EXPERIMENTAL EVALUATION OF PI TUNING TECHNIQUES FOR FIELD ORIENTED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTORS

Transcription

1 Advance n Electcal and Electonc Engneeng 4 EXPERIMENTAL EVALUATION OF TUNING TECHNIQUES FOR FIELD ORIENTED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTORS B. Zgmund, A. Telzz, X. T. Gaca, R. Pavlann, L. Salvatoe Poltecnco d Ba, Datmento d Elettotecnca ed Elettonca, V. Oabona 4, 75 Ba, Italy, alvatoe@olba.t Unvety o Glamogan, School o Electonc, CF7 DL Pontydd, Wale, UK, xdeltoo@glam.ac.uk Unvety o Zlna, Faculty o Electcal Engneeng, Deatment o Mechatonc and Electonc, Unveztna, 6 Zlna, SK, bano.zgmund@gmal.com, avlann@el.utc.k Summay Th ae eent the exemental evaluaton o a commonly ued methodology to tune the egulato o the Feld Oented Contol (FOC) tategy o Pemanent Magnet Synchonou Moto (PMSM). The methodology ued baed on the Abolute Value Otmum (AVO) and Symmetc Otmum (SO) cteon. Thee method emloy a mled model o the lant to be contolled. Due to the comlexty and non-lneate eent n the FOC PMSM dve ome dvegence between the deal eone and the eal eult wll occu. In th ae a comaon between mulated and exemental eult caed out to evaluate the goodne o the oluton obtaned. The dvegence obeved between mulaton and the eult obtaned n the exemental etu ae hown and t attemted to juty the caue o them. Oveall t concluded that the method ovde a atactoy ntal commonng o the egulato o the dve ytem unde tudy.. INTRODUCTION D egulato ae wdely emloyed n nduty due to the atactoy behavou n mot o the contol alcaton. One o the mot motant engneeng tak dung the commonng o contol ytem the aametc otmzaton o the egulato to obtan the deed contol eone []. Deent method can be emloyed to eom the tunng o the D egulato. A oble clacaton o thee method can be a ollow: Exemental method baed on the dentcaton o cetan eone chaactetc o the ytem. The Zegle-Nchol oen and cloed loo method ae an examle o thee method []. Mathematcal model baed method. Thee method emloy a mathematcal model that aoxmate the behavou o the ytem [,, 4]. Otmzaton technque. By mean o a met uncton that can be evaluated n a tet, a numbe o oluton contng on deent et o aamete evaluated. At the end the bet-eomng oluton ound. Deent technque can be ued to eom the each o the bet oluton [5, 6]. In the eld o electcal dve egulato ae alo emloyed o moto contol. The tuctue and an equvalent tane uncton o th contolle ae hown n Fg.. The vaable to be contolled ae geneally oton, eed, toque, cuent o voltage. The act that the meauement o thee gnal can contan condeable noe make the tuctue wthout the devatve at moe utable. One examle o alcaton whee egulato ae emloyed the FOC tategy o PMSM dve. + = + = k / Fg.. contolle tuctue and tane uncton Th ae eent the alcaton o two oula method o tunng the egulato o the FOC PMSM dve: the AVO and SO cteon [, 7]. The model o the PMSM eented togethe wth the FOC contol cheme. The AVO and SO cteon ae exlaned and aled o the ytem unde tudy. Fnally ome mulated and exemental tet ae eomed n ode to evaluate the oluton obtaned.. PMSM FOC The model o the PMSM n a otatng d-q ame xed to the oto gven by the ollowng equaton: ψ d = Ld d + Ψ () ψ = L () q q q dd vd = Rd + Ld Lqq () dq vq = Rq + Lq + ( Ld d + Ψ ) (4) Γ e = P ( ψdq ψqd ) (5) whee ψ d, ψ q, v d, v q, d and q ae eectvely the moto luxe, voltage and cuent n d-q axe; the electcal angula eed, Γ e the electomagnetc toque, Ψ the lux o the emanent magnet and P the numbe o ole a. R the tato etance and the tato nductance can be dvded nto two deent comonent L d and L q due to the atculate o the PMSM. The model comleted by the mechancal equaton, whch dened a: dm J = Γe Γl Bm (6) = P (7) whee J the neta o the moto and couled load, the load toque, B the cton coecent and m m Γ l

