An Improved Anti-windup Control Using a PI Controller

Transcription

1 05 Third nernaional Conference on Arificial nelligence, Modelling and Simulaion An mroved Ani-windu Conrol Uing a P Conroller Kyohei Saai Graduae School of Science and Technology Meiji univeriy Kanagawa, Jaan ce4039@meijiacj Yohihia hida School of Science and Technology Meiji univeriy Kanagawa, Jaan ihida@meijiacj Arac n hi udy, we have rooed an imroved aniwindu uing a Proorional-negral (P) ler P ha een widely ued for he indurial alicaion However, P ler i uually deigned in a linear region ignoring he auraion-ye nonlineariy An ani-windu comrie a linear feedac ler ha aifie he deired non-auraion ecificaion and an ani-windu comenaor ha oerae during he auraion Thi mehod reven large overhoo caued y he windu henomenon However, ince he led lan i no ye-, eady-ae error can occur and he inu o he inegral acion i limied To avoid hee rolem, we ranformed he led yem ino a ye- lan Therefore, no eadyae error occur when uing a ye-0 lan and he ouu converge o he arge value Keyword-Ani-windu ; P ; negraor windu NTRODUCTON n acual yem, we reven damage caued y exceive inu y eing an uer and a lower limi However, if he yem incororae an inegraor uch a a P or PD, he inu coninue o increae afer reaching he arge quaniy reuling in an exceive overhoo [] Thi i called he inegral windu henomenon A numer of ani-windu echnique have een rooed o overcome he windu henomenon []-[4] An aniwindu comrie a linear feedac ler ha aifie he deired non-auraion ecificaion and an aniwindu comenaor ha oerae during auraion The ani-windu reven huge overhoo caued y he windu henomenon Thu, i only conider iuaion where he inu limi i uraed and o he inegraor wihou exceeding he limi and reven exceive overhoo However, if he inu ignal i a e and he led lan i of ye-0, eady-ae error can occur and he inu o he inegral acion i limied n hi udy, we rooe an imroved ani-windu mehod We convered he led lan from yem Therefore, even if he led lan i of ye-0, he ouu of he ani-windu yem will follow he arge value wihou reuling in a eady-ae error Thi aer i organized a follow n Secion, we decrie he influence of he ani-windu uing a ye-0 lan n Secion 3, we decrie a echnique o conver a ye-0 lan ino a ye- lan and he rooed mehod n Secion 4, we confirm he effecivene of he rooed mehod uing variou imulaion Finally, in Secion 5, we reen our concluion ANT-WNDUP COMPENSATOR A a ree windu counermeaure, a mehod o o he inegral calculu funcion when an oeraional quaniy reache i uer or lower limi exi [5],[6] The yem i hown in Fig e r y z d z ˆ( ) u ˆ( ) u d u d u Figure Ani-windu comenaor Here, he dead zone (from u d o u d ) i exreed a a linear range of an acuaor and i decried y he following equaion [5],[6]: u ud if ud u, u ud, u ˆ( ) 0 ele if ud u( ) ud Thi yem ecome a P ler when he inu i wihin he limi f an inu auraion occur, he following equaion i ued: u e zd, z e ( u u d ) Suiuing ino, we ge he following equaion: z e ( e zd ud ) zd ud Alying he Lalace ranform, we oain ud Z (5) From he final value heorem, we oain /5 $ EEE DO 009/AMS

2 ud lim z lim Z( ) lim 0 (6) 0 0 Thu, he inu o he inegraor ecome zero Nex, we conider he final value of he inegraor ouu, z ˆ( ) We aume ha he inu i a e ignal, r() = R For a ye- lan, u() ecome zero in eady ae Therefore, we oain he following equaion: u e z ˆ r y z ˆ 0 (7) From he inernal model rincile, he eady-ae error converge o zero Thu, r() = y(), and we have z ˆ( ) 0 Meanwhile, for a ye-0 lan, we have wo condiion derived from he imulaion udy: (i) r u, (8) d And (ii) r u d (9) Cae (i): Afer alying he Lalace ranform, u() can e exreed a U R Y Zˆ ud E E ( U ) ud ( R Y ) ( U ) (0) n he eady ae, we have y u Equaion (0) can e wrien a follow: U ( R U) u ( ( ) d U ) ud R From (0) and, we oain Z ˆ( ) U R Y U R U ( ) U( ) R( ) ud n he eady ae, we oain he following equaion: ud lim z ˆ( ) lim ud 0 Cae (ii): The ouu of he dead zone ecome zero, o U can e exreed a U E E ( R U ) Equaion can e wrien a follow: U( ) R( ) U( ) R( ) U R ( ) (5) From (0) and (5), we oain Zˆ( ) ( ) U R ( ) R( ) R ( ) ( ) ( )( ) ( ) R ( ) R (6) ( ) n he eady ae, we oain he following equaion: R R lim z ˆ( ) lim 0 ( ) (7) From hee wo condiion, we can define an uer limi for he ouu of he inegraor a zˆ( ) u d (8) Meanwhile, a lower limi for he ouu of he inegraor can e decried a ud zˆ( ) (9) Therefore, he range of he inegraor ouu i decried y ud zˆ( ) ud (0) Hence, for a ye-0 lan, he ouu of he inegraor i limied y he uer and lower limi of he dead zone Nex, we conider a cloed-loo yem given y Y G ˆ EZ G ( )( ( ) ( ) ˆ RY Z ( )) Y GY ˆ GR GZ GZ ˆ Y ( G ) R ( G ) R Thu, he cloed-loo yem can e decried a 98

