter PWM_XH PWM_XL PWM_YH PWM_YL -phses BLDC PWM_ZH ATUCB056 (56K flsh, K RAM) Sensor FeldOrented Ccontrol Process PWM_ZL IA IB IC Current Speed Hll Effect A USB Tsk USB-CDC PC 16A-AVR-06/09
The USB connecton s used through PC pplcton for rel tme motor remote control nd dsply of regulted vrbles. Ths dt montor dsplys feedbck control remotely. Ths GUI provdes: - grphs nd 1 cursor dsply. - 4 nputs control. The purpose s to be ble to connect to the pplcton wthout dsturbng the behvor of the pplcton. The pplcton offers the followng fetures: - Implements vector control of Brushless DC motor. - Speed rnge from 400 rpm to 000 rpm. 1 - Wth 100 µsec control loop, the CPU s used t 5% by the Sensor Feld Orented Control Process t 4MHz. - Dsply n rel tme the current nd speed mesured. - Control of speed n rel tme. 4 AVR7 1 See secton 5.9 for the explnton of ths lmtton. 16A-AVR-06/09
AVR7 16A-AVR-06/09 4 Motor Control Theory 4.1 Generl Model. The mthemtcl model n constnt domn lnked to the sttor s lnked to dfferentl equton wth constnt coeffcents defnng the motor behvor. Applyng the Lenz-Frdy model, we hve: [ ] [ ] [ ] bc bc bc dt d I R V + Wth: [ ] c b bc v v v V, [ ] c bc I b nd [ ] c b bc R s the sttorc resstnce, [ ] t c b v v v re the sttorc voltges, [ ] t c b re the sttorc current nd [ ] t c b re the globl felds n the sttorc solenod. [ ] [ ][ ] [ ] sf bc Ibc L + We cn wrte : Ls (constnt) s the nductnce n sttorc gyres. M (constnt) s the mutul nductnce between the sttorc gyres θ s the electrcl poston of the rotor (θ θ élec ) Ф sf s the mx vlue (constnt) of the flux crete by the permnents mgnet through the sttorc gyres. + + + ) cos( ) cos( ) cos( π θ π θ θ sf sf sf c b c b c b dt d Ls M M M Ls M M M Ls dt d R v v v In order to smplfy the mthemtcl resoluton of ths system, some mthemtcl trnsformtons re used. Usng the Prk P1(θ), the nstntneous power s kept nd t llows to hve mthemtcl expresson of the torque stll cceptble for the rel motor. [ ] + + ) cos( ) cos( ) cos( π θ π θ θ sf sf sf c b bc Ls M M M Ls M M M Ls
Usng the Prk nverse trnsformton, t s possble to return to the vlues spce from regulted vlues nd generte commnds. 4.1.1 Prk Trnsformton (P1(θ)) nd Clrke Trnsformton (nv P-1(θ)). The Prk trnsformton s defned from the mtrx P1(θ), t defnes the lnk between the rel vectors [ V bc], [ I bc] et[ bc], the new vectors [ V 0 dq],[ I 0 dq] et[ 0dq]. 1 cos( θ ) 1 π P 1( θ ) cos( θ ) 1 π cos( θ ) Fgure 4-1. Prk Trnsformton sn( θ ) π sn( θ ) π sn( θ ) V q v b V d v [P1(θ)] -1 θ v [x bc ]P1(θ)[X 0dq ] V 0 v c Wth V 0 0V, I 0 0A nd 0 0Wb, the normlzed Prk trnsformton s the ddton the Concord Trnsformton T nd the rottng mtrx p(θ) : + 0 1 cosθ snθ T + p ( θ) snθ cosθ Fgure 4-. D to D Trnsformton x x b x c T t x α x β P(-θ) X d X q 6 AVR7 The Prk nd Clrke trnsformtons re mplemented s softwre lbrry component n the softwre pckge ssocted wth ths pplcton note. See lso secton 5. 16A-AVR-06/09
AVR7 4. Power Brdge Commnd. The power brdge stge s here to power the BLDC motor wth lterntves voltges from contnuous source. Ths brdge llows modultng frequency nd mpltude. Fgure 4-. Power Brdge Stge I T T b T c E b b b n c c c T T b T c m C C C b C b C c C c Fgure II-1 Onduleur de tenson trphsé. Power Brdge Stge The logcl sgnls C, C, Cb, C b, Cc nd C c re commnd sgnls for the power brdge. The output voltges re gven from the ground m of source genertor nd from the vrtul neutrl pont n of BLDC motor. V V V m bm cm C E Cb Cc (II-1) V V V m bm cm V V V n bn cn + V + V + V nm nm nm For n equlbrted lod: n + Vbn + Vcn 0 In tht wy, we hve: V V, so : V nm ( Vm + Vbm + Vcm) 1. V V V n bn cn 1 1 1 1 1 1 V 1 V V m bm cm E 1 1 1 1 1 C 1 Cb Cc 16A-AVR-06/09