2 5 Exemental evaluaton o tunng technque the mechancal angula eed. Smlaly to nducton moto, n PMSM a decouled contol o the toque and lux magntude can be acheved, emulatng a DC moto, by mean o the FOC tategy. Th done ung the d-q tanomaton that eaate the comonent d and q o the tato cuent eonble o lux and toque oducton eectvely [8]. Due to the eence o the contant lux o the emanent magnet, thee no need to geneate lux by mean o the d cuent, and th cuent can be ket equal to zeo value, whch n tun deceae the tato cuent and nceae the ecency o the dve. The contol cheme o the FOC tategy hown n Fg.. * * d d + + L q q d,q L d d a,b,c d q d,q a,b,c Fg.. FOC contol cheme o PMSM a b PMSM The contol ytem dvded nto thee deent loo: the d loo, whch contol the lux, the q loo, whch contol the toque and the eed contol loo. The d loo eom the contol o d wth a cuent egulato. The eeence value. The q-ax contol ytem contan two contol loo n cacade. The nne loo contol the toque by mean o contollng q wth a cuent egulato. The act that the toque can be contolled by mean o q come om the ollowng mlcaton o (5), vald o Suace Mounted (SM) PMSM: Γ e = PΨ q (8) The eeence o th nne loo gven by the oute loo, whch contan a eed egulato. Fom the voltage equaton o the PMSM model () and (4) t can be een that d and q axe ae not comletely ndeendent and thee ae coulng tem whch deend on the cuent om the othe ax. To acheve comletely ndeendent egulaton t neceay to cancel the eect o thee coulng tem at the outut o the cuent egulato. Wth the ue o decoulng t acheved the lneazaton o the contol ytem a well a hghe dynamc. Th decoulng acton can be een n Fg. [9, ].. TUNING WITH THE AVO AND SO CRITERIONS In ode to obtan a atactoy contol eomance t neceay to adjut the aamete o the egulato ncluded n the FOC cheme. In the eld o electcal dve two method ae equently emloyed n th aametc otmzaton: the AVO and SO cteon [, 7]. The AVO cteon can be aled to degn both cuent egulato, whle the SO can be emloyed to degn the eed egulato hown n Fg. []. Thee two method emloy an aoxmate tane uncton o the ytem to be contolled. Some modellng and aamete dentcaton o the ytem ae theeoe needed. The AVO method aume the ytem tane uncton n oen loo o the ollowng om []: G( ) = τ ( + τ ) (9) On the othe hand, the SO method conde the ytem oen loo tane uncton a ollow: + 4τ G( ) = 8 τ ( + τ ) () whee τ um o all mall delay n loo. Both method can be aled when the τ much malle than the tme contant o the ytem. The te eone o both tane uncton n cloed loo ncooatng the egulato degned ung the AVO and SO cteon a hown n Fg.. Table eent the man eatue o the te eone obtaned wth both method. Amltude.5.5 SO AVO 4 5 Tme () Fg.. AVO and SO chaactetc te eone Tab.. Ste eone o AVO and SO method AVO SO Re Tme 4.7 τ. τ Settlng tme (%) 8.4 τ 6.5 τ Ovehoot 4.% 4.4% Phae Magn 65.5º 7º I both method ae comaed t can be ad that the SO ate egadng ubance ejecton, whch make t utable o the eed loo. On the othe hand AVO ha a malle ettlng tme and lowe ovehoot, whch make t aoate to have qucke and moe accuate nne loo [].

