Design of an Optimized Intelligent Controller of Electromechanical System in Aerospace Application

Transcription

1 Deig of a Opimized Iellige Coroller of Elecromechaical Syem i Aeropace Applicaio Tribei Praad Baerjee, Swagaam Da, Ajih Abraham 2, 3 Dep. of Elecroic ad Telecommuicaio Egieerig, Jadavpur Uiveriy, Kolkaa 7 32, Idia. 2 Machie Ielligece Reearch Lab (MIR Lab) Scieific Nework for Iovaio ad Reearch Excellece, WA, USA 3 IT For Iovaio, EU Ceer of excellece, Faculy of Elecrical Egieerig ad Compuer Sciece VSB - Techical Uiveriy of Orava, Czech Republic [email protected], [email protected], [email protected] Abrac-The objecive of codiio baed maieace (CBM) i ypically o deermie a opimal maieace policy o miimize he overall maieace co baed o codiio moiorig iformaio. I Aircraf operaor ad he maieace people arvig o reduce he co of aircraf maieace. So he codiio baed moiorig for elecromechaical corol valve i very popular recely. Thi paper ha bee propoed a opimized Fracioal order Proporioal-iegral-derivaive (FOPID) coroller for elecromechaical acuaed worm gear operaed fuel hu off valve. Keyword: Compuaioal Ielligece; elecromechaical Syem Maieace; Differeial Evoluio; Proporioal Iegral ad Derivaive corol; Fracioal Corol, CBM. I. INTRODUCTION For Aeropace yem Codiio Baed Maieace (CBM) i much differe ha he oher idurial yem, civil ad elecro-mechaical maieace yem. I Aeropace applicaio he major iue are ize, weigh ad airworhy cerificaio of ay compoe. I alo have o coider cerificaio of aviaio ad high level afey criical iue. CBM i gaiig imporace i idury becaue of he eed o icreae machie availabiliy. Eve I rece year, everal diagoic ad progoic model baed o aiical, arificial ielligece (AI) ad of compuig (SC) echique have bee propoed [-4] ad geig he aifacory reul. I hi work we apply he DE o opimize he corol parameer o reducig he mechaical fricio of he worm gear ad reducig he faul occurrece due o fricio i he elecromechaical corol ball -valve. I [5] preeed combiig wih Paricle wam opimizaio (PSO) [9] oher compuaioal ielligece (CI) echique like ANN ad SVM for auomaed elecio of feaure ad deecio of machiery faul. Fracioal order dyamic yem ad coroller, i baed o fracioal order calculu [6]. Fracioal calculu i a brach of mahemaical aalyi ha udie he poibiliy of akig real umber power of he differeial operaor ad iegraio operaor. From a purely mahemaical poi of view here are everal way o defie fracioal order derivaive ad iegral. The geeralized differe iegraor operaor may be pu forward a: q q d f() D f() a q [ d ( a)] Where q repree he real order of he differe iegral (a i ued i ome lieraure o deoe a ieger order), i he parameer for which he differe iegral i ake, ad a i he lower limi. Ule oherwie aed he lower limi will be ad lef ou of he oaio. Capuo ued a popular defiiio ued o compue differe iegral i 96. The defiiio for Capuo fracioal derivaive of order wih repec o he variable ad wih he arig poi goe a follow [2, 2], ( ) m + y ( ) d D τ τ y(), Γ( δ ) ( τ ) δ γ m + δ, m Z, < δ ) (2) Here, Γ(z) i Euler Gamma fucio. If γ <, he we have a fracioal iegral of order γ give a: γ γ y( τ) dτ y( ) D y( ),( < ) Γ( ) γ + γ γ ( τ) () I (3) Oe diic advaage of uig he Capuo defiiio i ha i oly allow for coideraio of eaily ierpreable iiial codiio bu i i alo bouded, which mea he derivaive of a coa i equal o zero. I ime domai, a fracioal order yem i govered by a -erm ihomogeeou fracioal order differeial equaio (FDE): β β β ad y () + a D y () ad β + y () + ad y () (4) u () Where D D i he Capuo fracioal derivaive of order. Coverig o frequecy domai, he fracioal order rafer fucio of uch a yem may be obaied hrough he Laplace raform fucio a follow, c 2 IEEE 5

