Performance Comparison of Sliding Mode Control and Conventional PI Controller for Speed Control of Separately Excited Direct Current Motors

Transcription

1 Journl of Science nd Technology Vol. 13, No. 2 Engineering nd Computer Sciences (ECS) Performnce Comprison of Sliding Mode Control nd Conventionl PI Controller for Speed Control of Seprtely Excited Direct Current Motors Amir Hshim Obeid Ahmed Control Engineering Deprtment, Sudn University of Science nd Technology (SUST) mirhmed@sustech.edu Abstrct- Direct Current (DC) motors hve been used extensively in industry minly becuse of the simple strtegies required to chieve good performnce in speed or position control pplictions. This pper ddresses controlling of speed of seprtely excited DC motor which remins mong the vitl issues. A seprtely excited DC motor is generlly controlled by Proportionl plus Integrl (PI) controller. PI controller is simple but sensitive to prmeter vritions nd externl disturbnce. Due to the robustness of Sliding Mode Control (SMC), especilly ginst prmeters vritions nd externl disturbnces, nd lso its bility in controlling liner nd nonliner systems; seprtely excited DC motor sliding mode speed controller technique is proposed in this pper. Performnce of these controllers hs been verified through simultion results using MATLAB/SIMULINK softwre. The simultion results showed tht SMC ws superior controller thn PI controller for speed control of seprtely excited DC motor. Keywords: Direct Current Motors, Speed Control, Proportionl plus Integrl Controller, Sliding Mode Control. (DC) '()*&!" #$ "# % &+ $ #,,'-. / 0-5 &(PI) / 0 & $ :$ "; $ 672 0$ : (SMC)(.-6$ +- (.-6$ #% ; 0 <=# 3>?'7,)*!",#&()* / 0 (.-6$ /$ "3>? MATLAB/SIMULINK>+ & / 0 4 Introduction Direct current motors hve been widely used in mny industril pplictions such s electric vehicles, steel rolling mills, electric crnes, robotic mnipultors, nd home pplinces due to precise, wide, simple, nd continuous control chrcteristics. Therefore, the control of speed of DC motor is n importnt issue nd hs been studied since the erly decdes in the lst century (1). DC motors re generlly controlled by conventionl Proportionl plus Integrl controllers, since they designed esily, hve low cost, inexpensive mintennce nd effectiveness. 74

2 Journl of Science nd Technology Vol. 13, No. 2 Engineering nd Computer Sciences (ECS) With only the clssicl PI controller pplied to control of DC motor, good performnce chrcteristic of the controller cn be obtined, if ll the model prmeters of DC motor nd operting conditions such s externl lod torque, disturbnces re exctly known (2). However, the performnce of PI controller for speed or position regultion degrdes under externl disturbnces nd mchine prmeter vritions. Furthermore, the PI controller gins hve to be crefully selected in order to obtin desired response (3). This mkes the use of trditionl PI controller poor choice for industril vrible speed drive pplictions where higher dynmic control performnce with little overshoot nd high efficiency is required (4-7). The bove issues cn be solved by dvnced control techniques such s sliding mode control. Sliding mode control ws first proposed in erly 1950 s in Soviet Union by Emelynov nd severl co-reserchers. After seventies, SMC hs become more populr control strtegies nd powerful control technology to del with the nonliner uncertin system. The min reson of this populrity is the ttrctive superior properties of SMC, such s good performnce even in the cse of nonliner systems, pplicbility to Multi-Input Multi-Output (MIMO) systems. The best property of the SMC is its robustness. Loosely speking, system with sliding mode control is insensitive to prmeter vritions nd externl disturbnces (8-14). Nevertheless, this type of control hs disdvntge, which is the chttering phenomenon. The chttering phenomenon is understood to be n oscilltory motion in the neighbourhood of the sliding surfce. There re two possible mechnisms which produce chttering. First, chttering my be cused by the switching nonidelities, such s time delys or time constnts. Second the presence of prsitic dynmics (ctutor nd sensor dynmics) in series with the plnt. The chttering phenomenon problem is considered s mjor obstcle for sliding mode control to become one of the most significnt discoveries in modern control theory. Severl solutions hve been proposed in the reserch literture to eliminte or reduce the chttering (15-17). The orgniztion of this pper is s follows. In section II, the stte spce model of seprtely excited DC motor is given. The bsic concept of SMC is briefly reviewed in section III. The section IV, the speed control of seprtely excited DC motor using SMC technique is discussed. The simultion results re stted in section V. The lst section contins the conclusion. The Stte Spce Model of DC Motor Direct current motors re widely used for industril nd domestic pplictions. The control of the speed of DC motor with high ccurcy is required. There re vrious DC motor types. Depending on type, DC motor my be controlled by vrying the input voltge or by chnging the input current. In this pper, the seprtely excited DC motor model is chosen due to its good electricl nd mechnicl performnces compred to other DC motor models. The seprtely excited DC motor is driven by pplied rmture voltge. Figure 1 shows seprtely excited DC motor equivlent model (1-4). Figure 1: A seprtely excited DC motor model The dynmics of seprtely excited DC motor my be expressed s: 75

