World Academy of Scence, Engneerng and echnology Vol:5, No:5, 11 Fuzzy Logc Speed Controller wth Reduced Rule Base for Dual PMSM Drves Jurfa Mat Laz, Zulkfle Ibrahm, Marzan Sulaman, Fzatul An Patakor, St Noormza Mat Isa Internatonal Scence Index, Electrcal and Computer Engneerng Vol:5, No:5, 11 waset.org/publcaton/1885 Abstract Dual motor drves fed by sngle nverter s purposely desgned to reduced sze and cost wth respect to sngle motor drves fed by sngle nverter. Prevous researches on dual motor drves only focus on the modulaton and the averagng technques. Only a few of them, study the performance of the drves based on dfferent speed controller other than Proportonal and Integrator (PI) controller. hs paper presents a detaled comparatve study on fuzzy rule-base n Fuzzy Logc speed Controller (FLC) for Dual Permanent Magnet Synchronous Motor (PMSM) drves. wo fuzzy speed controllers whch are standard and smplfed fuzzy speed controllers are desgned and the results are compared and evaluated. he standard fuzzy controller conssts of 49 rules whle the proposed controller conssts of 9 rules determned by selectng the most domnant rules only. Both desgns are compared for wde range of speed and the robustness of both controllers over load dsturbance changes s tested to demonstrate the effectveness of the smplfed/reduced rulebase. Keywords Dual Motor Drves, Fuzzy Logc Speed Controller, Reduced Rule-Base, PMSM I I. INRODUCION N many applcatons, one motor s controlled by one converter. hese systems are called SMSC, Sngle Machne Sngle Converter system [1]. Mult Machne Systems (MMS) are more and more used for ndustry today. hese systems allow to extend the feld of hgh power applcatons or to ncrease ther flexblty, mechancal smplcty and safety operatng. However, t ncludes a lot of power swtches whch are large n sze, costly and bulky. he hgh cost and large sze of the nverter make such dual nverter, dual motor drve confguratons economcally less compettve. herefore, the need for dual motor drves fed by sngle nverter s growng consequently to reduce sze and cost wth respect to the sngle motor drves, ether n ndustral or n tracton applcaton. But, the reducton number of power electroncs swtches and other components wll results the parallelng of the drves systems. If the load torque for each motor s stll the same, there s no speed changes wll be encountered because every motor wll J.M.Laz s a PhD student n Faculty of Electrcal Engneerng, Unuverst eknkal Malaysa, Melaka. (e-mal: jurfa@utem.edu.my). Z. Ibrahm s wth Faculty of Electrcal Engneerng, Unverst eknkal Malaysa Melaka, Malaysa. (e-mal: drzulkfle@utem.edu.my). M. Sulaman. s wth Faculty of Electrcal Engneerng, Unverst eknkal Malaysa Melaka. (e-mal: marzan@utem.edu.my). F. A. Patakor s a PhD student n Faculty of Electrcal Engneerng, Unuverst eknkal Malaysa, Melaka (e-mal: fzatulan@student.utem.edu.my) S.N.M.Isa s a MSc student n Faculty of Electrcal Engneerng, Unversty eknkal Malaysa, Melaka. (e-mal: st_noormza@yahoo.com) have the same behavor []. On the other hand, a varaton of load for both motors wll create perturbatons on the electrcal part and perhaps a malfunctonng of the system. For ths type of dsturbance, a control drve s needed to compensate the dsturbance n order to make the system back to ts orgn. After several readng, mean and dfferental torque [],[4],[5],[6] technque s selected to overcome the loss of adhere of the motor, rather than conventonal averagng technque that treat the dual motor as a sngle motor. II. FUZZY LOGIC CONROLLER For wdespread ndustral applcatons, such as hgh performance motor drves, accurate motor speed control s requred n whch regardless of sudden load changes and parameter varatons [7]. Hence, the control system must be desgn very carefully as t requred to ensure the optmum speed operaton under the envronmental varatons, load varatons and structural perturbatons. Alternatve control strateges have been studed extensvely n attempts to provde accurate control capablty. Among many knds of control schemes, fuzzy logc controller (FLC) s one of the superor schemes used for plants havng dffcultes n dervng mathematcal models or havng performance lmtatons wth conventonal lnear control schemes [8]. Reference [7] also mentoned that the FL and neural network (NN) became a pleasng approach to hgh performance controllers for non lnear systems and has been practcal to electrcal drves. he present paper presents a study of a DC motor wth FL speed controller. Besdes that, FLC s broadly used by numerous publcatons wth