Speed Anti-Windup PI strategies review for Field Oriented Control of Permanent Magnet Synchronous Machines Servo Drives with Matrix Converters

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1 Seed Ani-Windu PI raegie review for Field Oriened Conrol of Permanen Magne Synchronou Machine Servo Drive wih Marix Converer J. Eina, A. Aria, J. Balcell, C. Orega & S. Galceran Dearamen d Enginyeria Elecrònica, Univeria Poliècnica de Caalunya. C/ Colom nº Terraa, Sain Tel : +34 / Fax: +34 / eina@eel.uc.edu URL: h:// Acknowledgemen The auhor acknowledge he financial uor received from Minierio de Ciencia e Innovación de Eaña for realizing hi work under TEC reearch rojec Keyword Ani-Windu, Marix converer, PMSM, Servo drive, PI. Abrac When facing real yem PI uning, he lan i modeled diregarding i hyical limiaion. Conequenly, he PI ouu may increae indefiniely i value; henomenon called Windu. Thi aer reen a review and a comarion beween differen Ani-Windu PI raegie ued in eed moion and oiion conrol for Marix Converer PMSM ervo drive. Inroducion Recenly fully inegraed adjuable eed drive alicaion have araced more aenion for a wide range of indurial alicaion uch a hybrid elecrical drive, more elecrical aircraf acuaor, robo and machine ool drive. [] [2] Wih he imrovemen in he rare magne maerial uch a (NdFeB), Permanen Magne Synchronou Machine (PMSM) are gaining marke when comared o oher AC Machine due o i higher efficiency, lower ineria, weigh reducion and volume[3]. In order o ge a fa PMSM erformance in erm of eed and orque, he Field Oriened Conrol (FOC) i one of he be vecor conrol raegie []. Figure, how he FOC cheme, where hree PI conrol are ued, one for he ouer eed conrol loo and wo for he inner curren loo. However, linear PI conroller do no have ouu magniude limier, and herefore, he ouu can ake value relaively large and a a conequence, he real yem can be damaged by he large conrol acion [4] [5]. For inance, in he FOC PMSM drive, an exceive curren and volage migh end u damaging he PMSM ielf and he ower elecronic converer. In order o roec PMSM, hee commanded value are limied and conequenly he ouer eed PI accumulae error, roducing a big overhoo on he eed reone which, in he wor cae, could even deabilize he yem; henomenon known a Windu [4]. In order o avoid he unwaned Windu henomenon, he inegraor ouu value will be ke wihin a maximum limi; raegy which i known a Ani-Windu (AW). Anoher oluion migh be o coninuouly une he PI arameer o kee he reone undamed a all ime [6]. Thi aer review differen AW raegie, roviding a general claificaion, which i firly divided beween he mehod which do deend on he Sauraion and he one which do no. The laer are normally named a PI limied or PI dead zone which have he advanage of being eay o imlemen wherea i drawback i he uning difficulne [7].

