REALIZATION OF FPGA/CPLD BASED SERVO CONTROLLERS FOR MBDCM

Transcription

1 REALIZATION OF FPGA/CPL BASE SERVO CONTROLLERS FOR MBCM Chh-We T, T-We Ln nd Chun-Lng Ln eprtment of Electrcl Engneerng, Ntonl Chung Hng Unverty Abtrct: Th pper preent new degn ung dvnced evolutonry trtegy (ES) to relze robut ervo controller for mcro bruhle C motor (MBCM) bed on FPGA/CPL (Feld Progrmmble Gte Arry/Complex Progrmmble Logc evce. Control degn requrement nclude robut tblty, control conumpton nd trcng performnce. Evolutonry computton trtegy propoed for fndng the optml oluton of the contrned mult-objectve problem. The controller relzed n FPGA/CPL devce for compctne. Smulton nd expermentl reult re llutrted to verfy performnce nd pplcblty of our pproch. Copyrght 006 Interntonl Conference Control Keyword: robut control, evoluton trtegy, mcro bruhle C motor, FPGA/CPL.. INTROUCTION MBCM re wdely ued n feld of eropce engneerng. Applcton nclude flp nd empennge ctutor on unmnned vton vehcle (UAV). The ytem model for lner BLCM w dentfed ung the curve-fttng method. The novel C motor wth permnent mgnet h hgh ccelerton torque whch permt drect couplng of the motor x nd vod nherent bclh nd frcton of the motor n trnmon (H. Butler, et l., 989). fferent method re ppled to mprove wtchng effcency of PWM nd enhnce motor operton(m.p. Kzmerow, et l., 998;. Jouve, et l., 990; R.A. Mmmno, et l., 989). Speed control of the permnent mgnet ynchronou motor (PMSM) w relzed by men of ldng control compred to feedbc lnerzton-bed controller whch ue proportonl plu dervtve (P) controller (I.C. B, et l., 000). Speed control ung lod-torque oberver n torque feedforwrd loop w ued to relze robut peed control ytem (M. Iw, et l., 993). A new oberver wth recedng horzon concept w propoed to provde effectve etmte of the tte vrble n the preence of lod dturbnce (K.S. Low, et l., 000). It hd mproved trcng performnce nd ncreed controller Trdtonl PI tunng uch the Zegler Nchol method only uffcent for prmry tunng phe of the controller nd enure tblty durng revoluton. However, the Zegler Nchol method fl to cheve prece potonng nd rottonl velocty. Th pper propoe robut PI control degn for MBCM. The performnce ndce n tme nd frequency domn re condered under pecfed contrnt for the control ytem degn. ES ppled to ee optml prmeter nce ccurte Preto oluton re dffcult to obtn n th type of mult-objectve optmzton. The expermentl pltform cont of MBCM, PWM bed drver nd FPGA/CPL. Smulton nd expermentl reult re preented to verfy utblty nd prctclty of the propoed method.. CONTROL SCHEME ESIGN Sytem tructure relzton. Conder cloed loop control ytem contng of MBCM hown n Fg.. where P () the uncertn plnt model, C () the controller, H() the enor model, dt () the reference nput, ut () the control commnd, yt () the plnt output, nd et () dt () Hyt () the trcng error. Frequently t derble n prctce to ue only error nd chnge rte of error ytem nput to mplfy nd obtn dered PI controller

