Adaptive Controllers for Permanent Magnet Brushless DC Motor Drive System using Adaptive-Network-based Fuzzy Interference System

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1 Amerin Journl of Applied Sienes 8 (8): , 2011 ISSN Siene Pulitions Adptive Controllers for Permnent Mgnet Brushless DC Motor Drive System using Adptive-Network-sed Fuzzy Interferene System 1 V.M. Vrthrju, 2 Bdrill Mthur nd 3 Udhykumr 1 Deprtment of Eletril Engineering, Ann University, Chenni, , Indi 2 Deprtment of Eletril Engineering, SSN College of Eingineering, Klvkkm, , Indi 3 Deprtment of Eletril Engineering, Ann University, Chenni, Indi Astrt: Prolem sttement: The tuning methodology for the prmeters of dptive speed ontroller uses trnsient devition of the response from the set referene following vrition in lod torque in permnent-mgnet rushless DC (BLDC) motor drive system. Approh: This study develops mthemtil model of the BLDC drive system, firstly. Seondly, disusses design of the losed loop drive system employing the Adptive-Network-sed Fuzzy Interferene System (ANFIS). The nonliner simultion model of the BLDC motors drive system with ANFIS ontrol sed is simulted in the MATLAB/SIMULINK pltform. Results: The neessitted dt for trining the ANFIS ontrol is generted y simultion of the system with onventionl PI ontroller. Conlusion: The simulted eletromgneti torque nd rotor speed signify the superiority of the proposed tehnique over the lssil method. Key words: Adptive ontrol, PMBLDC motor, speed ontrol, ANFIS INTRODUCTION The Permnent Mgnet Synhronous Motor (PMSM) hs sinusoidl k emf nd requires sinusoidl sttor urrents to produe onstnt torque while the rushless DC (BLDC) motor hs trpezoidl k emf nd requires retngulr sttor urrents to produe onstnt torque (Vrthrju et l., 2010). The BLDC motor is permnent-mgnet synhronous mhine supplied from six-trnsistor inverter whose on/off swithing is determined y the rotor position (Sing et l 2003; Pilly nd Krishnn, 1989). The omplete performne nlysis with design exmple of n xil field permnent mgnet motor servo drive hs een disussed (Rdwn nd Goud, 2005). A digitl speed ontroller for BLDCM nd implemented in digitl signl proessor hs een proposed (Singh et l., 2003). Vs (1998) hs developed the rotor position nd the speed of permnent mgnet hs een estimted y Extended Klmn Filter (EKF). The Hll Effet sensor re usully needed to sense the rotor position whih senses the position signl for every 60 degree eletril (Jdri nd Terzi, 2001). The rhiteture nd lerning proedure under lying ANFIS (dptive-network-sed fuzzy inferene system) hve een well disussed. The ANFIS is fuzyy inferene system implemented in the frmework of dptive networks (Kisi, 2005; Hung nd Uddin, 2006). ANFIS hs een inorported with two input vriles nd one ontrol output vrile (Uddin et l., 2007). This study dels with the losed loop modeling of PMBLDC motor onsidering the non-linerity in the torque-lne eqution nd development of n ANFIS ontroller for improving the trnsient response following torque disturnes. MATERIALS AND METHODS PMBLDCM drive nd modeling: Figure 1 desries the si uilding loks of the PMBLDCM drive. The drive onsists of speed ontroller, referene urrent genertor, PWM urrent ontroller, position sensor, the motor nd IGBT sed Current Controlled Voltge Soure Inverter (CC-VSI). The PMBLDC motor is modeled in the 3-phse vriles. The generl volt-mpere eqution for the iruit shown in the Fig. 2 n e expressed s: V n = R i + p λ (1) n V n = R i + p λ (2) n Corresponding Author: V.M. Vrthrju, Deprtment of Eletril Engineering, Ann University, Chenni, , Indi 810