Or : 1 1 V n t 1 t T. 1 1 Vα t T. nd T Vbn 1 1 Vβ Vcn C Vα t t We conclude so: T. E b C, ( T s the trnslton of T ) Vβ Cc The followng tble gves the voltge vlues n the spces (α, β ) nd (, b, c). Tble 4-. Voltge Vlues n the spces (α, β ) nd (, b, c) Vector C C b C c V α V β V n V bn V cn V 0 0 0 0 0 0 0 0 0 V 1 1 0 0 1 0-1 -1 V 1 1 0 1 1 1 - V V 4 0 1 0 0 1 1 E 1-1 0 E -1-1 - 1 1 V 5 0 0 1 1-1 -1 V 6 1 0 1 1 1-1 V 7 1 1 1 0 0 0 0 0 We show tht ll vectors components (V α, V β ) re wth modules locted n the regulr hexgon. E nd re Fgure 4-4. Spce Vector vlues n the regulr hexgon. (0, 1, 1) (0, 1, 0) V 4 V V β V 1 4 5 6 V 5 (0, 0, (1, 1, V 6 (1, 1, 0) V 1 (0, 0, 1) (1, 0, 1) (1, 0, 0) V α 8 AVR7 16A-AVR-06/09
4..1 Spce Vector PWM. The vectorl modulton uses drectly the sgnl for the Concord trnsformton. It AVR7 supposes tht regulton loop s ever mplemented for the generton of V α nd V β components. As stted below, t nstntneous pont, the power brdge s ble to generte only 8 voltges (V, 0,,7) n the spce of trnsformton Concord (V α, V β ) wth two components equl to 0 nd 6 wth the module equl to E nd the ngle to ( π ) ( 1). Two successve vectors, clled V nd V +1 defned sector (Fgure 4-4) wth I from the ntervl [I, VI]. V V V α β E π cos ( 1) E π sn ( 1) π 1 p ( 1) 0 The power stge s only ble to delver voltges nstntneous voltges on smplng perod T, we cn wrte: ( Vαβ ) δ V+ δ + 1 V + 1 Where δ nd δ + 1 re the durton for reltve vlues re the reltves voltges when V nd V +1 ; δ V nd δ + 1 V + 1 re the projecton of vector (V αβ ). The Spce Vector Modulton s mplemented s softwre lbrry component n the softwre pckge ssocted wth ths pplcton note. See lso secton 5. 16A-AVR-06/09
Fgure 4-5. Sector Determnton Algorthm. V α nd V β Yes No V β 0 1 or or 4 or 5 or 6 Yes V α 0 No Yes V α 0 No 1 or or 5 or 6 4 or 5 Yes No Yes No Yes No Yes V β - V α 0 V β + V α 0 n V β + V α 0 V β - V α 0 No Yes 1 5 6 5 4 In ll cses, t s needed to determned sector number where s locted the vector V. To reduce tme executon computng δ et δ + 1, we hve used ths lgorthm. In tht wy, δ et δ + 1 re clculted drectly from V α nd V β : And so V V α β V δ V α β + δ V α + 1 V β + 1 V V α β E π 1 δ p ( 1) + 0 Π p( δ + 1 1 ) 0 10 AVR7 16A-AVR-06/09
AVR7 Tble 4-. Sector expressons Sector 1 T 1 τ 1 + τ + τ 0 T τ + τ 0 T τ 0 T 1 τ + τ 0 T τ + τ + τ 0 T τ 0 4 T 1 τ 0 T τ + τ 4 + τ 0 T τ 4 + τ 0 T 1 τ 0 T τ 4 + τ 0 T τ 5 + τ 4 + τ 0 5 T 1 τ 0 + τ 6 T τ 0 T τ 0 + τ 5 + τ 6 6 T 1 τ 0 + τ 1 + τ 6 T τ 0 T τ 0 + τ 6 16A-AVR-06/09
4. Current Mesurement Stge Three dentcl shunts re used to red the current I,Ib nd Ic. These vlues should be mplfed to be n the rnge of the ADC. Indeed, f we mesure current of severl mllmps (500mA), the mxmum voltge s round 0.05V. Fgure 4-6. Amplfer stge R Shun R R VA - + R ADC V V1 V1 V R V Offset For exmple: R Vs Offset + ( V V1) R1 When mesurng the three currents I,Ib nd Ic, only two mesures re requred, ndeed I + Ib + Ic 0. Fgure 4-7. ADC nd PWM synchronzton T T PWM T1 ADC t m t m t m t The ADC mesures re done every perod of the PWM. The frst ADC mesure should be done n the tme rnge nmed tm. Ths tme s the mnmum tme where none of the -phses re drven. For exmple: In cse of sector 1, T1 s the longest tme so t mens tht T1 > T-tm, n tht cse t s not possble to mesure I. So Ib nd Ic re mesured nd I s derved from the two others mesures wth the equton I Ib Ic. 1 AVR7 16A-AVR-06/09