3 Journl of Science nd Technology Vol. 13, No. 2 Engineering nd Computer Sciences (ECS) d i V = R i + L + E b d t (1) d i V = R i + L + K ω b d t d ω T = K i = J + B ω T (2) d t where V is the input terminl voltge (rmture voltge) in volt, E b is the bck emf in volt, R is the rmture resistnce in ohm, L is the rmture inductnce in H, J is the moment of inerti of the motor in kgm 2 /s 2, T is the motor torque in Nm, B is the viscous friction coefficient in Nms, K T is the torque fctor constnt in Nm/A, K b is the bck emf constnt in Vs/rd, ω is the ngulr speed in rd/s, nd i is the rmture current in A. Equtions (1) nd (2) re rerrnged to obtind i R K V b = i ω + (3) d t L L L d ω d t K T B i J = ω (4) J In the stte spce model of seprtely excited DC motor, Equtions (3) nd (4) cn be expressed by choosing the ngulr speed (ω) nd rmture current (i ) s stte vribles nd the rmture voltge (V ) s n input. The output is chosen to be the ngulr speed (1-4). R K di b 0 i L L i dt = = + 1 V dω ω K T B ω L dt J J y 0 1 i = ω (5) Tble 1 lists the numericl vlues for the prmeters of the seprtely excited DC motor studied in this pper. Bsic Concept of SMC The theory of sliding mode control hs been developed firstly in the Soviet Union in erly 1950s (18). However, sliding mode control did not receive wide cceptnce mong engineering professionls until the mid 1970s when book by Itkis (8) nd survey pper by Utkin (19) were published in English. Since then, nd especilly during the lte 80 s, the control reserch community hs shown significnt interest in sliding mode control. Tble I: Prmeters of the seprtely excited DC motor Prmeters Vlues Armture resistnce, R 5Ω Armture inductnce, L 0.01H Moment of inerti, J kgm 2 /s 2 Viscous friction 0.136Nms coefficient, B The bck emf constnt, K b 0.245Vs/rd The torque fctor 0.245Nm/A constnt, K T This incresed interest is explined by the fct tht robustness hs become mjor requirement in modern control pplictions. Sliding mode control concepts hve subsequently been utilized in the design of robust regultors, trcking system, stte observers, model reference systems nd fult detection schemes. The ides hve successfully been pplied to problems s diverse s control of electric motors, ircrft nd spce crft flight, control of flexible structure, robot mnipultors, nd chemicl processes. In generl, the phse trjectory of sliding mode control cn be investigted in two prts, representing two modes of the system s shown in Figure 2. The first prt, the trjectory strting from nywhere on the phse plne moves towrd sliding surfce nd reches the surfce in finite time. This is known s reching, hitting, or non-sliding phse nd the system is sensitive to prmeter vritions nd disturbnce rejection in this prt of the phse trjectory. The second prt is the sliding phse in which the stte trjectory moves to the origin long the sliding surfce nd the 76