3 Advance n Electcal and Electonc Engneeng 6 a) Cuent loo ( d and q contol) In ode to degn the egulato an aoxmated tane uncton ha to be dened accodng to the AVO cteon. Ft o all, the extng delay n the ytem need to be taken nto account. Thee delay n the cae o a moto dve ae due to the dgtal mlementaton o the contol (whch mle the amlng o gnal), the ue o lte, the oceng o the contol algothm and the ue o Pule Wh Modulato (PWM). Fg. 4 how the block dagam o the cuent contol n cloed loo wth all the delay condeed. q * egulato q q q Poceng delay q Cuent lte VSI Samlng Fg. 4. Cuent loo block dagam Moto R L q R To make t oble to aly the AVO cteon, the eedback delay mut be taneed to the owad ath. The eultng block dagam hown n Fg. 5. * q q k q q q q R L q R q q q q q L q q k q τ = τ + τ ; = ; k = (5) q q τ τ The eultng cloed loo tane uncton o the econd ode tye. Becaue econd ode tane uncton can be aoxmated by a t ode tane uncton wth the ame ettlng tme, the nne loo can be aoxmated a ollow: G q cloe ( ) = (6) q + In ode to tune the cuent egulato n d ax t can be ollowed the ame ocedue decbed, but n th cae ung the nductance n d ax L. b) Seed loo The eed loo degned by mean o the SO method. A n the cuent loo, the eed loo contan ome delay that need to be dened. Fo th loo, t common to ue a amlng tme ten tme hghe than the amlng tme o the cuent loo. Fg. 6 how the tane uncton o the eed loo wth all the delay condeed and ncooatng the nne q ax cuent loo tane uncton dened n (6). τ d Fg. 5. Smled block dagam o the cuent loo * egulato Poceng delay q G P cloe + q - Cuent contol and moto P J The ollowng aoxmaton can be made due to act q that τ = τ : G( ) = ( + τ )( + ( τ / ) )( + ( τ / ) )( + τ q ) ' () G( ) G ( ) = () + ( τ + τ q ) In ode to adat the tane uncton to the denton o the AVO method, the egulato tme contant ha to be equal to tme contant o the lant. Th n tun wll deceae ode o oen loo tane uncton. Samlng and eed lte Fg. 6. Seed loo block dagam A mla degn oce a n the AVO method ollowed to adat the tane uncton to the SO cteon n the eed contol loo. Fo mlcty the load toque and cton tem ae neglected. The mled block dagam ang the eedback delay to the owad loo and goung all the delay hown n Fg. 7. * T l P J G L q q τ = () R ( ) = = (4) L q q q q ( + ( τ ) ) ( ) + τ τ + τ q k q oen q q Fnally the value o k and k can be calculated a ollow: Fg. 7. Smled eed loo block dagam The um o all delay n the owad loo τ dened a: q τ q τ = τ + τ + τ τ (7)

4 7 Exemental evaluaton o tunng technque and the eultng oen loo tane uncton ha the aoate om to aly the SO method: G oen + τ + 4τ + + τ ( ) = = τ 8( τ ) ( τ ) J ( ) ΨP k (8) Fnally the value o the egulato can be obtaned a ollow: J τ = 4 τ ; = ; k = ΨP τ τ (9) 4. SIMULATED AND EXPERIMENTAL RESULTS The method decbed n the evou ecton have been emloyed to tune the d and q cuent egulato (AVO cteon) and the eed egulato (SO cteon). The eultng egulato have been teted ung a mulaton model and alo an exemental etu. The exemental etu cont on a Semen KF7 PMSM wth the chaactetc hown n Table, a Dano VLT56 owe convete and a DSPACE DS contol boad. Tab.. PMSM chaactetc (Semen KF7) Nomnal Outut Powe (P n ) 5W Nomnal Seed ( n ) Nomnal Toque (M n ) m 6.8N m Nomnal Cuent (I n ) 4.4A Numbe o ole a (P) 4 Stato etance (R ).9 Stato nductance (L d and L q ).4H Ineta (J) 4.5e -4 Kg m Pemanent Magnet Flux ( Ψ ).8Wb The eultng et o contol aamete calculated ae hown n Table. Tab.. Calculated aamete egulato k Outut Satuaton d I n q I n.94.8 V DC Some adonal nomaton egadng the contol hown n Table 4. Tab. 4. Adonal contol aamete Samlng tme o cuent ( τ ) Samlng tme o eed ( τ ) m DC-lnk Voltage (V DC ) 8 Cuent lte tme contant Seed lte tme contant 5 5m The t tet eomed cont on the eed te eone. A comaon between the deal eone obtaned emloyng the AVO method and the mulated and exemental eult hown n Fg. 8. It can be een that mulated and exemental eult ae vey mla. In both cae the ovehoot malle than the deal eone. Th due to the cton tem o the mechancal equaton (6) that nceae the damng o the ytem. It can be alo aecated the noe eent n the exemental eone and a hghe ettlng tme. eed [ad/] Smulated Ideal Exemental tme [] Fg. 8. Comaatve te eone The next tet mlemented a eed ole whch eom a eed eveal. Fg. 9 and Fg. how the mulated and exemental eult. The vaable hown ae the moto electcal eed ( ), the cuent ( d and q ), and two hae cuent ( a and b ). The mulated and exemental eult ae alo vey mla o the eed ole tet. Thee eult llutate a atactoy tackng o the eed ole. The load toque n th tet only due to the cton. It can be een how the d ket to zeo excet o the tanent whee ome cuent eak ae oduced. Fgue and how the mulated and exemental eult eectvely to the tackng o an q ole. Fo th tet the eed elmnated and the eeence o q gven by a ole whch nclude a toque eveal. It can be een that the exemental eult eent moe ocllaton and oton caued by the noe o the eal ytem and the oeaton o the owe convete.