AVR7 4.4 Current regulton nd speed Regulton 4 In order to reduce tme consumng effect of regultor, we hve used the Integrtor Proportonl (IP) regultor. 4.4.1 Current Regulton In contnuous domn, the closed loop hs the mthemtcl expresson: K Id Idref Lc s + ( R + Kd ) s + K It s possble to esly dentfy the second order of the trnsfer functon: Wth s + ε ωn s + ωn n nd Kd K Lcω εω Lc R n These correctors hve been chosen to hve deprecton rte ε nd response tme of 5 (T r W n ). Fgure 4-8. Response tme vs Deprecton rte. Response Tme Deprecton rte For tht ω n R L c wth K 4R Lc nd Kd 7. R 4.4. Speed Regulton The externl closed loop for speed regulton hs the followng mthemtcl expresson: Ω Ω ref J s K + Kdv s + K Kv Wth ωn et ε ωn J v s K J dv + ε ωn s + ωn 4 The PI regultor s mplemented s softwre lbrry component n the softwre pckge ssocted wth ths pplcton note. See lso secton 5. 16A-AVR-06/09
4.5 Executon Tme nd Regulton Loop We choose ω n 0.1R/L c nd ε, So K R.01 L v 0 J et Kdv 0. 4 c R J Lc The followng tble gves the number of opertons for ech functon Tble 4-. Opertons costs Functon Add Mul Dv Shft Concord 7 0 0 17 bc-to- αβ Clrk 4 0 6 αβ-to-dq Clrk Inv 4 0 6 dq-to- αβ Regulton 7 4 0 14 Decouplng 5 5 0 6 SVPWM 7 0 0 54 14 AVR7 5 The decouplng stge s the stge to seprte torque nd power loss regultons fter the current mesurement stge. The de s to be sure to only regulte torque (wthout dsturbng the power loss loop). 16A-AVR-06/09
AVR7 4.6 Generl Algorthm As shown n Fgure 4-9, the regulton_loop_tsk() process s sequenced on tck reference (every 100µs). Ths tsk synchronzes current mesurement nd computes ll mthemtcl trnsformtons to execute the Feld Orented Control lgorthm. Insde ths tsk, there re two regulton loops nterlnked: - Current regulton loop. - Speed regulton loop. Fgure 4-9. Regulton Loop Tsk Step Mchne regulton_loop_tsk() MC_current_mesurement() Current mesurement of the -phses Hll Interrupt Yes No Wt hll_estmtor_updte() Updte Tet nd Speed vlues Compute new Tet nd Speed Clrke() Relze the Clrke Trnsformton prk() Relze the Prk Trnsformton Speed Regulton? Yes Proceed Speed Regulton No prk_nv() Execute Speed Regulton ² Relze the Inverse Prk Trnsformton Current Regulton Execute Current Regulton svpwm() Compute new vectorl commnd Messge Redy? Prepre New Messge for the HMI CDC Tsk Sleep() 16A-AVR-06/09
5 Source Code Archtecture 5.1 Softwre Archtecture Fgure 4-10. Softwre Archtecture Feld Orented Control pplcton mn.c CDC communcton tsk HMI usb_tsk() devce_cdc_tsk() devce_cdc_tsk.c Motor Control regulton_loop_tsk() Motor Drver mc_control.c mc_drver.c Motor Control Lbrry PI Regultor SERVICES/MOTOR//PI Spce Vector Modulton SERVICES/MOTOR/SVPWM PARK SERVICES/MOTOR/PARK CLARKE SERVICES/MOTOR/CLARKE HALL ESTIMATOR SERVICES/MOTOR/HALL DRIVERS usb.c dc.c pwm.c flshc.c pm.c gpo.c Ths pplcton does not requre ny opertng system to run. The mn() functon s n chrge of cllng the softwre «tsks» (usng scheduler) relzng FOC lgorthm computton nd USB communcton wth the Communcton Devce Clss (CDC) for HMI mngement. There re tsks: regulton_loop_tsk()the regulton tsk tht computes ll clculton for dedcted FOC lgorthm. usb_tsk() / devce_cdc_tsk()the USB Tsk: Ths tsk s n chrge of the CDC communcton mngement. The mn loop of the pplcton s smple free-runnng tsk scheduler: whle(true) { #fdef USB_DEBUG usb_tsk(); devce_cdc_tsk(); #endf mc_regulton_tsk(); } 16 AVR7 16A-AVR-06/09