2 Am. J. Applied Si., 8 (8): , 2011 λ = LSi M(i + i ) (5) λ = LSi M(i + i ) (6) λ = LSi M(i + i ) (7) Fig 1: Blok Digrm of PMBLDC motor drive where, Ls nd M re the self nd mutul indutnes, respetively. The PMBLDC motor hs no neutrl onnetion nd hene this results in: i + i + i = 0 (8) Sustituting (8) into (5), (6) nd (7) the flux linkges re given s: λ = i (L + M) s λ = i (L + M)nd s λ = i (L + M) s (9) Fig. 2: Inverter nd BLDCM equivlent iruit By sustituting (9) in volt-mpere Eq. 1-3 nd rerrnging these equtions in urrent derivtive of stte spe form, gives: Fig. 3: Adptive neurl network V n = R i + p λ (3) n where, V n, V n nd V n re phse voltges nd my e defined s: V n = V o V no, V n = V o V no nd V n =V o V no (4) where, V o, V o, V o nd vno re three phse nd neutrl voltges with respet to the zero referene potentil t the mid-point of d link (0) shown in the Fig. 2. R is the resistne per phse of the sttor winding, p is the time differentil opertor nd e n, e n nd e n re phse to neutrl k emfs. The λ, λ nd λ re totl flux linkge of phse windings, nd respetively. Their vlues n e expressed s: p i = ( V n R i n ) / ( L s + M ) (10) p i = (V n R i n ) / ( L s + M ) (11) p i = (V n R i n ) / (L s + M ) (12) The developed eletromgneti torque my e expressed s: T e = (e n i n i n i ) / ( ω r ) (13) where, ω r is the rotor speed in eletril rd./se. ANFIS sed ontrol: An dptive network, s its nme implies, is network struture onsisting of nodes nd diretionl links through whih the nodes re onneted. Moreover, prt or ll of the nodes re dptive, whih mens eh output of these nodes depends on the prmeter(s) pertining to this node, nd the lerning rule speifies how these prmeters should e hnged to minimize presried error mesure. The si lerning rule of dptive networks is sed on the grdient desent nd the hin rule. Fuzzy Logi Control (FLC) is gret tool to del with omplited, non-liner nd ill-defined systems. Artifiil Neurl Network (ANN) hs the powerful 811

3 Am. J. Applied Si., 8 (8): , 2011 pility for lerning, dpttion, roustness nd rpidity. In ANFIS the dvntges of oth the FLC nd ANN hve een omined. ANFIS is lss of dptive networks tht is funtionlly equivlent to fuzzy inferene system. This ontrol methodology solves the prolem of non-linerity nd prmeter vritions of PMBLDC drive. ANFIS is designed for PMBLDC motor. The dptive network, shown in Fig. 3, is multilyer feed forwrd network in whih eh node performs prtiulr funtion (node funtion) on inoming signls s well s set of prmeters pertining to this node. The formule for the node funtion my vry from node to node. Consider sugeno type of fuzzy system hving the rule se: If x is A 1 nd y is B 1, then f 1 =p 1 x+q 1 y+r 1 If x is A 2 nd y is B 2, then f 2 =p 2 x+q 2 y+r 2 If the firing strengths of the rules re w 1 nd w 2, respetively, for the prtiulr vlues of the inputs A i nd integrl of B i, then the output omputed s weighted verge: wi wi = w + w 1 2 (17) Lyer 4: This lyer s i th node output is liner funtion of the third lyer s i th node output nd the ANFIS input signls: wi fi w i(pix qiy r i) = + + (18) Lyer 5: This lyer sums ll the inoming signls: f = w f + w f (19) RESULTS AND DISCUSSION In this work the drive model with PI Speed ontroller is developed nd simulted, first. The set of equtions representing the model of the drive system hs een disussed. Experimentl results re reorded for the sme motor using developed SIMULINK model in MATLAB. Figure 4-8 show simulted results. The trnsient nd stedy stte responses re otined for 3 phse, 2.0 hp, 4- pole 1500 rpm, 4 A, motor (Detiled motor speifitions re given in ppendix). w f f = w + w f + w (14) Let the memership funtions of fuzzy sets A i, B i, i=1,2, e µ Ai nd µ Bi. Lyer 1: Eh neuron i in lyer 1 is dptive with prmetri tivtion funtion. Its output is the grde of memership funtion; n exmple is the generlized ell shpe funtion: 1 µ (x) = x 1+ 2 (15) Fig. 4: Sttor urrent of BLDC motor where, [,, ] is the prmeter set. As the vlues of the prmeters hnge, the shpe of the ell-shpe funtion vries. Lyer 2: Every node in lyer 2 is fixed node, whose output is the produt of ll inoming signls: W i = µ Ai (x) µ Bi (y), i=1,2 (16) Lyer 3: This lyer normlizes eh input with respet to the others (The i th node output is the i th input divided the sum of ll the other inputs): 812 Fig. 5: Represents the Trpezoidl k EMF of BLDC motor

