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  • M.P.Prasanna Kumar, P. Devendra, R. Srinivasa Rao, Indranil Saaki / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1416-1420. Optimal Tuning of PID Controller for a Linear Brushless DC Motor using Particle Swarm Optimization Technique M.P.Prasanna Kumar1 P. Devendra2 R. Srinivasa Rao3 Indranil Saaki4 Abstract— This Paper presents a novel Coming to the control point of view, theCultural Algorithm based particle swarm decoupled nature of field and armature mmfoptimization (PSO) technique which is helps in exhibiting sustainable controlintended to assist in converging to a characteristics [1]. Recently many tools haveaccurate solution in the control of Linear been evolved to facilitate optimized solutionsBrushless Direct Current motor (LBLDC). for the problems that were previously difficultWith the novel PSO-based approach the or impossible to solve [3],[4],[5],[6]. Theseoptimal Proportional-Integral-Derivative tools include complex theoretical basis such as(PID) controller parameters are deduced evolutionary computation, simulatedfor efficient speed control of Linear annealing, particle swarm and so forth [7].Brushless DC motor. In the present paper, These new heuristic tools have been joinedan modern heuristic algorithm based on the together with knowledge elements as well asbehavior of organisms, such as bird traditional approach to efficiently controlschooling has been implemented in various parameters.MATLAB and Linear Brushless DC motormodeled in Simulink. The proposed The Proportional-Integral-Derivative (PID)approach has efficient features including controller is the most common form ofstable convergence characteristic and good feedback and also a requisite element of earlycomputational efficiency, reducing the governors. It has become the standard toolsteady-state error (Ess), rise time (Tr), when process control emerged in the 1940s.settling time (Ts) and maximum overshoot At present, more than 95% of the controllers(Mp) in speed control of a Linear Brushless are of PID type; most of the industriesDC motor. The experimental results employ Proportional-Integral-Derivativeimplicate the effectiveness of the approach. (PID) controllers because of their simple structure. PID control with its three termKeywords--Proportional-Integral-Derivative functionality covering both transient andController, Cultural Algorithm, Particle steady-states response, offers the simplest andSwarm Optimization, Linear Brushless DC the most efficient solution to many real worldmotor. control problems [8]. Yu et al. have presented a LQR method [9] to optimally tune the PIDI. INTRODUCTION gains. In this method, the response of the AMONG the different motors system is near optimal but it requiresconfigurations available, Linear Brushless DC mathematical calculation and solving(LBLDC) motor has considered to be strong equations.contender. This is due to several reasons,including higher efficiency, robust operation, Particle Swarm Optimization (PSO) is alower maintenance, and higher mechanical computational method that optimizes areliability, since the permanent magnets problem by iteratively trying to improve aprovides the necessary air gap flux instead of candidate solution with regard to a givenwire-wound field poles[1]. In addition, Linear measure of quality [8]. PSO was firstBrushless DC motor has the following introduced by Kennedy and Eberhart based onadvantages such as smaller volume, better the behavior of organisms, such as fishvelocity capability, high force and simple schooling and bird flocking. Generally, PSOsystem structure. Hence, these motors can be is characterized as a simple concept, easy toapplied widely in diversified fields where high implement, and computationally efficientperformance drives are needed [2]. [14]. Compared to other techniques, PSO has a well-balanced mechanism to enhance the global and local exploration abilities [15]. 1416 | P a g e