4 Journl of Science nd Technology Vol. 13, No. 2 Engineering nd Computer Sciences (ECS) sttes never leve the sliding surfce. During this period, the system is defined by the eqution of the sliding surfce nd thus it is independent of the system prmeters nd externl disturbnces (8-12). In generl, the sliding mode controller design pproch usully consists of two steps. First, the sliding or switching surfce(s) is designed such tht the system motion in sliding mode stisfies design specifictions. Second, control lw is designed mking the switching surfce ttrctive to the system stte. Sliding surfce cn be either liner or nonliner. For simplicity, only liner sliding surfce is used in this pper. Stte Trjectory Sliding Surfce Figure 2: Phse portrit of sliding motion (12) Slotine proposed form of generl eqution to determine the sliding surfce which ensures the convergence of vrible towrds its desired vlue s: n 1 d s = + λ e (6) dt where n is the system order, e is the trcking error, nd λ is strictly positive constnt tht determine the bndwidth of the system. Hving chosen the sliding surfce t this stge, the next step would be to choose the control lw (u) tht will llow the error vector ( e, e ) to rech the sliding surfce. To do so, the control lw should be designed in such wy tht the following condition, lso nmed reching condition, is met: ss < 0 (7) In order to stisfy this condition, the bsic discontinuous control lw of sliding mode control is given by: u = Ksign( s) (8) where K is positive constnt known s the hitting control gin or prmeter, s is the sliding surfce, nd sign is the signum function defined s (8-14) : { 1 if s > 0 sign (s) = (9) -1 if s < 0 The discontinuous control lw described by Eqution (9) presents high robustness, insensitive to prmeter fluctutions nd disturbnces. However, using sign function often cuses chttering phenomenon in prctice. Severl solutions hve been proposed in reserch literture to llevite the chttering phenomenon (9-11). Design of Sliding Mode Speed Control of DC Motor In this section, the design procedure for the speed control of seprtely excited DC motor which is under control by SMC technique is discussed. Thus, the stte spce model of seprtely excited DC motor is obtined s shown in Eqution (5). The speed control gol is to force the speed ω to trck the desired speed reference ω d. For the sliding mode controller technique, the sliding surfce is chosen s: s = ωe + λωe (10) where ωe is the trcking speed error. λ is strictly positive constnt tht determine the bndwidth of the system. The given speed control problem cn be treted s regultor problem, where the desired ccelertion is chosen to be zero. In this pper to reduce the chttering phenomenon of the sliding mode control, the signum function is replced by pseudo sliding with smooth control ction. The pseudo function is defined s (20) : s u = K (11) s + δ where is smll positive design constnt lso clled s tuning prmeter used to 77

5 Journl of Science nd Technology Vol. 13, No. 2 Engineering nd Computer Sciences (ECS) reduce chttering phenomenon (0<δ<1), K is positive constnt, nd the sliding surfce hs the sme definition s Eqution (10). Simultion Results In this section, the overll model of seprtely excited DC motor with sliding mode control ws implemented in MATLAB/ Simulink. Simultion results of the SMC were compred with the PI controller. Simultions were bsed on the fcts tht whether the sliding mode controller is better nd more robust thn the PI controller or not. Firstly the response of seprtely excited DC motor is observed under norml condition, secondly under lod torque chnge, finlly under high moment of inerti, respectively. Simultion results for the nominl system re presented in Figure 3, which shows the rotor speed responses for SMC nd PI controller when seprtely excited DC motor is operting t reference speed of 10 rd/s. In terms of the rotor speed control trjectories shown in Figure 3, two different controllers hve similr performnce in term of fst trcking of the desired speed. The sliding mode controller shows little overshoot which is resonble nd then trcks the reference speed closely. However, the settling time nd rise time for SMC is shorter thn for PI controller. In order to testify the robustness of the controlled system, 0.5Nm lod torque ws suddenly dded t time 0.3s nd then removed t time 0.4s while the commnd speed ws set s 10rd/s. Figure 4 gives the rotor speed responses under these conditions. The PI controller hd the worse rotor speed response t these two instnts. However, the system controlled by the SMC demonstrted n excellent rotor speed response whether the lod ws dded or removed. Agin the SMC performed better trcking bility thn the PI controller. Therefore, it could be concluded tht the PI controller is not robust to lod torque vritions. Rotor Speed (rd/sec) Rotor Speed (rd/sec) Time (sec) Reference SMC PI Figure 3: Speed responses of SMC nd PI controller for step commnd Reference SMC PI Time (sec) Figure 4: Speed responses of SMC nd PI controller ginst sudden chnge in torque lod To nlyze the sensitivity of the sliding mode controller to prmeter vritions, the moment of inerti of the seprtely excited DC motor hd been substntilly modified throughout the test. The motor ws commnded to ccelerte from rest to reference speed of 10 rd/sec under no torque lod. Figure 5 shows the motor responses of SMC nd PI controller when the moment of inerti ws incresed by 100% of its originl vlue. It cn be seen tht the PI controller 78