4 Am. J. Applied Si., 8 (8): , 2011 Fig. 6: Phse voltge (v n ) Fig. 9: Memership funtions of Speed Error fter trining () Fig. 7: Torque nd speed-moment of inerti kgm 2 Fig. 8: Torque nd speed-moment of inerti kgm 2 for step time 0.5 se () () () Fig. 10: Memership funtions of hnge in speed error fter trining In Fig. 7 shows the torque nd speed wveforms for moment of inerti kg-m 2 it rehes the stedy stte torque nd speed suddenly t time 0.03 se. It is inferred tht inresing the moment of inerti then it tkes lrge time to reh stedy stte. The speed error nd hnge in speed error otined using PI ontroller is fed s the input of lyer 1 in ANFIS struture nd trined through GUI tool ox of ANFIS in MATLAB simultion softwre. The resultnt memership funtions for speed error nd hnge in speed error re shown in Fig. 9 nd10 respetively. The omplex ANFIS lyer otined from GUI tool ox fter trining the dt is shown in Fig.11. ANFIS uses the neurl network s ility to lssify dt nd find ptterns. It then develops fuzzy expert system tht is more trnsprent to the user nd lso less likely to produe memoriztion error thn neurl network. ANFIS keeps the dvntges of fuzzy expert system, while removing (or t lest reduing) the need for n expert. The prolem with ANFIS design is tht lrge mounts of trining dt require developing n urte system. Figure 12 shows the retngulr sttor urrent resulted with ANFIS ontroller while Fig. 13 nd 14 show the torque nd speed responses. 813

5 Am. J. Applied Si., 8 (8): , 2011 CONCLUSION Fig. 11: ANFIS lyer otined The performne of the developed MATLAB sed speed ontroller of the BLDC drive hs een nlyzed. The dvntges of fuzzy logi nd neurl network re fused together to form onnetionist dptive network sed fuzzy logi ontroller. The trnsient devition of the response from the set referene following vrition in lod torque is found to e negligily smll long with desirle redution in settling time for the ANFIS ontroller. Beuse of high dynmi performne nd urte speed trking ontrol with good stedy-stte hrteristis, it is proposed for speed ontrol of PMBLDC drives. Firstly, neurl network sed rhiteture is desried for fuzzy logi ontrol. The speified rules nd their memership funtions re to e tuned y the k propgtion lerning lgorithm. The performne of the proposed ontroller is evluted under vrious operting ondition. Fig. 12: Sttor urrent-anfis ontroller Fig. 13: Torque-ANFIS ontroller Fig. 14: Speed-ANFIS ontroller The speed urve does not show ny overshoot nd proves the triumph of the designed ANFIS ontroller. The ANFIS oserves the ehvior of the drive system nd ompres the tul performne to desired referene trk. The lerning lgorithm modifies the ANFIS to more losely mth the desired system ehvior. 814 REFERENCES Hung, Z.R. nd M.N. Uddin, Development of simplified Neuro- Fuzzy ontroller for n IM drive. Proeedings of the IEEE Interntionl Conferene on Industril Tehnology, De , IEEE Xplore, Mumi, pp: DOI: /ICIT Jdri, M. nd B. Terzi, Design nd Implementtion of the Extended klmn filter for the speed nd rotor position estimtion of Brushless motor. Trns. IEEE Indus. Elet., 48: DOI: / Kisi, O., Suspended sediment estimtion using neuro-fuzzy nd neurl network pprohes. Hydrol. Si. J., 50: &ETOC=RN&from=serhengine Pilly, P. nd R. Krishnn, Modeling, simultion, nd nlysis of permnent Mgnet motor drives. Prt II: The rushless d motor drive. IEEE Trns. Ind. Appl., IA-25: DOI: / Rdwn, T.S. nd M.M. Goud, Intelligent speed ontrol of permnent mgnet synhronous motor drive sed-on neuro-fuzzy pproh. Proeedings of the Interntionl Conferene Power Eletronis nd Drive Systems (ICPEDS 05), IEEE Xplore, Kul Lumpur, pp: DOI: /PEDS

6 Am. J. Applied Si., 8 (8): , 2011 Singh, B., B.P. Singh nd K. Jin, Implementtion of DSP sed digitl speed ontroller for permnent mgnet rushless d motor. J. Instit. Eng. Ind. Prt El Elet. Eng. Div., &ETOC=RN&from=serhengine Uddin, M.N., Z.R. Hung nd M.M. Chy, A simplified self-tuned neuro-fuzzy ontroller sed speed ontrol of indution motor drives. Proeedings of the IEEE Power Engineering Soiety Generl Meeting, Jun , IEEE Xplore, Tmp, FL., pp: 1-8. DOI: /PES Vrthrju, V.M., B.L. Mthur nd K. Udhykumr, Comprehensive model of trpezoidl PMBLDC motor nd drive system performne with PI speed ontroller. AMSE Periodils Model., Mesurement Control, php&pg=/dtosrti.php&vis=1&editrt=1&id_ rt=2627 Vs, P., Sensorless Vetor nd Diret Torque Control. 1st Edn., Oxford University Press, USA., ISBN-10: , pp: