Modeling and Simulation of Self-Tuning PI Control for Electrical Machines

Transcription

1 oelng an Smlaton of Self-nng PI Contol fo Electcal achnes Zan Abstact hs pape pesents the wok of moelng an smlaton of a self-tnng PI contol fo ncton motos. A mathematcal moel of a thee-phase ncton moto, togethe wth ts self-tnng PI contolle wll be llstate. By sng the compte smlaton, t has been fon that the popose esgn appoach s obst to the vaatons of ncton moto paametes an t acheves the pefomance of global asymptotc spee tackng. Keywos - oelng an smlaton, self-tnng PI contol, nect vecto contol, ncton moto I. INRODUCION he conventonal popotonal-ntegal (PI) contol emans the most popla esgn appoach se n nstal applcatons e to ts smplcty an elablty fo the contol of fst an secon oe plants, an even hgh oe plants wth well-efne contons. A welltne PI contolle s capable n achevng an excellent pefomance. Howeve, t sffes a ccal savantage of gettng a poo pefomance wheneve the plant s sbjecte to some kn of stbance o, the plant has hgh oe nonlnea stcte. Incton moto s a pme choce of vaable-spee ve n a we ange of applcatons e to ts low cost, elablty, an ggeness. Becase of the hghly cople non-lneaty an the vaatons of ntenal paametes, the tnng of PI contolle becomes a challengng poblem when the conventonal PI esgn s apple to the contol poblem of ncton motos [], []. In oe to eal wth ths poblem, self-tnng PI contol fo ncton moto ve has eceve conseable attenton n the lteate [3], [4], an [5]. In ths pape, we have aopte a self-tnng PI contol whch has been evelope n [6]. Conseently, the PI contol gans n ths esgn ae atomatcally ajste onlne. heefoe, ths makes o contolle beng obst to the changes of ncton moto paametes. oelng an smlaton s sally se n esgnng a moto ve n oe to avo blng a system pototype e to the hgh expense. If all components ae coectly selecte, the smlaton pocess col emonstate both the steay state an the ynamc pefomance that wol have been obtane f the ve was actally neee. hs pactce saves tme, an eces the cost of blng a pototype, an most mpotantly t enses that the eements ae beng acheve. Fthemoe, smlaton-base esgn plays an mpotant ole n nestanng an evalatng ncton moto Dgtal ef: A Bsness Development Cente, Ingesoll-Ran Co. t, USA e-mal: zan99@embamal.com he pape fst eceve on 9 ach 006 an n evse fom 9 ach 007. ves. Recently, the wok of moelng an smlaton by sng atlab / Smlnk has been wely se n the Along ths way, we evelope an ente smlaton pogam fo the whole system an also ceate seveal ne moles to eplace the exstng ones n atlab/smlnk. Fo example, n oe to vsalze clealy the elatonshp between ntenal paametes an system pefomances, all of the ffeental eatons have been embee nto the moels of electcal machnes. he theoetcal evaton, moelng wok, an smlaton eslts wll be llstate as follows. II. HE PRINCIPE OF INDUCION OOR ODEING WIH INDIREC VECOR CURREN CONRO Gven seveal assmptons ([7] an [8]), the ynamcal moel of an ncton moto n a fxe efeence fame attache to the stato can be escbe as follows: ( ab ba ) a a b a b R b a b a a ( s ) s b b ( s ) s R Rs b b ( s ) s b () () (3) (4) (5) whee: oto spee, oto flxes ( a, b ), an stato cents ( a,b ) ae state vaables. oto neta, stato (, ) an oto nctances s, mtal nctance, ( R,R ) stato an oto esstances s ae system paametes. Contol npts ae stato voltages ( a,b ). Fo the ppose of cent contol of ncton moto sng the techne of oto-flx-oente vecto contol, the moel of ncton moto can be epesente on - otatng axs, whee the -axs s algne wth the oto flx at all tme an the -axs s always 90 ahea of the - axs. heefoe, we take new vaables smla to [9] an [0] as follows. cos sn a sn cos b a (6) 58