3 Exended Conrolled Plan G Ani-windu Comenaor Conrolled Plan G r e z d z ˆ( ) u v u ua B d A C x y u d u ˆ( ) u d A u Figure Bloc diagram of he rooed mehod Y F R GZ ˆ G G ( ) R ( ) G ˆ Z G ( ) R ( ) Here, he ranfer funcion of a ye-0 econd-order lan i G a a Therefore, he cloed-loo yem i a a Z ˆ( ) F R a a Zˆ( ) ( ) R a a Meanwhile, he ae-eady error i decried y lim e ( ) lim E ( ) lim R ( ( ) Y( )) 0 0 (5) lim ( F( )) R( ) 0 R( lim F( )) (6) 0 Conidering lim F ( ) and he condiion in (i) (ie, 0 zˆ( ) ud ), we have Zˆ( ) R lim F( ) lim 0 0 a a ( R ud) R( ) (7) Thu, he ae-eady error i wrien a R ud lim e ( ) r From he condiion in (ii) (ie, zˆ( ) ), we have 0 (8) lim F ( ) (9) Thu, he ae-eady error i given y lim e ( ) 0 (30) Therefore, for a ye-0 lan, a eady-ae error can occur in he yem DESGN OF AN MPROVED ANT-WNDUP CONTROL The ranfer funcion G can e exreed in he form of ae-ace equaion x Ax Bua, y Cx where, x R, A R, B R, C R, and u are, reecively, defined a x 0 0 x,,, 0, x A a a B C a um if u um, ua u ele if um u um, um ele u um Here, he marice in (33) are alied o a a ae feedac, ie, a A u 0 (33) Therefore, he maniulaed variale i decried in (34) Here, v() i a new maniulaed variale uch ha ua Ax u v (34) Here, A R, B R, and C R are defined a 0 0 A,, 0 a B C 0 99

4 Therefore, he exended led yem i decried a G C A B (36) a n hi udy, we deigned an ani-windu ler uing he exended led yem The rooed mehod i hown in Fig V SMULATON STUDY n hi ecion, we confirm he effecivene of he rooed mehod We imulaed he yem uing MATLAB/Simulin We aumed ha he inu wa a e ignal The iniial value of he e ignal wa r() = 00, and he value changed o r() = 50 a = 00 An inu-ide diurance of magniude wa alied a = 50, and an ouu-diurance of magniude wa alied a = 50 Conider he econd-order lan defined a G, (37) aa where, a = 0033, a = 0375, and = 0033 A CASE : r u d The limi range of he auraion and dead zone are e o ud 04 and um 0, reecively K = 5, = 30, and A u = 0 Fig 3 comare he ouu reone of he rooed and convenional mehod Fig 4 how he maniulaed variale u a () Thee reul how ha he ouu reone of he convenional mehod had a eadyae error, wherea he ouu of he rooed mehod did no Figure 4 Maniulaed variale of he rooed and convenional mehod, for Cae Prooed mehod, convenional mehod wih ani-windu, and convenional mehod wihou ani-windu B CASE : r u d The limi range of he auraion and dead zone were e o ud 4 and um 0, reecively K = 5, = 30, and A u = 0 Fig 5 comare he ouu reone of he rooed and convenional mehod Fig 6 how he maniulaed variale u a () Thee reul how ha he ouu reone of he convenional and rooed mehod did no have a eady-ae error Figure 3 Se reone of he rooed and convenional mehod for Cae Targe value, rooed mehod, convenional mehod wih ani-windu, and convenional mehod wihou ani-windu Figure 5 Se reone of he rooed and convenional mehod, for Cae Targe value, rooed mehod, convenional mehod wih ani-windu, and convenional mehod wihou ani-windu 00

5 Figure 6 Maniulaed variale of he rooed and convenional mehod for Cae Prooed mehod, convenional mehod wih ani-windu, and convenional mehod wihou ani-windu V CONCLUSONS n hi udy, we rooed an imroved ani-windu ler for a ye-0 lan We analyzed he condiion of he arge value i larger han u d (cae (i)) and he arge value i maller han u d (cae (ii)) n addiion, he effecivene of he rooed mehod wa confirmed uing variou imulaion Our echnique reven eady-ae error Alhough i i a imle yem, i ha no overhoo Alo, when a led lan i ye-, we oain he ame reul n indury, in he cae of acuaor ha hyical limiaion, i i execed o how uerior erformance REFERENCES [] H Ogawa, K Saai, K Maumoo, and Y hida, A imle aniwindu aed on a P wih an iniial value of he inegral ae variale, Proceeding of he nd nernainal Conference on Comuer and Auomaion Engineering, Singaore, Singaore, vol, 49-5, 00 [] N Ban, M Ono, K Saai, K Maumoo, H Shiaai, and Y hida, Aniwindu Conrol Scheme wih Dicree Modified nenal Model Conrol, Proceeding of 00 nernaional Conference on Comuaional neligence and Vehicular SyemSeoul, Korea, 6-64, 00 [3] HB Shin, and JG Par, Ani-Windu PD Conroller Wih negral Sae Predicor for Variale-Seed Moor Drive, EEE Tranacion on ndurial Elecronic, vol 50, , 0 [4] JW Choi, and SC Lee, Aniwindu Sraegy for P-Tyoe Seed Conroller, EEE Tranacion on ndurial Elecronic, vol 56, , 009 [5] Wahyudi, T Faial, and A Alagul, Ani-Windu Scheme For Pracical Conrol of Poiioning yem, UM Engineering Journal, vol 5, -5, 004 [6] C Bohn, and DP Aheron, An Analyi Pacage Comaring PD Ani-Windu Sraegie, EEE Conrol Syem Magazin, vol 5,