dversty of ndustral drve applcatons such as vector controlled nducton motor [9],[1],[11], permanent magnet synchronous motor [1],[1], brushless DC motor [14] and swtched reluctance motor [15],[16].heoretcally, FL s based on human reasonng, provdng algorthms whch can convert a set of lngustc rules based on expert knowledge nto an automatc control strategy. here s no need of mathematcal models to deal wth a problem, but skll s needed to create the rules n a partcular FL controller [17]. hs pont also beng supported by [1] whch stated that a fuzzy control algorthm embeds the ntuton and experence of an operator desgner and researcher as the concept of FLC s to utlze the qualtatve knowledge of a system to desgn a practcal controller.dual PMSM drves are at frst modeled n MALAB/Smulnk program. As mentoned before, the standard controller s desgned based on the Internatonal Scholarly and Scentfc Research & Innovaton 5(5) 11 6 scholar.waset.org/17-689/1885
World Academy of Scence, Engneerng and echnology Vol:5, No:5, 11 Internatonal Scence Index, Electrcal and Computer Engneerng Vol:5, No:5, 11 waset.org/publcaton/1885 common crtera of fuzzy speed controller that have been revewed from varous publcatons. hs means 49 rules s a standard approach for the FL speed control wth PMSM drve applcaton. Meanwhle, the proposed controller conssts of 9 rules whch are formed by mnmzng the number of membershp functon used. In ths case, three rules for speed error and three rules for change n speed error s used, so that x = 9 rules are produced. he same PMSM drve model s beng used for standard 49 rules and smplfed 9 rules, so that a far comparson s enabled. It has to be noted that 49 rules are represented by standard desgn and the proposed controller are represented by case desgn.he results from both controllers are beng compared and evaluated to show the approprateness and effectveness of the proposed controller whch ams to acheve the followng propertes: robustness around the varety of operatng condtons and nvarant dynamc performance n presence load dsturbance whle mantanng the performance obtaned by standard desgn controller. III. DUAL PMSM DRIVE SYSEM he basc structure of the dual PMSM drves wth hysteress current control n the statonary reference frame and wth Fuzzy Logc speed controller s shown n Fg.1. hree ndependent hysteress current controllers n the three phase a,b,c reference frame are appled n ths scheme. In hgh performance servo drves, hysteress current controllers are used to ensure that the actual currents flowng nto the motor are as close as possble to the current references. ω 1 ω d,1 d, q,1 q, DQ abc DQ abc ω 1 ω 1( a, b, c ) a, b, c ( a, b, c ) Fg. 1 Hysteress Current Control for Dual PMSM confguraton b* 1 a* c* 4 c,act 5 b,act 6 a,act HCCa HCCb HCCc Fg. Hysteress Current Control Fg.. shows the block dagram for hysteress controller n order to produce the output sgnal. he 1 a b c actual phase currents ( a, b, c ) are compared wth reference phase current ( a *, b *, c *) usng three ndependent comparator n hysteress controller. he logc condton for sx nverter swtches s chosen by the output of the comparator [1].When the phase a current s smaller than (*-Δ), where Δ s the hysteress band, the output of the comparator s 1, the a phase wll be connected wth the postve track of DC lnk. In contrast, f the phase a current s bgger than ( *- Δ ), the output of the comparator wll become, and the a phase wll connected to the negatve track of DC bus. A smlar procedure exsts n the other legs. he reason that ths s called a hysteress controller s that the leg voltage swtches to keep the phase current wthn the hysteress band. he phase currents are, therefore, approxmately snusodal n steady state. he smaller the hysteress band, the more closely do the phase currents represent sne wave. Small hysteress band, however, mply a hgh swtchng frequency, whch s a practcal lmtaton of the power devce. Increased swtchng frequency also mples ncreased nverter losses. A. Mathematcal model he smulated machnes are smooth ar gap PMSMs wthout any dampng crcuts n the rotor. he rotors feld are constant and created by permanent magnets and the e.m.f are consdered as snusodal. he smplfed electrc equatons for motor 1 can be presented as below []: d1 v1 = R1 + L + jpω r,1ψ r,1 dt (1) dω r,1 1 L,1 = J dt () wth 1 = pim{ 1 ψ r,1 } dθ1 ω r,1 = () dt Where; ω r : Motor Angular velocty, Ψ r : Rotor flux, : Electrcal torque, L : Load torque, J : Moment of Inerta. θ : Instantaneous angular poston he model of the motor can be derved from (1) to () by changng the subscrpt 1 to. Wth the assumptons, motor 1 and motor are equal n all parameters but have dfferent loads. he space vectors of the rotor fluxes, ψ r,1 and ψ r, are equal n magntude and ts nstantaneous poston θ 1 and θ respectvely n the statonary frame. Consder a rotatng reference frame d,q whose drect axs d s along the drecton of (ψ r,1+ ψ r, )/ and ts nstantaneous angular poston s θ=(θ 1+ θ )/. Based on ths reference, the electromagnetc torque of the motors 1 and can be expressed as: 1 p. ψ r,1. q,1 = (4) Internatonal Scholarly and Scentfc Research & Innovaton 5(5) 11 64 scholar.waset.org/17-689/1885