2 Mehod deending on he Sauraion migh be divided ino wo differen ubgrou, he digial and analogue one. There are mainly wo differen digial aroache, he one which ree he inegral acion of he PI when he Sauraion i reached and he econd one which hold he inegral value when he Sauraion i alo reached [8]. The analogue aroache are conidered o be a bi more accurae ince i AW mehod deend no only in he fac ha he yem i auraing bu alo conider he amoun of hi Sauraion o roorionally comenae he inegral acion. Among hem, he PI racking or Back calculaion i baed on removing from he inu, of ju he inegral ar, eiher he difference beween he non auraed ouu and he auraed one mulilied by a gain facor from 0 o [7] [9] [0] or ju he inu of he Sauraion block []. Anoher aroach i he analogue comenaion of no only he inegral acion bu in boh he roorional and inegral [8]. Oher more comlex echnique are baed on inernal lan model [2], where he model ouu i coninuouly comared wih he acual reone. In [3], an H-infinie feedback conroller i in charge of geing rid of he overhooing rouble. Thi aer review all non model deenden AW raegie inroducing a comarion of i erformance when driving PMSM wih FOC uing Marix Converer. Volage Source Inverer wih Pule Widh Modulaion (PWM) are normally ued o drive PM AC moor, bu Marix Converer (MC) can alo be ued, eecially in high-ower-deniy alicaion where elecrolyic caacior are inaroriae. MC are alo inherenly bidirecional, draw inuoidal inu curren, and have imilar efficiencie o bidirecional PWM inverer. Alhough he MC can only ouu 86% of he inu volage, hi i no a diadvanage if he machine i deigned ecially for a given alicaion. Thee characeriic of he MC have led o inere in he MC-PM AC drive for aeroace alicaion [4]. In addiion, MC have been exloied for inegraed inducion moor drive in which he converer i laced in he machine frame [5]. Noe all he ani-windu raegie reened in hi aer could be imlemened a well in he radiional VSI converer. However, hi aer i focued in he ue of MC for all he above menioned advanage and he oible indurial marke ha hi ye of converer migh achieve. K S Fig.. Marix Converer Field Oriened Conrol of Permanen Magne Synchronou Machine cheme wih eed AW PI. Table I: Moor PMSM Yakawa Ouu ower 200 W Magne flux Wb Curren/Volage 2A/00V Raed orque 0.64 Nm Pole air 4 Raed eed 3000 r..m R 2.5 Ω Fricion 0.05 Nm Ld/Lq 8.3/8.6 mh Ineria kg m 2

3 Real Syem wih he Windu henomena. Every real yem reen ome hyic limiaion or ha ome conrol conrain o afeguard yem inegriy. The ideal conrol, which ha been inroduced above, i comleely valid, alhough i fail when he inu reference or load are deely changed. Under hee condiion, becaue of he Windu henomena, he yem erformance woren and evenually i may become unable wr iq* w* w* (rad/), wr (rad/), iq* (A) Fig. 2. Effec of curren limiaion () Thi ecion how he wo ye of oible unable reone. The fir one arie when he curren reference command i limied o roec he yem a Fig. 2 how, and he econd aear when he Volage Source Inverer (VSI) DC-bu i rericed a Fig. 3 illurae. Thee wo limiaion, imlie no only an inabiliy roblem a hown in Fig. 2 and 3, bu alo bring he Windu roblem in he inegral ar of he PI conrol wr vq w* w* (rad/), wr(rad/), vq (V) Fig. 3. Effec of D.C volage limiaion () Nex oin ummarize how hi Windu henomena emerge: Difference beween inu reference and he feedback generae a large error. PI ac in conequence alying an ouu value according wih PI gain. The inegral acion ar accumulaing error, increaing i value. Evenually, he PI ouu value, mainly due o he inegral accumulaed magniude, can be larger han he Sauraion limi level. Under hi condiion he Sauraion block ac roviding he maximum olerable value o he lan. Once he acual ouu reache i reference, he error i again zero, bu he inegral accumulaed value ill remain a a value which can be much higher han he Sauraion limi bringing he reone reviouly hown in Fig 2 and 3.

4 Baic Ani-Windu The main goal of AW cheme i o avoid he over value in he Inegraor, herefore he Inegraion ouu will be ke wihin a limied range. Fig. 4 how he baic AW PI comenaor, where an inegraor limier ha been added which doe no deend on he Sauraion. Fig. 4. AW PI-limied. Fig. 5 how he eed reone wih and wihou he AW. Noice how he AW low down he eed reone when comared o he ideal one wihou any ye of auraion. On he oher hand, he overhoo ha been reduced w (rad/) Fig. 5. Ideal and AW eed reone. Ani-Windu Sraegie 20 w* wr ideal reone wr PI ani-windu () AW PI wih dead zone. In hi cae he limi i conrolled by a dead zone elemen a Fig. 6 how. Whenever he inegral value doen achieve he dead zone limi, he inegral value remain linear and herefore, unchanged. On he conrary, when he inegral ouu i larger han he dead zone limi, he oal inegral value i reduced due o he elf ubracion acion [7]. Fig. 6. AW PI wih dead zone. K e _ ou < e _ a ( ) ou() = K K e _ ref () + K i e _ ref () d e _ in < e _ dead () () = K ( K e _ ref + K i ( e _ ref () K i e _ in) ) e _ in e _ dead ou K e _ ou e _ a { ou() = e _ a A oible drawback may aear due o inegraor limi, which work indeendenly of he Sauraion elemen, o if he limi value i no correcly adjued, he PI could roduce eiher a large overhoo or an underhoo a if he inegral ar wan working. AW PI condiioned The working rincile of he Fig.7 AW i really imle and robu hank o i dicree behavior. When difference beween inu and ouu Sauraion aear, he inegraor hold i la value. When he inu and ouu Sauraion difference vanihe, he inegral acion work again.

