A Novel Speed Controller Based on Lagrange s Interpolation for Closed-loop Control of a CSI-fed Induction Motor Drive

Transcription

1 A Novel Speed Cotroller Based o Lagrage s terpolato for Closed-loop Cotrol of a CS-fed ducto Motor Drve S. M. Trpath A. K. Srvastava A. K. Padey 3 Abstr Ths work ams to vestgate the feasblty of a ovel speed cotroller based o Lagrage s terpolato (L for better performace of a self-commutated curret source verter-fed ducto motor drve. The L speed cotroller s based upo the look-up table prepared from a seres of smulated patters of referece p speed vs. speed error of the classcal P speed cotroller. The performace of the drve employg ths ovel L speed cotroller s evaluated aalytcally for a -hp ducto motor ad s compared to that wth classcal P speed cotroller usg MATLAB smulato. Keywords Closed-loop cotrol, curret source verter, ducto motor drve, Lagrage s terpolato (L, speed cotroller. 6. NTRODUCTON ducto motors hgh performace varable speed drve applcatos have a seres of advatages. For such kd of applcato, the varable speed drve requres a good power processg system ad a good cotroller. A good power processg system s charerzed by ts smplcty, ruggedess, ad lower cost. The curret source verter (CS has all these features. CS-fed ducto motor drve, the curret source at the frot ed makes the system aturally capable of power regeerato []-[3]. Proportoal plus tegral (P cotrollers, whch are covetoally employed for CS-fed ducto motor drves; suffer from some lmtatos as the desg of these cotrollers depeds o ex mathematcal model wth accurate parameters [4]. A model referece adaptve cotroller (MRAC was reported to mprove the behavor of CS-fed ducto motor drve. However, wde rage of speed cotrol, the desg of MRAC cotroller becomes rather complcated [4]. The desg of tellget cotrollers based o artfcal tellgece (A does ot eed the ex mathematcal model of the system. Therefore, artfcal eural etwork (ANN ad fuzzy logc cotrol (FLC demad specal atteto for speed cotrol of hgh performace ducto motor drves [5]-[6]. The ma desg problem wth FLC les the determato of cosstet ad complete rule set ad shape of the membershp fuctos. The paper frst receved 9 Feb ad revsed form 6 July. Dgtal Ref: A974 Departmet of Electrcal Egg., Kamla Nehru sttute of Techology, Sultapur (U.P., da, E-mal: ma_excel@yahoo.co. Departmet of Electrcal & Electrocs Egeerg, Kamla Nehru sttute of Physcal & Socal Sceces, Sultapur (U.P., da, E-mal: aakt.srvastava3@gmal.com 3 Departmet of Electrcal Egeerg, M. M. M. Egeerg College, Gorakhpur (U.P., da, E-mal: akp34@gmal.com O the other had, ANN aloe s suffcet f the trag data are ot eough to take care of all the operatg modes [6]. the preset paper, the closed-loop scheme of a selfcommutated curret source verter-fed ducto motor drve employg a ovel Lagrage s terpolato (L based speed cotroller s vestgated for better performace.. LAGRANGE S NTERPOLATON (L BASED SPEED CONTROLLER The covetoal CS-fed ducto motor drve system essetally cossts of a three-phase AC source, a PWM rectfer, a DC lk smootheg reor, a curretcotrolled verter, a three-phase squrrel cage ducto motor, a three-phase capor bak, ad two P cotrollers oe the outer speed feedback loop ad the other the er curret feedback loop. the preset work, the outer P speed cotroller of the covetoal CS-fed ducto motor drve system [7]-[8] has bee replaced by a ovel speed cotroller based o the Lagrage s terpolato (L techque as show Fgure. The closed-form mathematcal model of the CS-fed ducto motor drve system has bee cosdered the same as developed [8] excludg the speed cotroller outer feedback loop. The cotrol law for the L based speed cotroller outer feedback loop s developed ths secto. The L based speed cotroller compares the referece speed ad the ual rotor speed ad processes the speed error to obta the referece p speed (. The fuctoal relatoshp betwee referece p speed ad the speed error ref ca be expressed as: ( r ( ; Polyomal terpolato s based o the well kow f that ay th order polyomal s uquely determed by ( pots wth dstct argumet values. Complat wth a famous theorem due to Weerstrass [9], the sglevalued fucto ca be approxmated by a polyomal P passg through the ( pots [, ( ] ;,,, wth very small error,.e. P ( A A A A ( where A s are costats.

