Parameters Identification of Separately Excited DC Motor using Adaptive Tabu Search Technique

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1 Ltest Trends on Circuits, Systems nd Signls Prmeters dentiiction o Seprtely Excited DC Motor using Adptie Tbu Serch Technique S. Udomsu, K-L. Areer, K-N. Areer * nd A. Sriew Abstrct This pper presents the prmeters identiiction or DC motor using dptie tbu serch technique. The speed responses rom testing re used in the ATS serching process. The results show tht the ATS technique is ery useul nd esily pplied or system identiiction ppliction. Keywords Seprtely Excited DC motor, Adptie Tbu Serch, dentiiction.. NTODUCTON DC motors re widely used in industries. The dntges o DC motor re s ollows: it cn be controlled or wide rnge, cn be esily used or constnt torque nd speed, cn be quicly ccelerted or decelerted, nd cn response to eedbc control [1]. Hence, DC motors re the importnt mchine in the most control systems such s electricl systems in homes, ehicles, trins, nd ircrts. t is well nown tht the mthemticl model is ery crucil or control system design. For DC motor, there re mny models to represent the mchine behior with good ccurcy. Howeer, the prmeters o the model re lso importnt becuse the mthemticl model cnnot proide correct behior without correct prmeters in the model. Normlly, the prmeters cn be determined by the testing. These prmeters rom testing sometime re incorrect or not good enough or the design becuse the testing process is ery complicted. As result, the mthemticl models proide some errors. Thereore, there re mny techniques to determine mchine prmeters to chiee the better ccurcy. The reported techniques or serching prmeters re Tbu serch [], Klmn ilter [3], genetic lgorithm [4]-[5], rtiicil neurl networs [6], nd etc. This pper presents the ppliction o dptie Tbu serch (ATS) to determine the DC motor prmeters. The ATS technique is widely used or the optimiztion problem becuse it cn escpe the locl optimum point to the globl point. The oeriew o DC motor model is described in Section. The testing results o DC motor or the identiiction process re gien in Section. The concept o ATS or mchine The uthors re with the School o Electricl Engineering, Surnree Uniersity o Technology (SUT), Nhon tchsim, Thilnd. The inncil supports rom SUT re grethly cnowledged *Correspondence: ongpn@sut.c.th identiiction is explined in Section V nd the results o serching mchine prmeters i the ATS technique re shown in Section V. Finlly, the conclusion nd discussion re ddressed in Section V.. THE MATHEMATCAL MODEL OF DC MOTOS A. The equilent circuit The equilent circuit o seprtely excited DC motor [7] consists o independent two circuits, rmture circuit nd ield circuit, in which lods re connected to the rmture circuit s shown in Fig. 1. ω Fig. 1 The equilent circuit o seprtely excited DC motor. The mthemticl model From Fig. 1, Kircho s oltge lw (KVL) is pplied to the rmture circuit. These cn be written. di eg (1) i L Setting e g in (1) equl to K i ω, the rmture oltge eqution in (1) becomes di i L Ki ω () where K is oltge constnt (V.s/rd). SSN: SN:

Ltest Trends on Circuits, Systems nd Signls Ting the Lplce trnsorm into () yields V L s K ω( s) (3) The eqution (3) cn be rewritten to new orm to gie V K ω( s) sl From Fig.