Internatonal Scence Index, Electrcal and Computer Engneerng Vol:5, No:5, 11 waset.org/publcaton/1885 pψ r,. q, = (5) And the average Σ and dfferental Δ of the current and torque and torque are as follows: 1 + 1 = 1 + = ; : Δ = (6) 1 Δ = (7) he FLC, as llustrated n Fg., s a standard structure wth nputs of speed error, e and change n speed error, ce and output s change n q-axs reference current, qs * he trangular membershp functon s used and the nput and output scalng factors are determned. By referrng to Fg. b, the FLC executes the rule base takng the fuzzy varables e and ce as the nputs and quantty of qs * as the output are processed n the defuzzfcaton unt. Fg. Fuzzy Logc Controller Internal Structure of FLC ABLE I PMSM ES MOOR No Motor Specfcatons Value 1 Rated orque 8 Nm Rated Speed 9 rad/s Inerta.69 kgm 4 Resstance.9585 Ω 5 Inductance.55 H 6 Magnet Flux.187 Vs 7 DC lnk Voltage B. Desgn of Fuzzy Logc Controller he man goal of the control system s to determne the effectveness of the case desgn for hgh performance PMSM drve by comparng the speed response wth standard desgn obtaned.he standard desgn s desgned frst, on the bass of the speed response to the step rated speed command (9 rad/s) under no-load condtons wth rated nerta. he desgn crtera are set n terms of a speed overshoot less than.1 rad/s and mnmum rse tme consderng the lmted current capablty of the nverter. he scalng factors, G e, G ce and G cu are chosen for fuzzfcaton, as well as for obtanng the actual output of the command current. hese scalng World Academy of Scence, Engneerng and echnology Vol:5, No:5, 11 factors play a vtal role for the FLC whch effect the stablty, oscllatons and dampng of the system, hence needs to be chosen wth utmost care [11]. he factors G e and G ce are chosen to normalze the speed error and the change n speed error respectvely. he factor G cu s so chosen that one can get the rated current for rated condtons. Fne tunng to the specfcaton s acheved by tral and error. herefore, the constants are taken as G e =., G ce = 4 and G cu = n order to get optmum drve performances. For the next step, the membershp functons of e, ce and cu are determned whch perform mportant tasks of the FLC and beng man focused n ths paper. wo dfferent fuzzy sets are desgned as shown n Fg. 4 and Fg. 5 respectvely. he shape of the fuzzy sets on the two extreme ends of the unverse of dscourse s taken as trapezodal whereas all other ntermedate fuzzy sets are trangular wth overlap to each other as standard approach. he wdth of trangular membershp functon s dvded equally n a range (Unverse of Dscourse) wth overlap to each other. Fg. 4 Membershp functons of standard desgn for speed error, change n speed error and q-axs command current he fuzzy rule-base matrx for standard desgn and case desgn are shown n able II and able III respectvely. As declared prevously, the rules of the standard desgn are determned by common crtera from many publcatons whle the rules of the case desgn parameters are determned by standard approach wth reducng the number of fuzzy rule-base. he lngustc elements used are the same as those used n most publcatons [9],[17]. Fxed-step mode s selected for the computatonal tme nterval. Numercal method for solvng dfferental equatons s Dormand-Prnce and Mamdan-type fuzzy nference s used [11]. he values of constants, membershp functons and fuzzy sets for nput/output varables n ths study are selected by tral and error to obtan the optmum drve performance. Internatonal Scholarly and Scentfc Research & Innovaton 5(5) 11 65 scholar.waset.org/17-689/1885