2 Asa Power Electrocs Joural, Vol. 6, No., Oct Fg. : Varable speed self-commutated curret source verter-fed ducto motor drve wth L speed cotroller O puttg, P ( ;,,, (, ( A, A, A ad elmatg, A the followg expresso s obtaed: ( ( ( ( ( ( ( ( ( ( ( ( Expadg terms of the elemets of the frst colum, the requred cotrol law for Lagrage s terpolato based speed cotroller s obtaed as follows: j ( (4 j j j Numerous patters for referece p speed vs. speed error wth covetoal P speed cotroller, keepg parameters such as k ad k to optmal values for a gve ps s loadg codto, are obtaed through a MATLAB program. A few of these patters are selected to costtute a look-up table, whch of course s the result of a few repeated trals. These look-up data sets are cosdered as ( pots vz. [, ( ] ;,,, the cotrol law (4 for Lagrage s terpolato based speed cotroller. Usg (4 the value of referece p speed ca be determed wheever speed error s. Ths referece p speed ( s requred to estmate the referece stator ve curret (, referece stator reve curret ( re of the ducto motor ad the (3 swtchg frequecy of the verter ( e usg the followg equatos: k costat (5 re k costat (6 e r (7 Here, k ad k are the opes of the stator ve curret vs. p speed ad stator reve curret vs. p speed charerstcs respectvely. These charerstcs are obtaed expermetally [7]. The referece DC lk curret s determed usg the equatos: ref re c'. k (8 c ' re c (9 c k e c ( rated ( e ( rated k ( (. SMULATON RESULTS AND DSCUSSONS Smulatos are fually focused o whether or ot the performace of the drve wth L-P (L speed ad P curret cotrollers s better tha that wth P-P (P speed ad P curret cotrollers. For the comparso terms of the percetage overshoot, settlg tme ad steady-state error, MATLAB smulatos of the covetoal CS drve employg P-P cotrollers ad the proposed CS drve employg L-P cotrollers are performed for dfferet step varatos referece speed each after a terval of secods as show Fg.. For a clear judgmet, the resposes of the drve are cosdered separately for each alterato referece speed. 7

3 Fg. : Respose of the drve for step chages referece speed each after a terval of secods Fg.3: Respose of the drve for step chages referece speed from rad/s to 98.9 rad/s Fg.4: Respose of the drve for step chages referece speed from 98.9 rad/s to 75 rad/s Fg. 5: Respose of the drve for step chages referece speed from 75 rad/s to 5 rad/s 8

4 Asa Power Electrocs Joural, Vol. 6, No., Oct Fg. 6: Respose of the drve for step chages referece speed from 5 rad/s to 98.9 rad/s Fg. 7: Respose of the drve for step chages referece speed from 98.9 rad/s to 5 rad/s Fg.8: Respose of the drve for step chages referece speed from 5 rad/s to 75 rad/s Fgs: 3-8 show the speed ad DC lk curret resposes of the drve separately for step chages referece speed from rad/s to 98.9 rad/s (start-up, 98.9 rad/s to 75 rad/s (decelerato, 75 rad/s to 5 rad/s (decelerato, 5 rad/s to 98.9 rad/s (accelerato, 98.9 rad/s to 5 rad/s (decelerato, ad 5 rad/s to 75 rad/s (accelerato respectvely. The steady-state DC lk curret, percetage overshoot, drve settlg tme ad steady-state error correspodg to dfferet alteratos referece speed stated aforesad, are summarzed Table-. t has bee foud that the steadystate value of the DC lk curret s creased / decreased wth crease / decrease motor speed. The percetage overshoot ad settlg tme of the drve wth L based speed cotroller s less tha that wth the covetoal P speed cotroller. t s also observed that the steady-state error speed respose of the drve wth L based speed cotroller s more tha that wth covetoal P speed cotroller. f, ths s due to the error assocated wth the approxmato of the fucto by meas of a polyomal P. However, the percetage steady-state error s wth the prescrbed lmt of %. Ths way the speed ad curret respose curves obtaed through MATLAB smulato ad fs Table show the success of proposed L based speed cotroller. 9