2 G () (5) β β β β a + a a + a Where, β,,..., ) i a arbirary real umber, ( k k β > β >... > β > β > ad ( k,,..., ) a k i a arbirary coa. Fially we would like o meio here ha he Laplace raform of he fracioal derivaive migh be give a, m k ( k ) e γ γ γ D y() d Y( ) y ( θ ) (6) k For, γ < (i.e., for he cae of a fracioal iegral) he um i he righ had ide mu be omied. I [7] i wa advocaed ha fracioal order calculu would play a major role i a iellige mecharoic yem. I coveioal gear ha more fricio bu worm gear i pure lidig ad hee aracive feaure deirable i Aeropace applicaio. Worm gear are frequely ued i elecro-mechaical yem. The fricio play a domia role i he performace of he worm gear yem [8] I FOPID coroller I ad D operaio are uually of fracioal order, herefore beide eig he proporioal, derivaive ad iegral coa K, T, T we have wo p d i more parameer: he order of fracioal iegraio ad ha of fracioal derivaive μ. Fidig a opimal e of value for K T, T,, ad μ o mee he uer p, i d pecificaio for a give pla (worm gear eeh fricio miimizaio corol) parameer i muli-dimeioal hyperpace. The deig mehod focue o opimum placig of he domia cloed loop pole ad icorporae he corai hu obaied uig DE algorihm. The opimizaio-baed deig proce ha bee eed for acuaig he repoe of four proce pla of which wo are of ieger order ad wo are of fracioal order. The performace of he DE baed PI D μ coroller ha bee compared wih. have bee ued o make he claificaio proce faer ad accurae uig he miimum umber of feaure which primarily characerize he yem codiio wih opimized rucure or parameer of ANN ad SVM []. II. PROBLEM DESCRIPTION I corol egieerig i i iere o deig or model a mechaical fricio. The iere o deig ad corol raegie i becaue i alleviae he performace of he yem. If a good fricio model available he he performace of he yem beig icreae, which ca improve he maieace co ad reduced he faul occurrece i he criical yem uch a elecromechaical acuaor i aeropace applicaio, proce corol valve, ad roboic. The predicive moio corol cheme [] ha bee propoed earlier i hi yem we do coider he fricio i oliear aalyi. I hi paper we iroduced he fricio ad ry o reduce he BLDC moor orque by reducig he fricio. PID coroller have bee ued for everal decade i idurie for corol applicaio. The reao for heir wide populariy lie i he impliciy of deig ad good performace icludig low perceage overhoo ad mall elig ime for low repoe yem like elecromechaical yem [2]. The mo commo form of o-ieger model i PI D μ coroller. I he order of he iegraor ad, μ i he order of differeiaor. The rafer fucio of uch a coroller wrie a: K i μ c() K p + + K d (7) Or i ime domai coroller oupu wrie a: u μ () K e() + K D e() + K D e() p i Wih differe value of he parameer ad he eimaed rucure of he coroller i uch ha: For,, μ a claical PID coroller K i c() K p + + K d (9) For, K d, a claical PI coroller K c() i K p + () For, d K a o-ieger PI coroller K i c() K p + () No-ieger or Fracioal PI D μ coroller ha he mo impora advaage lie i he fac ha hee ype of coroller are le eiive o chage of parameer of a corolled yem. Thi i due o he exra degree of freedom o beer adju he dyamical properie of a oieger order corol yem. I [3].Differeial Evoluio (DE) [4, 5] ha recely become quie popular a a imple ad efficie cheme for global opimizaio over