World Academy of Scence, Engneerng and echnology Vol:5, No:5, 11 IV. RESULS 1 speed(s) -1 Internatonal Scence Index, Electrcal and Computer Engneerng Vol:5, No:5, 11 waset.org/publcaton/1885 Fg. 5 Membershp functons of case desgn for speed error, change n speed error and q-axs command current Change n speed error, ce ABLE II MARIX OF SANDARD DESIGN Speed error, e NL NM NS ZE PS PM PL NL NL NL NL NL NM NS ZE NM NL NL NL NM NS ZE PS NS NL NL NM NS ZE PS PM ZE NL NM NS ZE PS PM PL PS NM NS ZE PS PM PL PL PM NS ZE PS PM PL PL PL PL ZE PS PM PL PL PL PL ABLE III MARIX OF CASE DESIGN Speed error, e N ZE P Change n speed error, ce N N N ZE ZE N ZE P P ZE P P Seven terms are assgned n able II: NL, negatve large; NM, negatve medum; NS, negatve small; ZE, zero; PS, postve small; PM, postve medum; and PL, postve large. hree terms are assgned n able III: N, negatve; ZE, zero; and P, postve. Each fuzzy varable s a member of the subsets wth a degree of membershp µ varyng between and 1. As mentoned before, for convenence, the rules have been wrtten n matrx form and should be nterpreted as (Refer to able II): IF speed error s NS AND change n speed error s PS HEN change n q-axs reference current s ZE.All the scalng factors, shape of membershp functon, method of fuzzfcaton and method of defuzzfcaton are predefned and kept constant durng the research except the number of rules. - speed m -..4.6.8 1 1-1 - speed m -..4.6.8 1 Fg.6. Speed response Fuzzy logc usng 49 rules, Fuzzy logc usng 9 rules for the case of L m 1 =1Nm, L m 1 =.5Nm at t=.9s Fg.6. shows the speed response durng start-up at t=s, reverse operaton at t=.s, then forward operaton at t=.5s for Fuzzy logc 49 rules and 9 rules respectvely. Both cases are appled torque load changes at t=.9s about 1Nm for motor 1 and.5nm for motor. For the case of low load, the motors are not too affected by the changes. But ths stuaton s dfferent n the case of hgher torque load appled as depcted n Fg.7. 1-1 - -..4.6.8 1 1-1 - speed m speed m -..4.6.8 1 Fg.7. Speed response Fuzzy logc usng 49 rules, Fuzzy logc usng 9 rules for the case of L m 1 =8Nm (rated speed), L m 1 =4Nm at t=.9s Internatonal Scholarly and Scentfc Research & Innovaton 5(5) 11 66 scholar.waset.org/17-689/1885
World Academy of Scence, Engneerng and echnology Vol:5, No:5, 11 Internatonal Scence Index, Electrcal and Computer Engneerng Vol:5, No:5, 11 waset.org/publcaton/1885 1 Fuzzy logc 49 rules Fuzzy logc 9 rules -1.5.1.15. 1-1 - -.15..5..5.4 (c) 18 16 14 Fuzzy 49 rules L=4Nm Fuzzy 9 rules L=4Nm Fuzzy logc 49 rules Fuzzy logc 9 rules L=8Nm Fuzzy logc 49 rules L=8Nm Fuzzy logc 9 rules 1.88.9.9.94.96.98 1 Fg.8. Speed responses comparson durng start-up durng reverse operaton and (c) durng varaton of load dsturbance for Fuzzy logc 49 rules and Fuzzy logc 9 rules Fg.8. shows that, the proposed Fuzzy logc desgn usng 9 rules gves better performance compared to standard desgn wth 49 rules, n term of rse tme. Both desgns are good enough so, that no overshoot happen durng start-up and reverse operaton. Only for the case of dfferent load appled, both motors wll produce small undershoot responses before get t steady-state operaton after.6s. 18 16 14 1 m1 : L=1Nm m : L=.5Nm m : L=4Nm m1 : L=8Nm (rated torque).85.9.95 1 18 16 14 m1 : L=1Nm m : L=.5Nm m : L=4Nm m1 : L=8Nm(rated torque) 1.85.9.95 1 Fg.9. Fuzzy logc 49 rules, Fuzzy logc 9 rules, zoom n for dfferent type of load torque Fg.9. shows the effect of load varaton of both standard and case desgn n order to test the robustness of the proposed controller. From ths fgures, t show that, the case desgn wth 9 rules gve better response n term of less undershoot at t=.9s compared to standard desgn. hs s due to the number of rules that the system need to calculate s much lower n the case of 9 rules compared to 49 rules. hese fgures also prove that, the hgher load appled, the more severe mpact to the system. 4-15% of rated speed 1% of rated speed 5% of rated speed -4..4.6.8 1 4-15% of rated speed 1% of rated speed 5% of rated speed -4..4.6.8 1 Fg.1. Fuzzy logc 49 rules, Fuzzy logc 9 rules, zoom n for dfferent type of rated speed at rated torque ( L m 1 =8Nm, L m =4Nm) Fg.1. proves the robustness of the Fuzzy logc controller, whch both desgns produce almost consstent undershoot for wde range of dfferent speed, and able stable agan after several mllsecond (.6s) after unbalance load condton. V. CONCLUSION hs paper presents the results of a detaled comparatve study on Fuzzy logc speed controller n Dual PMSM drves. wo fuzzy speed controllers whch are standard desgn 49 rules and case desgn -9 rules are studed. Performance of both desgns are compared for dfferent type of load dsturbance and for wde range Internatonal Scholarly and Scentfc Research & Innovaton 5(5) 11 67 scholar.waset.org/17-689/1885
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