2 chrctertc when degnng controller. We decrbe the tndrd PI controller n the form: u KPe+ KI edt+ K e () the erch pce. The vector evluted to obtn the objectve functon vlue of n ndvdul pont. A et of w ndvdul denoted by S, clled populton, frt expreed follow: where K, P K nd I K re clng mtrce { } S,,, w (5) For the current problem, the populton et for w ndvdul gven by {,,,, } S (6) P I w where T P T P T I T I T T T vec vec n vec vec n vec vec n, wth the vec opertor beng defned T m m vecp [ p pm p pm p m pmm], P R. correpondng to e nd e repectvely. Fg.. Generlzed PI control cheme Stblty Crteron. The tuton of SISO plnt condered wth regrd to the cloed-loop ytem. Frt let the nomnl plnt model be fctorzed P n p ( ) N p( ) wth the tble rtonl functon mtrce N nd p p ( ) conttute the left-coprme fctorzton of P. The controller nd the n ( ) C () enor dynmc H() fctorzed C( ) H() N () () wth the tble rtonl c c functon mtrce Nc ( ) nd c ( ) conttute the rght-coprme fctorzton of C( ) H(). The nomnl chrctertc equton for the cloedloop ytem gven by ( p c p c ) Λ () det () () + N () N () 0 The tblzng prmeter pce chrcterzed by { KP KI K λ KP KI K } () Ψ0,, Re (,, ) < 0, (3) where λ denote the root of the chrctertc equton decrbed by (3). The retrcted, dmble controller prmeter pce cn be denoted by the followng equton under prctcl hrdwre lmtton mpoed on the devce: { K, K, K } PI,, PI,, PI,,, K,, 0 Ψ Ψ (4) n P I j j j P I 3. ES BASE PARAMETER OPTIMIZATION ES tochtc optmzton lgorthm whch wor drectly wth the rel repreentton of the prmeter et from n ntl populton. The bc element proceed by ES vector formed by ll, nd. Ech vector repreent pont n, j P, j I, j Selecton of potentl ndvdul. We frt need to chrcterze potentl ndvdul ued for the oluton erch. For SISO ce, the utble prmeter pce for ytem tblty cn be eprted from the prmeter pce by ung the root contour technque. Indvdul of S re elected rndomly from the utble prmeter pce by the ES mechnm. Evoluton trtegy (ES). The concept of ES to repreent n ndvdul pr of flot-vlued vector v (, N( 0, σ )). The frt vector repreent pont n the erch pce. The econd, N ( 0, σ ) repreent vector of ndependent rndom Gun number wth zero men nd tndrd devton of σ. The erch of new pont bed on one opertor,.e. the mutton opertor. In ( w, λ ) ES, the erch begn by genertng w prent n ech generton. Then λ offprng re generted by mutton, reultng from ddton of rndom number, nd t umed tht λ > w. Ech mutnt ubjected to the contrnt mpoed. The non-feble one elmnted. Selecton of the qulfed mutnt performed untl ll member re feble. Next, the λ member re orted ccordng to the mgntude of the objectve functon vlue. Then the w bet ndvdul of the λ member generted become the prent of the next generton. Note tht the offprng (mutnt) ccepted new member of the populton f nd only f t h better ftne. Otherwe, the offprng elmnted, nd the orgnl prent remn. To relze the prevou decrpton, we chrcterze the mutton by replcng the ndvdul by ( σ ) + + N 0,,,, w, j,, l (7) ( g ) ( g) j j where g the ndex of the generton number. Ftne functon degn. Operton peed of the computer relted wth the number of ndvdul n populton. Therefore, t necery to ether

3 conder the computer performnce or multe everl generton beforehnd whle ettng the populton. The offprng re propgted v mutton nd the number of offprng everl tme compred to the prent generton. The ftne functon defned n n ε + ε ( ) + ε ( ) f M T E o r 3 n 3 (8) where M the normlzed mxmum overhoot, o T the normlzed re tme, the normlzed r E tedy tte error, ε, ε nd ε re the weght of 3 performnce ndce wth repect to ech tme domn meurement. The entvty functon nd the control energy functon gven follow re lo condered + () S I P C H S n j ( ) C I P ( CH ) ( ) (9) () n j (0) Ω + Ω Mnmzng the entvty functon reduce ytem entvty. The control energy functon vod exceve control conumpton. The followng nequlte re condered here the degn contrnt: : g W S jω < () g : Wr jω where A( jω ) upσmx ( A( jω) ) ω Ω < () ; W nd re the weghtng functon (K. Zhou nd J. C. oyle, 998) gven by / M + ω b W + ωb ε ω / bc M u + Wr ω bc + ε W r (3) (4) where M the mxmum entvty, ω b the bndwdth, M the mxmum gn of open loop u nd ω controller bndwdth. bc A penlty functon nvolved n trnformng the contrned optmzton problem nto n uncontrned one. We dopt the followng penlty functon: S j exp σ Δbj gj (5) { } where Δb mx 0, g b, j, nd j j prmeter ued to djut the everty of the penlty functon. The trnformed ftne functon cn now be expreed f f S (6) egn procedure for determnng optml control prmeter uggeted follow. Intlly, populton of w potentl prent oluton,,, w, choen bed on the electon crteron.. Ech prent crete n offprng, where determned by the followng updte crteron: where ζ ~ N ( 0, σ ) N ( 0, σ ) + (7) σ σ exp( ζ ) (8) Δ determned ccordng to norml dtrbuton wth zero men nd vrnce Δ σ. Δ σ the dfference of σ between the lt two generton. 3. Clculte the vlue of ll objectve functon nd contrnt wth repect to ech offprng. Ech offprng oluton cored n lght of the contrned ftne functon. 4. Ech oluton (,, λ ) evluted gnt the other rndomly choen oluton from the populton. For ech compron, wn gned f the oluton core lrger thn or equl to tht of t opponent. 5. The w oluton wth the gretet number of wnner re retned to be prent to the next generton. The toppng crteron dopted termnte the erch proce when the mxmum number of generton reched or ( g ) ( g f ) mx fmn < ε where ε the cceptble upper bound, f mx f nd f mn f. mx,, w mn σ,, w Otherwe proceed to execute Step. When the toppng crteron ttned, n ndvdul hvng the hghet ftne n the converged populton defned the fnl oluton. 4. VERIFICATION OF SIMULATION AN EXPERIMENT Verfcton of Smulton. The motor llutrted n Fg. cn be eprted nto two prt, mechncl model nd electrcl model, follow Mm ( ), Em ( ) J+ L + R nd the trnfer functon of MBCM decrbed by