  • M.P.Prasanna Kumar, P. Devendra, R. Srinivasa Rao, Indranil Saaki / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1416-1420.This paper has been organized into following where Vapp(t ) is the applied voltage, (t ) issections i.e. in section 2 the Linear Brushless the motor speed, L is the inductance of theDC motor (LBLDC) is described and the speed stator, i (t) is the current of the circuit, R is themodel of it is shown. In section 3, the ParticleSwarm Optimization (PSO) method is resistance of the stator, Vemf (t ) is the backreviewed. Section 4, describes how PSO is electromotive force, T is the torque of motor,used to design the PID controller optimally for D is the viscous coefficient, J is the moment ofa Linear Brushless DC motor. A brief overview inertia, K t , is the motor torque constant, andof the results has been obtained by theproposed method via simulation the DC motor K b is the back electromotive force constant.is presented in section 5. The paper is Fig. 1 shows the block diagram of the BLDCconcluded in section 6. motor. From the characteristic equations of the BLDC motor, the transfer function of speedII. LINEAR BRUSHLESS DC MOTOR model is obtained. Generally, a Permanent magnet ( s) Ktsynchronous motor that converts electrical energy to mechanical energy uses an inverter Vapp( s ) LJS  ( LD  RJ ) S  Kt Kb 2corresponding to the brushes andcommutators. The Brushless DC motor adoptsHall Effect sensors instead of mechanical The parameters of the motor used forcommutators and also the rotors are the simulation are as followspermanent magnets, and stator of BLDCmotors are the coils which make the rotorrotating [17]. The Hall Effect sensors detect TABLE 1. PARAMETERS OF THE MOTORthe rotor position as the commutating signals. Parameters Values and UnitsHence, BLDC motors use permanent magnetsinstead of coils in the armature avoiding R 21.2 Ωbrushes in the configuration. In this paper, athree-phase and two poles BLDC motor is Kb 0.1433 Vs.rad 1studied. D 1* 10 4 Kg  ms / rad L 0.052H Kt 0.1433 Kg  m / A J 1* 10 5 Kgm.s 2 / radU Fig.1 Block diagram of BLDC Motor. III. OVERVIEW OF PARTICLE SWARMThe speed of the BLDC motor is controlled by OPTIMIZATIONmeans of a three-phase and half-bridge pulse- PSO is one of the optimal techniquewidth modulation (PWM) inverter. The and a evolutionary computation technique.dynamic characteristics of BLDC motors are The method has been found to be robust insimilar to permanent magnet DC motors. The solving problems featuring nonlinearity and nocharacteristic equations of BLDC motors can differentiability, multiple optima, and highbe represented as follows [18]: dimensionality through adaptation, which is derived from the social psychological theory di(t )Vapp (t )  L  R.i(t )  Vemf (t ) [13]. The technique is derived from research dt on swarm such as fish schooling and bird flocking. According to the research results for Vemf  K b .(t ) a flock of birds, birds find food by flocking (not by each individual). According to T (t )  K t .i(t ) observation of behavior of human groups, d(t ) T (t )  J  D.(t ) dt 1417 | P a g e
  • M.P.Prasanna Kumar, P. Devendra, R. Srinivasa Rao, Indranil Saaki / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1416-1420.behavior of each individual (agent) is also are complex and time-consuming [21]. Thebased on behavior patterns authorized by the IAE, ISE, and ITSE performance criteriongroups such as customs and other behavior formulas are as follows:patterns according to the experiences by eachindividual. The assumption is a basic conceptof PSO [16]. The velocity of each particle, Integral of absolute error (IAE) = e(t ).dt adjusted according to its own flyingexperience and the other particle‟s flying Integral of squared error (ISE) = {e(t )}2 .dt experience. For example, the ith particle isrepresented as xi =(x i,1, x i,2 ,, x i,d) in the d- Integral of time multiplied by Absolute Errordimensional space. The best previous positionof the ith particle is recorded and representedas [13]: (ITAE) = t.e(t ).dt Vi (t  1)  WiVi (t )  C1 rand ( Pbesti  X i (t ))  C 2 rand ( g besti  X i (t )) Integral of time multiplied by squared errorX i (t  1)  X i(t )  Vi (t )w  w Max  [( w Max  w Min )iter ] / Max iter  t.