5 Fig. 7. AW PI condiioned. { ou() = K e() + K e() eo = ou i ou = e _ a eo ou eo() = K e() + e _ in (2) AW PI racking Thi AW PI comenae for any exce of inegraor value hrough he difference beween Sauraion inu ouu.[7][9], a hown in Fig 8. eo = ou eo ou { ou() = K e() + Ki e() ou() = e _ a eo() = K e() + Ki ( e() ( eo( Δ) e _ a) ) (3) Fig. 8. AW PI racking. AW PI racking wih gain The generic cae of he AW PI racking include a gain (G), whoe margin are wihin 0 and (4) a Fig. 9 illurae, o vary he non linear feedback acion. Thi gain alo conrol he overhoo reone; The larger he gain (G) he maller he overhoo. eo = ou eo ou 0 < G { ou() = K e() + Ki e() eo ou = e _ a () = K e() + Ki ( e() G ( eo( Δ) e _ a) ) (4) Fig. 9. AW PI racking wih gain. Simulaion Reul All he AW cheme hown above have been eed o analyze heir behavior and a comaraive ha been made beween hem Fig. 0 how a zoom of he reone when a eed e wih no load i alied a one hird of he nominal eed, i.e. 00 rad/, where i i oible o oberve accuraely all differen overhoo wr (rad/) Dead zone Tracking Tracking wih gain PI condiioned wr reference w (rad/) Dead zone Tracking Tracking wih gain Condiioned wr reference (ec) Fig. 0. Differen AW PI reone again eed e inu reference () Fig.. AW eed PI reone when alying a load imac equal 2.5 ime he nominal orque.

6 All he AW cheme hown above have been imulaed o know heir behavior and a comaraive ha been made beween hem. Fig. 0 how a zoom of reone when a eed e wih no load i alied a one hird of he nominal eed, i.e. 00 (rad/), where i i oible o oberve accuraely all differen overhoo. Fig. i he reone of he PI when alying a load imac equal o 2.5 ime he nominal orque. Thi udy alo deal wih he AW behavior a a oiion ervo drive. Fig. 2 how he AW erformance when a e oiion reference i alied Condiioned & Condiional Limied & Dead Zone Limied Dead zone Tracking Tracking wih gain Condiioned Condiional Fig. 2. Servo drive reone when alying a e oiion reference and nominal load. From Fig. 2, i can be concluded ha, likewie in he eed conrol, he AW Tracking erform faer and wih le overho. On he conrary, he AW Tracking wih gain ha he wor behavior wih he large overhoo and eling ime. Table II: AW eed PI reone a one hird of nominal eed wih no load TL = 0% r (m) (m) M (rad/) (0.5%) (m) Dead zone Tracking Tracking wih gain Condiioned Exerimenal Reul The work bench ued o e he AW i howed in Fig 3. I i a four quadran work bench baed on he MC which drive he PMSM and a DC drive driving a DC machine which i in charge of imulaing he load. Main characeriic of he PMSM are hown in Table I.

7 Fig. 3 Exerimenal work bench. Fig. 4 how he exerimenal reul obained wih he e u of Fig. and he moor arameer hown on Table I. I i aaren ha he PI condiioned reone i much beer han he dead zone a execed from he imulaion. The larger overhoo in boh AW PI migh be due o he PWM naural delay in he real lan yem. Deie all AW PI eed reone are raher imilar, AW PI condiioned and AW PI racking erform wih le overhoo and have faer eling ime. However, he AW PI racking rongly deend on he lan arameer, while he AW PI i more lan and arameer indeenden. On he oher hand, he AW PI dead zone i he one wih he oore ranien erformance PI dead zone PI condiioned 00 w (rad/) () Fig. 4. Exerimenal AW PI dead zone and condiioned reone again eed e inu reference