4 ( ) Kt η θ (9) e LJ ( + L + RJ + R + KK t b) where e : ppled rmture voltge, V : rmture curretn, A f : feld current, A : equvlent vcou coeffcent of the motor to the motor hft, N-m/rd/ec J : equvlent moment of nert of the motor nd lod referred to the motor hft, g-m Kb : bc emf contnt, V/rd/ Kt : Torque contnt, N-m/A L : rmture nductnce, H R : rmture retnce, Ω T : torque developed by the motor, N-m η : ger rto of peed reducer θ : ngulr dplcement of the motor hft, rd R L The contrnt ωb 9.85 Hz mplemented to vod noe corrupton, where ω B denote the bndwdth. Next, conder the frequency domn pecfcton. The entvty functon elmnte tedy tte error nd the control energy functon vod exceve control energy emergence n the ytem loop whch my reult n burnng the FPGA/CPL chp. The weghtng functon of the entvty functon nd the control energy functon were jutfed by equton () through (4) nd were choen follow W () 5000 Wr On pplyng the ES for prmeter erch, the prent populton cont of 5 ndvdul; they re ntlly rndomzed. The offprng re mutted n norml dtrbuton nd ther number 7 tme to the prent generton. The number w numerclly verfed to be ble to fnd out the optml oluton. The prmeter of the ftne functon defned n (8) re choen follow: e θ K b T J ε ε 0.4, ε 0., n 4, n n 3 3 f Fg.. Schemtc dgrm of MBCM contnt We chooe the MBCM prmeter ccordng to the dt cqured from n experment pltform for the MBCM control ytem provded by the Pttmn Expre Compny lted n Tble. Tble Specfcton of MBCM Specfcton Torque Contnt t Bc-EMF Contnt ( Kb ) Vlue/Sttu K 4.86E-0 N-m/A 4.86E-0 V/rd/ Retnce ( R ) 9.3 (Ω) Inductnce ( L ).6 (mh) Equvlent moment of nert of the motor ( J ).4E-06 (g-m ) Equvlent vcou.5e-06 (N-/rd/) coeffcent ( ) Reference Voltge 38. (V) No-Lod Speed 775 (rd/) Ger rto of peed reducer /46 The envronment condton re choen wth conderton of the phycl property. We frt mplement the controller n MATLAB to verfy the ymptotc trcng performnce before ctul ytem mplementton. The term K t K b uully mller thn other contnt term o tht t my be neglected. The followng plnt model obtned P ( ) (0) Bed on the chrctertc equton n of the cloedloop ytem, the root contour for vrou vlue of P, I, nd re drwn n Fg. 3. It cn be ely een tht the tblzng rnge of P, I, nd re chrcterzed by > 0, > 0, > 0 P I Fg. 3 Root contour of the correpondng ytem Performng the developed erchng lgorthm for 50 generton of the populton, we obtn the controller prmeter: , , P I nd the PI controller ppled: C ()