{e(t )} .dt 2 (ITSE) =Where The fitness function is reciprocal of the performance criterion [13], in the other words:Vi (t) =Current velocity of agent i at iteration t 1Vi (t+1) =Modified velocity of agent i f  W (k )Xi (t) =Current position of agent i at iteration t B. Proposed PSO-PID ControllerWMax = initial weight, WMin = final weight In this paper a PSO-PID controller used to findMaxIter = maximum iteration number, the optimal parameters of LBDC speed control system. Fig. 2 shows the block diagram ofiter = current iteration number optimal PID control for the BLDC motor. In the proposed PSO method each particle contains three members P, I and D. It means IV. IMPLEMENTATION OF PSO-PID that the search space has three dimension and CONTROLLER particles must „fly‟ in a three dimensional A. Fitness Function space. In PID controller design methods, themost common performance criteria areintegrated absolute error (IAE), the integratedof time weight square error (ITSE) andintegrated of squared error (ISE) that can beevaluated analytically in the frequencydomain[19],[20]. These three integralperformance criteria in the frequency domainhave their own advantage and disadvantages.For example, disadvantage of the IAE and ISEcriteria is that its minimization can result in aresponse with relatively small overshoot but along settling time because the ISE Fig.2 Block diagram of Proposed PSO-PIDperformance criterion weights all errors Controller.equally independent of time. Although theITSE performance criterion can overcome the The flow chart of PSO-PID controller isdisadvantage of the ISE criterion, the shown in Fig.3derivation processes of the analytical formula 1418 | P a g e
  • M.P.Prasanna Kumar, P. Devendra, R. Srinivasa Rao, Indranil Saaki / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1416-1420. The optimal response of the PID controller is shown in Fig. 4. Fig.5 Speed curve attained using PSO-PID Controller. Fig.3 Flow Chart of PSO-PID Controller. The below figure illustrates about the convergence between the Maximum Fitness function and the Mean Fitness FunctionV. SIMULATION AND RESULTS Respectively A. Optimal PSO-PID Response To control the speed of the LBDCmotor at 1000 rpm, according to the trials, thefollowing PSO parameters are used to verifythe performance of the PSO-PID controllerparameters:Population size: 20; Wmax = 0.6, Wmin = 0.1;C1 =C2 =1.5;Iteration: 20; [P I D] [190.0176,50,0.0397] Rise time(ms) 0.3038Max overshoot (%) 0 Fig.6 Fitness Function used in PSO-PID Controller.Steady States error 0.77186 VI. CONCLUSION Settling time(ms) 0.60116 In this paper novels design method to deduce PID controller parameters as shown in Fig 3. using the PSO method is obtained. The Fig.4 List of the Performance of PSO-PID obtained results through the simulation of Controller. BLDC motor shows that the proposed controller can perform an efficient search for optimal PID controller and can improve the 1419 | P a g e