AVR7 5. Pckge The EVK1101-SENSOR-FIELD-ORIENTED-CONTROL-X.Y.Z.zp contns projects for ATUCB056 RevF or lter: EVK1101-SENSOR-FIELD-ORIENTED-CONTROL-X.Y.Z Defult hrdwre confgurton of the project s to run on the EVK1101 bord, lthough ny bord cn be used (refer to secton 5.5.5) 5. Documentton For full source code documentton, plese refer to the uto-generted Doxygen source code documentton found n: AVR7/APPLICATIONS/EVK110x-MOTOR-CONTROL/BLDC- FOC/EXAMPLE/redme.html 5.4 Projects/ Compler The IAR project s locted here: src/ APPLICATIONS/EVK110x-MOTOR-CONTROL/BLDC-FOC/EXAMPLE/IAR/ The GCC mkefle s locted here: src/ APPLICATIONS/EVK110x-MOTOR-CONTROL/BLDC-FOC/EXAMPLE/GCC/ The AvrStudo project s locted n the root-dr of the pckge: -./ 5.5 Implementtons Detls 5.5.1 Mn() The mn() functon of the progrm s locted n the fle: src/applications/evk110x-motor-control/bldc-foc/example/mn.c Ths functon wll: Intlze PWM outputs for Spce Vector Generton. Intlze ADC nputs for -phses current mesurement. Intlze USB connecton for CDC HMI connecton. 5.5. Motor Control Lbrry The motor control lbrry s locted here: src/services/motor_control/ Ths folder delvers: The Prk nd Clrke trnsformtons explned n secton 4.1.1 re delvered n the folder src/services/motor_control/park_clarke/ The Spce Vector Modulton explned n secton 4..1 s delvered n the folder src/services/motor_control/svpwm/ 16A-AVR-06/09
5.5. HMI CDC Tsk The HMI CDC Tsk s locted here: src/applications/evk110x-motor-control/bldc- FOC/EXAMPLE/devce_cdc_tsk.c Ths tsk receves nd sends messges through the USB communcton. Wth: The messge defnton locted n src/applications/evk110x-motor- CONTROL/BLDC-FOC/EXAMPLE/ENUM/frme.h 5.5.4 ATUCB Drvers The exmple frmwre uses the AVR UC drver lbrry vlble n src/utils/libs/drivers/atucb/ 5.5.5 Bord Fle Defnton 5.5.5.1 Bord customzton The pplcton s desgned to run on the EVK1101. All projects re confgured wth the followng defne: BOARDEVK1101. The EVK1101 defnton cn be found n the src/boards/evk1101 drectory. For IAR project, open the project optons (Project -> Optons), choose the «C/C++ Compler», then «Preprocessor». Modfy the BOARDEVK1101 defnton by BOARDUSER_BOARD. For GCC, just modfy n the confg.mk fle (src/applications/evk110x-motor-control/bldc-foc/example/gcc) the DEFS defnton wth D BOARDUSER_BOARD. For AvrStudo, open the project propertes (Project -> Propertes), go n the «C/C++ buld», then «Settngs», «tool settngs» nd «Symbols». Modfy the BOARDEVK1101 defnton by BOARDUSER_BOARD. 5.6 Project Confgurton The project confgurton fles cn be found n the src/applications/evk110x- MOTOR-CONTROL/BLDC-FOC/EXAMPLE/CONF/ drectory. Confgurton fles re not lnked to IAR, GCC or AvrStudo projects. The user cn lter ny of them, then rebuld the entre project n order to reflect the new confgurton. /CONF: confgurton heder fles of demo modules: CPU settngs, Perpherl Clock settngs nd Motor settngs 5.7 GUI Applcton The GUI pplcton nstller s locted here: src/applications/evk110x-motor-control/bldc-foc/labview/foc_gu.ms The USB drver s locted here: 18 AVR7 src/applications/evk110x-motor-control/bldc-foc/labview/usb_cdc.nf 16A-AVR-06/09