5 Sr. Step-chage referece speed (rad/s Table : Performace of the drve for each alterato referece speed Steady-state DC lk curret (A Speed overshoot (% Drve settlg tme (s Steady-state speed error (% From To L - P P - P L P P - P L P P - P L - P P - P V. CONCLUSONS A ovel speed cotroller based o Lagrage s terpolato has bee troduced for CS-fed ducto motor drve ad the cotrol law for L speed cotroller s establshed. The drve s smulated for both P ad L speed cotrollers for dfferet speed varatos the referece speed. The results for both cotrollers uder each varato referece speed are compared ad aalyzed. t s observed that the chages the DC lk currets, accordace wth ay dsturbaces the referece speed, are mmedate wth L-P cotrollers whe compared wth P-P cotrollers. Though, t s also see that the steady state error the speed respose of the drve s more wth L speed cotroller tha that wth covetoal P speed cotroller, yet t s wth prescrbed lmt ad s, therefore, acceptable. Moreover, the CS fed ducto motor drve system usg a L speed cotroller has reduced speed overshoot ad settlg tme compared to the system wth a P speed cotroller. Ths way, the smulato results have proved the feasblty ad better performace of the proposed speed cotroller based o Lagrage s terpolato for closed-loop cotrol of a selfcommutated CS-fed ducto motor drve. APPENDX Name plate ratgs of ducto motor hp, three-phase, 4 V, 5 Hz, 4-pole, 45 rpm, star ducto motor parameters R s = 3.5 R r =.78 L s =.65 H L r =.65 H L m =.5 H J =.89 kg-m Parameters of DC lk ad capor bak R f =.5, L f =.4 H, C = 5 µf DC Geerator specfcato hp, V, 4 A, 5 rpm, shut coected REFERENCES [] P. Agarwal ad V. K. Verma, Performace Evaluato of Curret Source verter-fed ducto Motor Drve, Jourals of sttuto of Egeers, vol.7, pp. 9-7, February 99. [] P.N. Ejet, P.D. Zogas ad J.F. Ldsay, Programmed PWM Techque to Elmate Harmocs: A Crtcal Evaluato, EEE Trasos o dustry Applcatos, vol. 6, o., pp. 3-35, March/Aprl 99. [3] Y. Xao, B. Wu, S. Rzzo ad R. Sotude, A Novel Power For Cotrol Scheme for Hgh Power GTO Curret Source Coverter, Coferece Record EEE-AS, pp , 996. [4] C. M. Law, C.T. Pa ad Y.C. Che, "Desg ad mplemetato of a Adaptve Cotroller for Curret-fed ducto Motor", EEE Tras. o d. Electrocs, vol. 35, o.3, pp , 988. [5] Rajesh Kumar, R.A. Gupta, S.V. Bhagale ad Hmashu Gothwal, ANN Based Cotrol ad Estmato of Drect Torque Cotrolled ducto Motor Drve, Asa Power Electrocs Joural, vol., o. 3, pp. 5-, Dec. 8. [6] Rajesh Kumar, R. A. Gupta ad Rajesh S. Surjuse, Adaptve Neuro-Fuzzy Speed Cotroller for Vector Cotrolled ducto Motor Drve, Asa Power Electrocs Joural, vol. 3, o., pp. 8-4, Sept 9. [7] Pramod Agarwal, A.K. Padey ad V.K. Verma, Performace vestgato of Modfed Self-commutated CS-fed ducto Motor Drve, Asa Power Electrocs Joural, vol. 3, o., pp. -9, Sept 9. [8] S.M. Trpath ad A.K. Padey, Dyamc Performace Aalyss of Self-commutatg PWM CS-fed ducto Motor Drve uder MATLAB Evromet, Asa Power Electrocs Joural, vol. 5, o., pp. 9-4, August. [9] S.S. Sastry, troductory Methods of Numercal Aalyss, Pretce-Hall of da, New Delh, 3 rd Edto, Chapter 3, May. BOGRAPHES Saurabh Ma Trpath s presetly workg as Assstat Professor of Electrcal Egeerg at Kamla Nehru sttute of Techology, Sultapur, (U.P., da. He obtaed hs B.Tech. degree Electrcal & Electrocs Egeerg 6 ad dd hs M.Tech. Electrcal Egeerg 9 from U.P. Techcal Uversty, Luckow. He has authored several books o Moder Cotrol System ad Basc System Aalyss. Hs areas of curret terest clude electrcal maches, cotrol systems, power electrocs ad electrc drves. Akt Kumar Srvastava s wth the departmet of Electrcal & Electrocs Egeerg at Kamla Nehru sttute of Physcal & Socal Sceces, Sultapur, (U.P. da. He receved hs B.Tech. degree Electrcal Egeerg 8 from V.B.S. Purvachal Uversty, Jaupur, (U.P., da. He dd hs M.Tech. Power Electrocs ad Drves from Kamla Nehru sttute of Techology, Sultapur, (U.P., da. Hs terests are the areas of power electrocs ad electrc drves. Ashok Kumar Padey receved hs Ph.D. degree Electrcal Egeerg from da sttute of Techology, Roorkee 3. He dd hs M.Tech. Power Electrocs, Electrcal Maches ad Drves from da sttute of Techology, Delh 995. Curretly, he s workg as a Assocate Professor wth the Departmet of Electrcal Egeerg at M.M.M. Egeerg College, Gorakhpur, (U.P., da. Hs areas of terest clude power electrocs, electrcal maches, ad drve.