6 Journl of Science nd Technology Vol. 13, No. 2 Engineering nd Computer Sciences (ECS) exhibited poor dynmic response. Furthermore, when crefully study Figure 5 ccording to the rise time, settling time nd overshoot, the best performnce belonged to sliding mode controller. This mens tht the sliding mode controller ws insensitive to prmetric vritions nd robust trcking performnce ws chieved in presence of the uncertin prmeters. Rotor Speed (rd/sec) Reference SMC PI Time (sec) Figure 5: Speed responses of SMC nd PI controller with vrition in J Conclusion- Sliding mode control nd PI controller hve been considered in this pper for controlling the speed of seprtely excited DC motor. The performnce of the controllers ws vlidted through simultions. A comprison method hd been studied to show the reltive dvntges nd limittions of ech controller. From the comprtive simultion results, one cn conclude tht the two controllers demonstrted nerly the sme dynmic behvior under nominl condition. However, simultion results show tht the sliding mode controller relized good dynmic behvior of the motor with rpid rise time nd settling time, nd hd better performnce thn the PI controller. But the comprison between the speed control of seprtely excited DC motor by the sliding mode controller nd PI controller showed clerly tht the sliding mode controller gives better performnce thn the PI controller ginst prmeter vritions nd externl lod torque. References- 1. Weiyo Ln nd Qi Zhou, Speed Control of DC Motor using Composite Nonliner Feedbck Control, (2009) IEEE Interntionl Conference on Control nd Automtion Christchurch, New Zelnd, December Moleykutty George, Speed Control of Seprtely Excited DC Motor, Americn Journl of Applied Sciences, Vol. 5: No. 3, pp , Y. J. Hung, T. C. Kuo, Robust position control of DC servomechnism with output mesurement noise, Electr. Eng, Vol. 88, pp , S. J. Chpmn, Electric Mchinery Fundmentls," The McGrw-Hill Compnies, K. Ang, G. Chong, Y. Li, PID control system nlysis, design, nd technology, IEEE Trns. Control System Technology, Vol. 13: pp , O. Yniv, M. Ngurk, Robust, PI controller design stisfying sensitivity nd uncertinty specifictions, IEEE Trns. Automtion Control, Vol. 48, pp , J. G. Jung, M. T. Hung nd W. K. Liu, PID control using prescribed genetic lgorithms for MIMO system, IEEE Trns. Systems, Mn nd Cybernetics, vol. 38, no.5, pp , Um Mheshwrro. Ch, Y. S. kishore Bbu nd K. Amresh, Sliding Mode Speed Control of DC Motor, Interntionl Conference on Communiction Systems nd Network Technologies, X. Yu nd O. Kynk, Sliding-Mode Control with Soft Computing: A Survey, IEEE Trns. Ind. Electron., Vol. 54, No. 9, pp , A. J. Koshkouei, K. J. Burnhm, nd A. S. I. Zinober, Dynmic sliding mode control design, IEE Proc.-Control 79

7 Journl of Science nd Technology Vol. 13, No. 2 Engineering nd Computer Sciences (ECS) Theory Appl., Vol. 152, No. 4, July V. I. Utkin: Sliding Mode Control Design Principles nd Applictions to Electric Drives, IEEE Trns. Ind. Electronics., Vol. 40, No. 1, pp , Brtoszewicz, A., Kynk, O., Utkin, V.I., Specil Section on Sliding Mode Control in Industril Applictions, IEEE Trns. Ind. Electron., Vol. 55, No. 11, M. Abid, A. Mnsouri, A. G. Aissoui et l., Sliding Mode Appliction in Position Control of n Induction Mchine, Journl of Electricl Engineering, Vol. 59, No. 6, pp , Z. Liu, F. Yu. nd Z. Wng, Appliction of Sliding Mode Control to Design of the Inverted Pendulum Control System, The Ninth Interntionl Conference on Electronic Mesurement & Instruments, pp , M. S. Chen, Y. R. Hwng, M. Tomizuk, Sliding mode control reduced chttering for systems with dependent uncertinties, IEEE Interntionl conference on network, Sensing nd control, Tiwn, pp , Mrch Y. K. Kim, G. J. Jeon, Error reduction of sliding mode control using sigmoidtype nonliner interpoltion in the boundry lyer, Interntionl Journl of Control, Automtion nd System, Vol. 2, pp , December M. Dul, Novel pproch to sliding mode control for field oriented induction motor drive, IEEE Interntionl Conference on Industril Technology, pp , 2004.

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