2 Ltest Trends on Circuits, Systems nd Signls Ting the Lplce trnsorm into () yields V L s K ω( s) (3) The eqution (3) cn be rewritten to new orm to gie V K ω( s) sl From Fig.1, the mechnicl motion eqution is gien by dω T J ω d T L Ting the Lplce trnsorm into (5) nd setting T d (s) K t (s) nd T L (s)0 yields Kt sj (4) (5) ω (6) From the boe prmeters, nd cn be determined rom the mesurement. For the DC motor o this pper, nd re equl to 13 Ω nd 591Ω, respectiely. Note tht these lues re set s n initil solution or the ATS method. For the our remining prmeters, their initil lues re rndomly determined. This is becuse the prcticl mesurement or these prmeters is ery complicted.. DC MOTO TESTNG The rted DC motor or this pper is s ollows: Armture circuit: V,rted 0 V,,rted. A, P rted 0.37 W, ω rted 360 rpm Field circuit: V,rted 0 V,,rted 0.3 A The results rom DC motor testing will be used or ATS serching. For testing, the rmture oltges o 60, 100, 160, 00, nd 0 V were imposed with constnt ield oltge (equl to rted oltge 0 V) under no-lod condition. The experimentl rig o the testing is shown in Fig.. The speeds o DC motor or ech rmture oltge re depicted in Fig. 3. where K t is torque constnt (N.m/A). Substituting (s) rom (4) into (6), the trnser unction between rmture oltge (V ) nd motor speed (ω) cn be written ω V J s K t J s 1 ( K V ) (7) Setting K K t [8] to gie ω V J s K J s 1 ( KV ) (8) Fig. The experimentl rig or DC motor testing where K K K t C. DC motor prmeters or ATS serching There re six prmeters o DC motor s shown in (8) or ATS serching. These prmeters re s ollows - is n rmture resistnce (Ω) - is ield resistnce (Ω) - L is n rmture inductnce (H) - J is moment o inerti (g.m ) - is iscous riction coeicient (N.m.s/rd) - K is constnt lue SSN: SN:

3 Ltest Trends on Circuits, Systems nd Signls speed (rpm) V 0V V 00V V 160V V 100V V 60V time (s) Fig. 3 The motor speed o ech rmture oltge rom the testing V. APPLYNG ATS ALGOTHM TO A DC MOTO DENTFCATON ATS technique is the extended ersion o the Tbu serch (TS) lgorithm by dding the both concepts, nmely bc trcing nd dptie rdius. These both concepts cn improe the perormnce o TS method. The TS technique normlly proides the locl solution when the problem is complicted hing mny locl points. Hence, the bc trcing prt nd dptie rdius dded to TS lgorithm (clled ATS) cn escpe the locl loc to proide the globl solution. The more detils o ATS cn be ound in [9]. The digrm o ATS or determining the DC motor prmeters is depicted in Fig. 4. n Fig.4, the ATS method will serch the DC motor prmeters (6 prmeters) nd then use these prmeters with eqution (8) to clculte the speed o ech rmture oltge. The speed clculted rom (8) with prmeters rom ATS is clled Speed (simultion) s shown in Fig. 4. The mchine prmeters in (8) re ried ollowing on the ATS lgorithm until mtched speed response between Speed (simultion) nd Speed (experiment) is obtined. The experimentl results o mchine speed re gien by the testing rom Section s shown in Fig.3. n terms o n optimiztion problem, the ATS will serch the pproprite prmeters o the motor to minimize the error lue between the simultion nd the testing. This error cn be clculted by using the root men squre (rms) deinition s gien by e N [ speedexp eriment, ( i) speed simultion, ( i) ] i 1 where e is the rms error or ech rmture oltge N is the number o used or both testing nd simultion n this pper, the number o rmture oltge used or serching is equl to 5 inputs (60, 100, 160, 00, nd 0 V). Thereore, the cost lue (W) or ATS lgorithm cn be clculted by N (9) Fig. 4 loc digrm or serching DC motor prmeters using ATS SSN: SN:

Ltest Trends on Circuits, Systems nd Signls m e W 1 (10) m where W is the cost lue or ATS lgorithm m is the number o the inputs tht re used or serching The reserch wor in [9] reported tht the ATS