8 Concluion Thi aer ha aed he well known effec of he Windu henomenon when andard PI are ued o drive a PMSM. In uch drive here are hree PI, wo inner one o conrol he curren and an ouer one o conrol he eed. In cae of a oiion ervo conroller, an exra ouer P loo i alo added. The eed PI Sauraion due o he lower dynamic of he PMSM i he one o be roeced and hence he inner loo i auomaically roeced again he Windu henomenon. Thi aer analye and review differen AW PI o overcome he auraion roblem. Simulaion, in eed and oiion conrol, are carried ou o comare all AW erformance and a ummary of he differen reone i rovided. Alo, ome iniial exerimenaion i carried ou wih he ame moor ued for imulaion corroboraing he imulaion. The waveform obained, in boh he eed and oiion conrol, how ha he be AW reone i obained wih he PI racking. I behavior i a good balance beween eed reone and overhoo. However, i i neceary o know he yem o une he PI reciely; oherwie, an imroer reone wih an unwaned overhoo could arie. When he lan i no know, and herefore he PI can no be uned reciely, PI condiioned erform wih a reaonable overhoo a he exene of geing lower ranien reone wih a bi larger ime rie. Reference [] Bimal K. Boe, Modern Power Elecronic and AC Driver. Penience Hall PTR, Ocober 200. [2] Richard M. Crowder, Elecric Drive and heir Conrol. Clarendon Pre, Oxford, 995. [3] T.J.E. Miller, Bruhle Permanen-Magne and Relucance Moor Drive. Clarendon Pre, Oxford, 989. [4] Karl J. Åröm and Tore Hägglund, PID Conroller: Theory, Deign, and Tuning. Inrumen Sociey of America, 995. [5] K. Ogaa, Modern Conrol Engineering. Penience Hall PTR [6] Yu-Sheng Lu, Non-overhooing PI conrol of variable-eed moor drive wih liding erurbaion oberver, ELSEVIER, Mecharonic. vol.5,.43-58, March [7] C. Bohn and D.P Aheron, A Simulink ackage for comaraive udie of PID Ani-windu Sraegie., IEEE/IFAC join Symoium, 7 March 994. [8] K. Ohihi and E. Hayaaka, High.Performance Seed Servo Syem Conidering Volge Sauraion of a Vecor-Conrolled Inducion Moor, IEEE ran on indurial elecronic, vol.53, NO.3, June [9] P. March and M. Turner, Ani-windu Comenaor Deign for Permanen Magne Synchronou Moor Seed Regulaion, The IEEE Inernaional Elecric Machine & Drive Conference, IEMDC Vol., 3-5 May 2007 Analaya. Turqkey. [0] Xiaofeng Xu, Deign of Curren Conrol of Fully Inegraed Surface-mouned Permanen Magne Synchronou Moor Drive Servo Acuaor, IEEE Euroean Conference on Power Elecronic and Alicaion, EPE , -4 Se 2005 Dreden, Germany. [] Hwi-Beom Shin, New Aniwindu PI Conroller for Variable-Seed Moor Drive IEEE ran on indurial elecronic, vol.45. no.3, June 998. [2] Zhang Jinggang and Chen Zhimei, A New Aniwindu Seed Conroller for Inducion Moor Drive Syem Inernaional Conference on Elecrical Machine and Syem, ICEMS 200, vol.2, 8-20 Aug [3] Xie Dongmei, Deign of H Feedback Conroller and IP-Poiion Conroller of PMSM Servo Syem., The IEEE Inernaional Conference on Mecharonic & Auomaion. Vol.2, , 29July-Aug 2005, Niagara Fall, Canada. [4] M. Aen, C. Whilely, P. W. Wheeler, J. C. Clare, K. J. Bradley, and G. Tower, Dynamic erformance of a marix converer driven elecro-mechanical acuaor for an aircraf rudder, in roc. IEE PEVD Conf., Edinburgh, U.K., 2004, [5] C. Klumner, P Nielen, I. Boldea, and F. Blaabjerg, A new marix converer (MCM) for indury alicaion, IEEE Tran. Ind Elecron., vol. 49, no.2, , Ar