coiuou pace. I ha reporedly ouperformed may ype of evoluioary algorihm ad earch heuriic like PSO whe eed over boh bechmark ad real world problem [6]. I hi work, a ae-of-he-ar verio of DE ha bee ued for fidig he opimal value of gear fricio miimizaio o ha he coroller chooe i be opimal value. I hi paper we deig he coroller ad e i i he fuel valve corol cheme ad imulaio how ha hi coroller give beer performace i pracical yem alo. Eve i [7] he reul ha bee how we alo compare wih ha alo ill our yem give more accurae corol for hi pecific applicaio. The chemaic diagram of he coroller ad he gear yem wih a how i figure.the pla ad he coroller fucio ha bee lied i able. Sice he coroller deig i model-baed approache o icludig high frequecie i eeial for deig a robu oliear coroller. Elecromechaical acuaed hydraulic yem are eeially oliear. So he dyamic behavior of he yem ad rackig performace ill ha o aalyze ad ha i he ex level of he work. d (8) 2 h Ieraioal Coferece o Hybrid Iellige Syem (HIS) 5

3 TABLE. TRANSFER FUNCTIONS OF PID CONTROLLER Proce Pla Trafer Fucio () G p Coroller Trafer Fucio ) G c ( The daa acquiiio ad he imulaio we ue adard PC wih XP, Core 2 Duo Proceor, Gb RAM, ad he LabVIEW ofware of Naioal Irume ad here daa acquiiio yem. We ue FOPID corol, for hi complex advaced corol wih muliple ipu ad oupu. Followig he ame fudameal priciple, we ue our compuer ad daa acquiiio hardware o ake eor meaureme, compare he meaured value wih he deired e poi i ofware, ad updae oupu igal accordigly. There are a umber of advaage o uig a Idurial PC for corol applicaio ha lead o flexibiliy, high performace, ad cuomizaio. The imulaio ha carried ou i MATLAB 2 plaform couplig wih LabVIEW ofware. Figure 2 how ha he coroller repoe afer opimized parameer DE i he yem ad Figure 3 illurae he comparaive imulaio reul wih, ad propoed DE. Fig.. Schemaic cofiguraio of he propoed coroller coupled wih elecromechaical gear III. EXPERIMENTAL RESULTS AND DISCUSSIONS The Fracioal order yem wih opimized coroller for he fir ime o corol worm gear fricio i applied i hi paper. Thee iovaive predicive maieace oluio, uilizig codiio-moiorig yem are currely uder eig i order o uppor he iroducio of ew elecrically acuaed aircraf fuel corol valve yem o provide reliabiliy aurace. A embedded iellige CBM ad corol mehod ha bee iroduced i hi paper. Thi would allow pre fligh warig ha ca help o reducig faul. Corollig he fricio by fracioal order PID (FOPID) coroller baed o he DE i preeed i hi paper. Fracioal calculu ca provide ovel ad higher performace exeio for FOPID coroller. The obaied reul give experimeal evidece of he capabiliy of he algorihm ad he propoed model. The experimeal reul are a igifica coribuio of hi work ad have bee obaied hrough he developme of a uiable ofware oluio ha allow ierfacig he opimizaio algorihm wih he eor ad he acuaor. The all experime ad he e of he yem have bee doe i laboraory ad he corol parameer eig doe by experimeal eig. Fig. 2. Coroller oupu repoe wih opimized DE Fig. 3. Coroller oupu repoe compario wih opimized DE ad 52 2 h Ieraioal Coferece o Hybrid Iellige Syem (HIS)

4 Fig. 4.Comparaio reul wih modified DE, DE ad TABLE 2. PERFORMANCE SUMMARY OF CLOSED LOOP SYSTEM UNDER DIFFERENT PID CONTROLLERS AINST THE UNIT STEP FUNCTION Gear Fricio Type. 2. Type of Coroller Ued Opimized Fracioal Coroller uig DE Ieger PID coroller uig DE Fracioal Coroller uig Opimized Fracioal Coroller uig DE Ieger PID coroller uig DE Fracioal Coroller uig Syem Sep Repoe Oberved Rie Time (Sec) Deviaio (Sec) Maximum Overhoo Deviaio 2. (.3) 3.23 (.34) 5.3 (.87).93 (.89).2 (.).27 (.7).25 (.5).2 (7).55 (.88).28 (.5).435 (.78).32 (.33) Seady Sae Error Deviaio 2.5 (). () 2. (.56).6 (.34).2 ().3 (.3) Fial Objecive fucio value obaied () ().22 (25) () ().522 (37) 2 h Ieraioal Coferece o Hybrid Iellige Syem (HIS) 53