4 Ltest Trends on Circuits, Systems nd Signls m e W 1 (10) m where W is the cost lue or ATS lgorithm m is the number o the inputs tht re used or serching The reserch wor in [9] reported tht the ATS method cn escpe the locl solution to chiee the better solution. To support the wor in [9], the results in Fig. 6 lso show the conergence o ATS or this problem. t cn be seen tht the ATS method cn escpe the locl point to the better W lue. According to (10), the objectie o the ATS method is to serch the mchine prmeters until minimum W is obtined. V. SEACHNG ESULTS FOM ATS METHOD The six prmeters in (8) cn be determined rom the ATS method nd these prmeters re gien in Tble. Tble Mchine prmeters rom ATS method prmeters lues (Ω) (Ω) L (H) J (g.m 3 ) (Nm.s/rd) 4.557e e-005 K (Nm/A) The comprison between the Speed (simultion) nd Speed (experiment) is ddressed in Fig.5. t cn be seen tht the speeds o ech rmture oltge input when we use the mchine prmeters in Tble re nerly the sme s those o the testing. speed (rpm) experiment simultion Fig. 6 The conergence o W V. CONCLUSON Normlly, the prmeters o DC mchine cn be determined rom the testing. Howeer, the testing or some prmeters is ery complicted. As result, the model proides some error becuse o the incorrect prmeters in the model. Thereore, this pper presents how to pply the ATS technique to identiy the mchine prmeters. The motor speeds o ech rmture oltge rom the experiment re used in the serching process. The pper shows tht the mthemticl model with the prmeters rom ATS method cn obtin the speed response (Speed simultion ) nerly the sme s those o the testing (Speed experiment ). Hence, the good greement o the speed responses is to conirm tht the prmeters rom the proposed method re correct. From the results, it lso shows tht the ppliction o ATS method to the system identiiction is ery useul or engineers. For the uture wor, other lgorithms such s genetic lgorithm or prticle swrm optimiztion will be used to determine the DC motor prmeters. The results will be compred with those o ATS method rom this pper time (s) Fig. 5 The comprison between the speed responses rom simultion nd testing EFEENCES [1] S. J. Chpmn, ELECTC MACHNEY FUNDAMENTALS. oston : McGrw-Hill, [] S. Pothiy, S. Chnposri, S. Kmswng nd W. Kinres, Prmeter dentiiction o DC Motor Using Tbu Serch, KKU Engineering Journl, ol. 30, no.3, pp , 003 [3] S. S. Sb nd. A. Ked-ey, Prmeter dentiiction o DC Motor: An Experimentl Approch, EEE nterntionl Con. on Elec. Circuit nd Systems. (CECS), ol.4, pp , 001. [4] A. Dupuis, M. Ghribi nd A. Kddouri, Multiobjectie Genetic Estimtion o DC Motor Prmeters nd Lod Torque, EEE nterntionl Con. on nd. Tech. (CT), pp , 004. SSN: SN:

5 Ltest Trends on Circuits, Systems nd Signls [5] M. Lnrny nd A. ezzde, Prmeter Estimtion Optimiztion sed on Genetic Algorithm Applied to DC Motor, EEE nterntionl Con. on Electricl Engineering. (CEE), pp.1-6, 007 [6] S. Weersooriy nd M. A. El-Shrwi, dentiiction nd Control o DC Motor using c-propgtion Neurl Networs, EEE Trn. on Engergy Conersion, ol.6, no.4, pp , [7]. C. Dor nd. H. ishop, Modern Control System. Msschussetts : Person Eduction, 008. [8] S-M. e nd T-Y. Kuc, An Adptie PD Lerning Control o DC Motors, EEE nterntionl Con. on Systems, Mn, Cybernetics, ol.3, pp , 1997 [9] D. Pungdownreong, K-N. Areer, A. Sriew, S. Sujitjorn nd P. Totrong, System dentiiction i Adptie Tbu Serch, Proc. EEE nterntionl Con. on nd. Tech. (CT0), pp , 00. SSN: SN:

Why symmetry? Symmetry is often argued from the requirement that the strain energy must be positive. (e.g. Generalized 3-D Hooke s law)

Why symmetry? Symmetry is often argued from the requirement that the strain energy must be positive. (e.g. Generalized 3-D Hooke s law) Why symmetry? Symmetry is oten rgued rom the requirement tht the strin energy must be positie. (e.g. Generlized -D Hooke s lw) One o the derities o energy principles is the Betti- Mxwell reciprocity theorem.