5 The entvty functon nd energy functon re, repectvely, gven follow S Ω ( ) 7.47e e e e e (3) (4) By multon, we get the tme-domn performnce of M, T, nd o 0.0% r 0.8ec. E for the unt tep nput nd t hown n Fg. 4. Frequency repone of the cloed-loop ytem hown n Fg. 5. Fg. 6. Implemented MBCM ytem nd Hll gnl wveform Fg. 4. Trnent repone w.r.t. unt tep nput EPM78 h hgh denty ntegrton, provdng 600~0000 logc gte. The devce progrmmed ung hrdwre-decrpton lnguge VHL/Verlog HL to cheve hrdwre mnmzton. It mn functon to perform control lw lgorthm nd drecton control of motor revoluton. Fg. 7. dply the ytem confgurton of the MBCM. A mcro bruhle C ervo motor mnufcture by Pttmn Expre, whoe rted-lod torque, rted voltge nd rted current were 0.04Nm, 38.V C, nd 4.0Arm, ued for the experment. A potentometer nd three Hll-effect enor re ued to meure the poton nd electrcl poton nformton of the rotry-member, repectvely. Other element nclude n ocllton crcut, CPL, voltge upply, motor drvng crcut, /A converter nd A/ converter. Fg. 5. Frequency repone of the cloed loop ytem Verfcton of experment. Next, the propoed controller expermentlly verfed; ee Fg. 6. Th mechnm ttn peed reducton by ger wth ger rto of :46. A potentometer wth 5v /90 reoluton ued to meure the rotry poton. A pule-wdth-modulton (PWM) nverter, whch ccept 4 V, ued. Robut PI controller degn bed on FPGA/CPL devce hown n Fg. 6. The EPM78S CPL devce of the Alter Mx7000 fmly bed on progrmmble only memory (EEPROM) element. The devce feture ocet mounted 84-pn pltc j-led chp crrer (PLCC) pcge nd 8 mcrocell. It wdely ued progrmmble logc devce n feld of control nd h the dvntge of feld progrmmng, reprogrmmblty, hrdwre emulton, hrdwre prototypng, nd cot effectvene. Fg. 7. Prctcl ytem confgurton of MBCM CPL receve et of control order n term of pule nd decde the drecton of motor rotton bed o the wdth of the pule(clocwe (CW), counter-clocwe (CCW))..0m ~.49 m: CW rotton.5 m ~.0 m: CCW rotton.5 m: Stop rotton

6 After recevng control gnl, CPL end 3- phed gnl to the motor drvng crcut whch end 6-phed gnl to drve the motor. 5. CONCLUSIONS Th pper propoe robut control degn whch poee the dvntge of hgh performnce, mnturzton nd low cot to contruct the ervodrvng ytem for MBCM. The propoed control cheme h cheved the requrement of prece potonng control, whch proved v multon nd expermentl verfcton. The excellent expermentl reult how tht t prctclly relzble nd relble. ACKNOWLEGEMENTS Th reerch w ponored by Ntonl Scence Councl, Twn, R.O.C. under the Grnt NSC 93- -E REFERENCES. Jouve, J.P. Rognon, nd. Roye(990). Effectve Current nd Speed Controller for Permnent Mgnet Mchne: A Survey. In: Conf. Appled Power Electronc nd Expoton, pp H. Butler, G. Honderd, nd J. vn Amerongen(989). Model Reference Adptve Control of rect- rve C Motor. IEEE Contr. Sytem Mgzne, vol. 9, pp I.C. B, K.H. Km, nd M.J. Youn(000). Robut Nonlner Speed Control of PM Synchronou Motor Ung Boundry Lyer Integrl Sldng Mode Control Technque. IEEE Trn. Contr. Sytem Technology, vol. 8, pp M.P. Kzmerow, nd L. Mlen(998). Current Control Technque for Three-Phe Voltge-Source PWM Converter: A Survey. IEEE Trn. Ind. Elect, vol. 45, pp K. Zhou, & J. C. oyle(998). Eentl of robut control. Prentce Hll, New Jerey. K.S. Low, nd Z. Hulng(000). Robut Model Predctve Control nd Oberver for rect rve Applcton. IEEE Trn. Power Elect., vol. 5, pp M. Iw, N. Mtu(993). Robut Speed Control of IM wth Torque Feedforwrd Control. IEEE Trn. Ind. Elect., vol. 40, pp R.A. Mmmno, nd J.J. Glvn(989). rvng three-phe bruhle C motor- new low lo lner oluton. In: Conf. Proc. Appled Power Elect. Conf. nd Expoton, pp