5 Advance n Electcal and Electonc Engneeng 8 w [ad/] q [A] d [A] a,b [A] tme [] tme [] Fg. 9. Smulated (let) and exemental (ght) eult o the eed ole tet 4 4 q [A] q [A] tme [] Fg.. Smulated eult o the q ole tet tme [] Fg.. Exemental eult o the q ole tet

6 9 Exemental evaluaton o tunng technque The nal tet eented ha been caed out only n mulaton to llutate the eect o the load toque on the eed eone. It can be een that nceang the load toque eult on a bgge e tme due to the atuaton o the eed egulato outut. The level o the atuaton theeoe nluence the eone tme o the eed loo. Fg. how the eed eone wth deent level o load toque. eed [ad/] 5 5 % Tload 5% Tload % Tload.5..5 tme [] Fg.. Comaatve te eone o deent load toque conon 5. CONCLUSION Th ae eent the exemental and mulated eomance o the tunng AVO and SO method aled to a FOC PMSM dve. The ocedue to obtan the aamete o the egulato ha been decbed o th alcaton. The eult o the deent dynamc tet eented how a atactoy contol eone o the eed and cuent loo. Oveall the tunng method emloyed eem to ovde a vald oluton o the ntal commonng o the dve ytem unde tudy. In adon the mulaton model emloyed ha oved to be vey accuate and the mlaty wth the exemental eult vey hgh. Any dvegence obeved between mulated and exemental eult ae due to: noe n the eal etu, naccuacy o the moto and load aamete and the oeaton o the convete. Acknowledgement Th eeach oject ha been uoted by a Mae Cue Ealy Stage Reeach Tanng Fellowh o the Euoean Communty Sxth Famewok Pogamme unde contact numbe MEST-CT Electcal Enegy Conveon and Conon. REFERENCES [] K.J. Atöm and T. Hägglund: D Contolle: Theoy, Degn, and Tunng, nd ed. Reeach Tangle Pak, NC: Intum. Soc. Ame., 995. [] J.G. Zegle and N.B. Nchol: Otmum ettng o automatc contolle, Tan. ASME, vol. 64, , Nov. 94. [] J. H. H. Go, J. Hamann and G. Wegatne, Electcal Feed Dve n Automaton: Bac, Comutaton, Dmenonng, Munch, Gemany: Semen Aktengeellchat,. [4] A. O Dwate: Handbook o and D contolle tunng ule, Imeal College Pe, London,. [5] K.J. Atöm and T. Hägglund: Advanced D Contol, ISA, 6. [6] C.-C. Yu: Autotunng o D contolle, New Yok: Snge-Velag, 999. [7] L. Szklak, K. Jaack and A. Hoodeck: Electc Dve Sytem Dynamc. Selected Poblem, Stude n Electcal and Electonc Engneeng 7. Eleve, 99 [8] R. Khnan: Electonc Moto Dve: Modelng, Analy and Contol, Ue Saddle Rve, New Jeey, USA: Pentce Hall, Feb.. [9] D. W. Novotny, T. A. Lo: Vecto Contol and Dynamc o AC Dve, Oxod Unvety Pe, 996. [] P. Balazovc: 6F8 Hybd Contolle ued n Contol o Electomechancal Bake, Feecale Semconducto, Alcaton Note, 999.