5 How he objecive fucio value decreae wih he umber of Fucio Evaluaio (FE) i illuraed i Figure 4. The graph idicae ha he DE baed mehod could fid beer oluio coumig leer amou of compuaioal ime. IV. CONCLUSIONS I hi paper pree a ew opimized coroller uig mehod. A ew hybrid corol mehod applied o eure precie corol io elecromechaical o-off valve acuaio. The advaage of he propoed yem i how fially, by he reul of evidece ha he ue of a deailed ad validaed model of he yem ca produce a complee proce of good performace. REFERENCES [] Jardie AKS, Li D, Bajevic D. A review o machiery diagoic ad progoic implemeig codiio-baed maieace. Mechaical Syem Sigal Proceig 26; 2: [2] Hardma W. Mechaical ad propulio yem progoic: US avy raegy ad demoraio. JOM 24; 56(3):2 7. [3] Hardma W, He A, Sheaffer J. SH-6 helicoper iegraed diagoic yem (HIDS) program diagoic ad progoic developme experiece. I: Proceedig of he IEEE aeropace coferece, Ape, CO, USA, March 6 3, 999. p [4] Samaa B. Gear faul deecio uig arificial eural ework ad uppor vecor machie wih geeic algorihm. Mechaical Syem Sigal Proce 24; 8: [5] Samaa B., Naaraj C., Progoic of machie codiio uig of compuig, Roboic ad Compuer-Iegraed Maufacurig, Volume 24, Iue 6, FAIM 27, 7h Ieraioal Coferece o Flexible Auomaio ad Iellige Maufacurig, December 28, Page [6] Oldham, K. B., Spaier, J., The Fracioal Calculu. Academic Pre, New York, 974. [7] Podluby, I., Fracioal-order yem ad PI D coroller, IEEE Tra. O Auomaic Corol, vol.44, o., pp , 999. [8] J.E.Shigley, C.R.Michke, Mechaical Egieerig Deig, McGraw-Hill, NJ, 989. [9] Keedy, J., Eberhar, R.C., Paricle warm opimizaio. I: Proceedig of he IEEE Ieraioal Coferece o Neural Nework, IV. IEEE Service Ceer,Picaaway, NJ, pp []Jack, L.B., Nadi, A.K., 2a. Geeic algorihm for feaure exracio i machie codiio moiorig wih vibraio igal. IEE Proceedig Viio Image ad Sigal Proceig 47, []Baerjee T.P., Roychoudhury, J., Da, S., Abraham, A., "Hybrid Iellige Predicive Corol Syem for High Speed BLDC Moor i Aeropace Applicaio," Emergig Tred i Egieerig ad Techology (ICETET), 2 3rd Ieraioal Coferece o, vol., o., pp , 9-2 Nov. 2. [2]Arom, K., Hagglud, T., PID Coroller; Theory, Deig ad Tuig, Irume Sociey of America, Reearch Triagle Park, 995. [3]Viagre, B. M., Podluby I., Dorcak L., ad Feliu V., O Fracioal PID Coroller: A Frequecy Domai Approach, Proceedig of IFAC Workhop o Digial Corol - PID, Terraa, Spai, 2. [4]Price, K., Sor, R., ad Lampie, J., Differeial Evoluio - A Pracical Approach o Global Opimizaio, Spriger, ISBN: , 25. [5]Sor, R., Price, K.: Differeial evoluio A Simple ad Efficie Heuriic for Global Opimizaio over Coiuou Space, Joural of Global Opimizaio, (4) (997) [6]Veerrøm, J., Thomo, R. A Comparaive Sudy of Differeial Evoluio, Paricle Swarm Opimizaio, ad Evoluioary Algorihm o Numerical Bechmark Problem, Proc. Sixh Cogre o Evoluioary Compuaio (CEC- 24). IEEE Pre. [7]Biwa, A., Da, Swagaam., Abraham, A., Dagupa, S., Deig of fracioal-order PI D μ coroller wih a improved differeial evoluio, Egieerig Applicaio of Arificial Ielligece, Volume 22, Iue 2, March 29, pp h Ieraioal Coferece o Hybrid Iellige Syem (HIS)