5.8 CPU Cost nd Memory Usge for Sensor Feld Orented Control lgorthm. AVR7 All results re gven usng IAR Workbench 5. compler revson.10a wth speed optmzton level nd Hmtrx optmzton. Crter CPU Occupton Code Sze Dt Const Result 5% wth tck vlue of 100 us t 4MHz. 17Kb 1Kb.5Kb 5.9 Lmtton of the Sensor Feld Orented Control lgorthm. All the pplcton hs been mplemented wth fxed pont lbrry wrtten n -bt formt (Q1.1) 6. The usge of ths lbrry llows ccelerted computtons but t genertes some lmttons n the vrton rnge of ech vrble. For exmple, when computng current regulton, every ADC smples re scled by vrble nmed E. Ths vrble mtches rto of the bus voltge. In the current mplementton, ths vrble hs been fxed to hlf of the nomnl voltge of the motor. In tht cse, the nomnl speed s equl to 000 rpm. 6 See the pplcton note: http://www.tmel.com/dyn/resources/prod_documents/doc076.pdf for more detls. 16A-AVR-06/09
5.10 Complng the pplcton 5.10.1 If you re usng AVRStudo The followng steps show you how to buld the embedded frmwre ccordng to your envronment. Lunch vrstudo Crete new AVR C project («Fle» -> «new» -> «AVR C Project»). Fll-n the dlogue box wth project nme, set trget MCU to UCB056 nd press fnsh. Choose Import rchve fle («Fle» -> «mport» ), press the next button. Select the EVK1101-SENSOR-FIELD-ORIENTED-CONTROL-X.Y.Z.zp rchve fle wth the browse button. Select «nto folder», check «Overwrte exstng resources wthout wrnng» nd press the fnsh button. The project s now vlble n the gven project nme. Press the buld button 5.10. If you re usng GCC wth the AVR GNU Toolchn Lod the Code: Plese refer to the pplcton note AVR7: AVR Studo gettng strted Open shell, go to the src/applications/evk110x-motor-control/bldc- FOC/EXAMPLE/GCC/ drectory nd type: mke rebuld progrm run 5.10. If you re usng IAR Embedded Workbench for Atmel AVR Open IAR nd lod the ssocted IAR project of ths pplcton (locted n the drectorysrc/applications/evk110x-motor-control/bldc- FOC/EXAMPLE/IAR) Press the Debug button t the top rght of the IAR nterfce. The project should comple. Then the generted bnry fle s downloded to the mcrocontroller to fnlly swtch to the debug mode. Clck on the Go button n the Debug menu or press F5. 0 AVR7 16A-AVR-06/09
AVR7 5.11 Strt the PC pplcton Plug the EVK1101 to the PC through USB Connecton. The USB enumerton should strt; new serl port ppered n Wndows. Power-up the power brdge. 5.11.1 Feld Orented Control GUI Once the GUI s lunched, the user cn select serl port number nd connect the pplcton. Fgure 4-11. Feld Orented Control GUI Iq Speed Id Serl port 5.11.1.1 Increse Speed Vlue When the speed reference ncreses wth constnt resstve torque vlue, the Iq ncreses smoothly to trget the new speed vlue. The Id remns t 0. Fgure 4-1. Increse Speed Vlue Step Speed Iq When the user wnt to ncrese speed vlue 16A-AVR-06/09
5.11.1. Increse Resstve Torque Vlue The resstve torque vlue ncreses so the mesured speed vlue decreses. To compenste t, the FOC lgorthm should ncrese the Iq reference nd fnlly the speed s regulted. The Id remns t 0. Fgure 4-1. Increse Resstve Torque Vlue Step Speed Iq AVR7 16A-AVR-06/09
AVR7 6 Reference [1] Commnde vectorelle sns cpteur de poston d'une mchne synchrone à mnts permnents Atmel Nntes & IREENA- [] NI LbWndows /CVI http://www.n.com/lwcv/ 16A-AVR-06/09
7 Appendx Fgure 14. Hrdwre Schemtc. 4 AVR7 16A-AVR-06/09
16A-AVR-06/09 AVR7
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