2 Asan Powe Electoncs onal, Vol., No., Ag 007 cos sn a sn cosb cos sn a sn cosb vaables on left se epesent the components of oto flxes, stato cents an stato voltage vectos, espectvely, wth espect to the - otatng axs at spee e an entfe by the angle. In the new state vaables (,,,, ) an new contol npts (, ), the moto ynamcs become: ( ) (9) ( e ) (0) R ( e ) () R s R ( ) e s ( s ) ( ) () s s s R s ( ) e s ( s ) ( s ) s s (7) (8) (3) when the cent-contolle PW nvete s apple, the moel can be ece to a th-oe system, whch s wely se n the ncton moto contol esgn ([], [], an [3]). ( ) (4) R ( e ) (5) R ( e ) (6) Accong to the oto-flx-oente vecto contol ([4] an [5]), the oto flx s algne wth the axs an kept at a constant so that we have the followng elatons n steay state: 0 (7) const. (8) Applyng (7) an (8) nto (5) an (6), we can get the slp feency an the flx cent n steay state s e (9) (0) he vecto contol techne shown above gaantees that the tansent tems vansh n shot tme. heefoe, the steay state eatons ae sffcent fo the evaton of spee contol esgn. he contol objectve now s to esgn a spee contolle so that tacks. As a conseence, Fg., n whch K agam of spee contol esgn. III. SEF-UNING PI CONRO DESIGN, shows the block De to ts smplcty an elablty, the conventonal PI contol emans the most popla metho se n moto contol. Howeve, snce the vaaton an the hgh ncetanty of ncton moto ntenal paametes, the tnng of PI contol gans becomes a challengng poblem. In ths sty, we apply the concept that has been pesente n [6] to evelop a self-tnng PI contol an elmnate any epenence on the contol moel of ncton moto. Fst, we ve the whole system nto thee pats as shown n Fg., whch s smla to the one gven n [6]. Pat s the popotonal pat wth the excepton of popotonal gan K P. Pat s the ntegal pat wth the excepton of ntegal gan K I. Pat 3 s the contol plant. hen we conse K P an K I as nepenent vaables. Base on the pncple of gaent escent optmzaton, we constct a cost fncton as E e ( ) () Usng the algothm of gaent escent E K, K { K P, K I K } () an followng the evatve of chan le, we can obtan the followng tnng algothm K P ey (3) K I ey whee s an aaptve coeffcent. IV. SIUAION RESUS In oe to evalate an valate the effectveness of o popose contol esgn pesente n the pevos sectons, a smlaton pogam has been evelope by sng atlab/ Smlnk. Fg. 3 shows the block agam of the ente moto ve system. he mole of the smlaton pogam s shown n Fg. 4. Fg. 5 shows the moel of ncton moto. he specfcatons fo the ncton moto ae [7]: moto powe = 5kW (ate), loa toe = 70Nm (ate), oto flx lnkage =.3Wb (ate), angla spee = 0 a/s (ate), n =, = kgm, Rs = 0.8, s = H, = 0.068H, = 0.5, = H. In o smlaton, we take the change of oto esstance as Rs(t) = Rs( exp(-at)) n whch a = an gve ffeent loa toes. et s see the ynamc behavos of ncton moto fom the eslts of Fg. 6 when the moto ns n fo aants. Fg. 6(a) shows that the moto ns wthot loa. Fg. 6(b) pesents that the moto ns wth 00% loa. In Fg. 6, one can see that the contol system of ncton moto acheves a goo tackng pefomance. 59

3 Spee Contolle K _ S Fg. : Spee contol esgn fo ncton moto wth oto-flx-oente vecto contol + e s y y K P K I K 3 S Fg. : he esgn of self-tnng PI fo ncton moto + - Self-tnng PI Contolle tg hee-phase Stato Cents Fast Cent PW Voltage Soce Fg. 3: he whole block agam of the ncton moto ve system Fg. 4: atlab/smlnk moel of the ncton moto ve system

4 Asan Powe Electoncs onal, Vol., No., Ag 007 Fg. 5: Smlnk moel of an ncton moto 40 0 Spee Comman Roto Spee Spee ( a/s ) me ( Sec. ) (a) 40 0 Spee Comman Roto Spee Spee ( a/s ) me ( Sec. ) (b) Fg. 6: (a) Spee esponse n fo aants wthot loa. (b) Spee esponse n fo aants wth 00% loa 6