  • M.P.Prasanna Kumar, P. Devendra, R. Srinivasa Rao, Indranil Saaki / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1416-1420.dynamic performance of the system in a better IEEE/ASME Trans. Mechatronics , vol.8,way. No. 1, pp. 56-65, 2003. [11] D. B. Fogel, EvolutionaryREFERENCES Computation toward a New Philosophy of[1] V. Tipsuwanporn, W. Piyarat and C. Machine Intelligence: New York: IEEE, Tarasantisuk, “Identification and control 1995. of brushless DC motors using on-line [12] R. C. Eberhart and Y. Shi, trained artificial neural networks,” in Proc. “Comparison between genetic algorithms Power Conversion Conf., pp. 1290-1294, and particle swarm optimization,” in Proc. Apr. 2002. IEEE Int. Conf. Evol. Comput.,[2] X.Li Q.Zhang and H.Xiao, “The design of Anchorage, AK, May 1998, pp. 611–616. brushless DC motor servo system based on [13] Z.-L. Gaing, “A particle swarm wavelet ANN, “in Proc. Int. Conf. optimization approach for optimum design Machine Learning and Cybernetics, pp. of PID controller in AVR system,” IEEE 929-933, 2004. Trans. Energy Conversion, vol. 19, pp.[3] N. Hemati, J. S. Thorp, and M. C. Leu, 384-391, June 2004. “Robust nonlinear control of Brushless dc [14] J. Kennedy and R. Eberhart, “Particle motors for direct-drive robotic swarm optimization,” in Proc. IEEE Int. applications,” IEEE Trans. Ind. Electron., Conf. Neural Networks, vol. IV, Perth, vol. 37, pp. 460–468, Dec 1990. Australia, 1995, pp. 1942–1948.[4] P. M. Pelczewski and U. H. Kunz, “The [15] M. A. Abido, “Optimal design of optimal control of a constrained drive power-system stabilizers using particle system with brushless dc motor,” IEEE swarm optimization,” IEEE Trans. Energy Trans. Ind. Electron., vol. 37, pp. 342– Conversion, vol. 17, pp.406- 413, Sep. 348, Oct. 1990. 2002.[5] F. J. Lin, K. K. Shyu, and Y. S. Lin, [16] H. Yoshida, K. Kawata, Y. Fukuyama, “Variable structure adaptive control for S. Takayama, and Y. Nakanishi, “A PM synchronous servo motor drive,” IEE particle swarm optimization for reactive Proc. IEE B: Elect. Power Applicat., vol. power and voltage control considering 146, pp. 173–185, Mar. 1999. voltage security assessment,” IEEE Trans.[6] E. Cerruto, A. Consoli, A. Raciti, and A. on Power Systems, Vol. 15, No. 4, Nov. Testa, “A robust adaptive controller for 2000, pp. 1232 – 1239. PM motor drives in robotic applications,” [17] Allan R. Hambley, Electrical IEEE Trans. Power Electron., vol. 10, pp. Engineering: Principles and Application, 62–71, Jan. 1995. Prentice Hall, New Jersey 1997.[7] C.-L. Lin, and H.-Y. Jan, “Evolutionarily [18] Chee-Mun Ong, Dynamic Simulation multiobjective PID control for linear of Electric Machinery, Prentice Hall, New brushless DC motor, ”in Proc. IEEE Int. Jersey, 1998. Conf .Industrial Elect. Society, Nov. 2002, [19] R. A. Krohling and J. P. Rey, “Design pp.39-45. of optimal disturbance rejection PID[8] K. Ang, G. Chong, and Y. Li, “PID controllers using genetic algorithm,” IEEE control system analysis, design, and Trans. Evol. Comput., vol. 5, pp. 78–82, technology,” IEEE Trans.Control System Feb. 2001. Technology, vol. 13, pp. 559- 576, July [20] Y. Mitsukura, T. Yamamoto, and M. 2005. Kaneda, “A design of self-tuning PID[9] G. Yu, and R. Hwang, “Optimal PID controllers using a genetic algorithm,” in speed control of brush less DC motors Proc. Amer. Contr. Conf., San Diego, CA, using LQR approach,” in Proc. IEEE Int. June 1999, pp. 1361–1365. Conf. Systems, Man and Cybernetics, [21] R. A. Krohling, H. Jaschek, and J. P. 2004, pp. 473-478. Rey, “Designing PI/PID controller for a[10] C. L. Lin, and H. Y. Jan, and N. C. motion control system based on genetic Shieh, “GA-based multiobjective PID algorithm,” in Proc. 12th IEEE Int. Symp. control for a linear brushless DC motor,” Intell. Contr., Istanbul, Turkey, July 1997, pp. 125–130. 1420 | P a g e
  • M.P.Prasanna Kumar, P. Devendra, R. Srinivasa Rao, Indranil Saaki / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1416-1420.Corresponding Authors:1. M.P.Prasanna Kumar1, PG Student, E.E.E Dept., G.M.R Institute of Technology, Rajam, Andhra Pradesh, India2. P. Devendra2, Associate Professor, E.E.E Dept., G.M.R Institute of Technology, Rajam, Andhra Pradesh, India3. R. Srinivasa Rao3, Assistant Professor, E.E.E Dept., G.M.R Institute of Technology, Rajam, Andhra Pradesh, India4. Indranil Saaki4, Assistant Professor, E.E.E Dept., Vishaka Institute of Technology, Visakhapatnam, Andhra Pradesh, India 1421 | P a g e