5 V. CONCUSION he wok of moelng an smlaton of an ente ncton moto ve system contolle by a self-tnng PI contolle has been pesente n ths pape. In aton a novel etale Smlnk moel fo ncton moto has been llstate, whch allows s to clealy vsalze the elatonshp between the ntenal paametes an the system pefomances. By sng the compte smlaton, t has been fon that the popose esgn appoach s obst to the vaatons of ncton moto paametes an acheves the pefomance of global asymptotc spee tackng. REFERENCES [] G.W. Chang, G.E. Peez, E. enes an R. Otega, nng Rle fo the PI Gans of Fle-Oente Contolles of Incton otos, IEEE ans. In. Electon., Vol. 47, ne 000, pp [] H. an,. Chang an.a. Chaffee, Pactcal oton Contol oelng an PI Desgn, Poceengs Amecan Contol Confeence Chcago, 000. [3]. She an. Chen, Self-nng Contol of Incton oto Dve Usng Neal Netwok Ientfe, IEEE ans. Enegy Conveson, Vol. 4, Decembe 999, pp [4]. A annan,. ata,. ama an. schya, Fzzy-ogc-Base Self-nng PI Contolle fo Spee Contol of Inect Fel-Oente Incton oto Dve, SICE Annal Confeence n Sappoo, 4-6 Agst, 004. [5]. okan, R. Abesseme, A Fzzy Self-nng PI Contolle fo Spee Contol of Incto oto Dve, IEEE Confeence Contol Applcaton, Istanbl, key, 003. [6] Z., Hyb Spee Contol wth Slng-oe Pls Self- nng PI fo Incton oto Dve, Poceengs IEEE WSCAS 006, Peto Rco, 006. [7] R. ano an P. ome, Nonlnea Desgn: Geometc, Aaptve an Robst, Pentce Hall, onon, 995. [8] P.C. Kase, Analyss of Electc achney, New Yok, cgaw Hll, 996. [9] R. ano, S. Peesaa an P. ome, Global Aaptve Otpt Feeback Contol of Incton oto wth Uncetan Roto Resstance, IEEE ans. Atomat. Cont. Vol. 44, ay 999, pp [0] K. Wang,. Chasson,. Boson an.. olbet, A Nonlnea east-saes Appoach fo Ientfcaton of the Incton oto Paametes, IEEE ans. Atomat. Cont. Vol. 50, Octobe 005, pp [] K. Shy an H.. Sheh, A New Swtchng Sface Slng-oe Spee Contol fo Incton oto Dve System, IEEE ans. Powe Electon, Vol., ly 996, pp [] R. ano, S. Peesaa an P. ome, Otpt Feeback Contol of Cent-Fe Incton otos wth Unknown Roto Resstance, IEEE ans. Cont. Syst. echnol., Vol. 4, ly 996, pp [3]. Boson,. Chasson an R. Novotank, Hgh- Pefomance Incton oto Contol va Inpt-Otpt neazaton, IEEE Cont. Syst. ag., Vol. 4, anay 994, pp [4] B.K. Bose, Powe Electoncs an AC Dves, Englewoo Clffs, N, Pentce-Hall, 986. [5] Y. Xa, X. Y an W. Oghana, Aaptve Robst Fast Contol fo Incton otos, IEEE ans. In. Electon., Vol. 47, Agst 000, pp [6] F. n, R.D. Ban, G. Sakals, Self-nng of PID Contolles by Aaptve Inteacton, Poc. Amecan Contol Conf., Chcago, 000. [7] R. ano, S. Peesaa an P. Valg, Aaptve Inpt- Otpt neazng Contol of Incton otos, IEEE ans. Atomat. Cont. Vol. 38, Febay 993, pp [8]. Kst, I. Kanellakopolos, P. Kokotov, Nonlnea an Aaptve Contol Desgn, ohn Wley & Sons, NY, 995. [9] W. eonha, Contol of Electcal Dves, 3 e. Beln, Gemany, Spnge-Velag, 00. 6