1 Faculty of Electrical Engineering, UTM, Skudai 81310, Johor, Malaysia

Transcription

1 Applied Mechanics and Materials Vols (2013) pp (2013) Trans Tech Publications, Switzerland doi: / PID Controller Tuning by Differential Evolution Algorithm on EDM Servo Control System Trias Andromeda 1,2, a, Azli yahya 2,b, Syahrullail Samion 3,c Ameruddin Baharom 1,d, Nor Liyana Hashim 4,e 1 Faculty of Electrical Engineering, UTM, Skudai 81310, Johor, Malaysia 2 Department of electrical engineering, Diponegoro University, Semarang 50275, Indonesia 3 Faculty of Mechanical Engineering, UTM, Skudai 81310, Johor, Malaysia 4 Faculty of Health Science and Biomedical Engineering, UTM, Skudai 81310, Johor, Malaysia a triasandromeda@undip.ac.id, b azli@fke.utm.my, c syahruls@fkm.utm.my d amer@fke.utm.my, e nlsafura88@gmail.com Keywords: Servo Control System, Electrical Discharge Machining (EDM), Proportional Integral Derivative (PID), Controller Tuning, Differential Evolution (DE). Abstract Maintaining gap between Electrode and workpiece in Electrical Discharge Machining (EDM) is very important since the capability of control system to keep the gap will improve the performance of this machine. Therefore to maintain the gap, a Proportional Integral Derivative (PID) controller is designed and applied to EDM servo actuator system. The objective of this work is to obtain a stable, robust and controlled system by tuning the PID controller using Differential Evolution (DE) algorithm. The controller for EDM die sinking is verified by simulation of the control system using MATLAB/Simulink program. Simulation results verify the capabilities and effectiveness of the DE algorithm to search the best configuration of PID parameters controller to control the electrode position. Introduction PID controller is the most popular ones on dealing with industrial control processes. It is simple in structure, reliable in operation, robust in performances and up to 90% of all control strategies are PID. Various applications have implemented using PID controller, such as process control, motor drives, automotive, flight control. On the contrary, it has been experimentally checked that more than 30% of the installed controllers are operating in manual mode and 65% of the automatic close loops is operated in poorly tuned condition[1], so new approaches algorithm to adjust PID constants controller are very important. Conventional methods such as Zigler-Nichols[2] and simplex methods are not excellent to be implemented in digital system. Recently, intelligent approaches such as genetic algorithm, particle swarm optimization have been proposed for PID optimization. Some tuning methodologies PID controllers have been proposed in literatures such as auto tuning, self-tuning and computational intelligence[3-5]. Many researchers have tried to propose a new strategy in order to obtain a good technique to determine parameters in PID controller. Conventional methods called Zigler-Nichols based on step response analysis. Kp, Ki and Kd gains of the controller are determined using this response graph[6]. It means that the accuracy of capturing the step response graph is significantly contributed to the determination of PID parameters. Artificial Intelligence algorithm tries to find optimum parameter in PID controller based on fitness function. It is not easy to find a proper configuration gains of PID controllers because many industrial plants are often burdened with problems such as high order, time delays, poorly damped, nonlinearities and time-varying dynamics. Over the years, several authors have proposed the tuning of PID to control variable processes by optimization methods, such as genetic algorithms[7], particle swarm optimization[8], tribes algorithm[9], harmony search[10], evolution strategy [11], All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, (ID: /01/13,07:52:50)

2 Applied Mechanics and Materials Vols ant colony [12]. In this paper, Differential Evolution as a new Evolutionary Algorithm is used as a tool for solving the class of multi objective optimization problems that results from a PID design problem for maintaining the gap between electrode and workpiece in EDM system process. System Description Electrical Discharge Machining (EDM) is a controlled metal removal process that is used to remove metal by means of electric spark erosion. The English scientist Priestley first reported the erosive effect of electrical discharges in In this process, an electric spark is used as the eroding tool to erode the workpiece to produce finished part (moulding). The metal removal process is performed by applying an electrical discharge of pulsed high frequency direct current through the electrode to the workpiece. The electrode location is controlled by the machine and is positioned so as not to contact the workpiece. A precise controlled space is maintained, allowing the spark to discharge its current from the electrode to the workpiece through an insulated dielectric fluid. This removes tiny particles of metal, called debris, from the workpiece. Figure 1. Basic Elements of an EDM system Fig.1 shows basic elements of an EDM system. When the gap between the electrode and workpiece is sufficiently small (10 50 µm), said gap being controlled by the position control servo system, an electrical spark occurs in the gap. Gap Control in EDM System Machining gap is adjusted using ram servo control system at a critical distance for the continuous occurrence of electric discharge. At the same power generator settings, machining stability and productivity depend on performance of this servo control mechanism. Fig. 2 shows block diagram of EDM servo control unit. Figure 2. Block Diagram of Existing EDM Servo Control System There are three components which constructs EDM servo control system. K c is applied at the controller block. The servo system block consist of model of dc motor and its accessories including ram and leadscrew. EDM process is a model for EDM discharge phenomenon. At this model, gap between electrode and workpiece is converted to voltage which represents voltage drop occurred during discharge state. Control system takes only the average gap voltage (V g ) as a feedback signal and then comparing it with a servo reference voltage (V s ). The differences between V g and V s, known as error, is fed to amplifier K c, denoted by V sd, drives the servo ram to adjust the gap distance so as to

3 2268 Innovation for Applied Science and Technology keep V g at a level determined by V s. The control gain K c and the level of V s are manually preset according to the operator's experiences. Conventional servo system does not effectively respond to either gap state parameters or process dynamic and stochastic features[13]. With this type of control system, therefore, the machining process is not optimal. Figure 3. Practical gap control system of an EDM[13] Fig. 3 shows a practical gap control system of EDM process. The dynamic relationship between the feed rate f r (s) and the speed V(s) can be expressed as, = (1) where is a magnification constant. The terms and is damping ratio and natural frequency of the servo system. Considering to the foregoing analysis, the system is a type 1 system when the gap controller y(s) is a pure proportional controller. A PD controller is applied to the system to improve the transient responses. Accordingly, f r (s) can be expressed as: = + (2) Differential Evolution (DE) Differential Evolution (DE) can be used in optimization problems and a variant of evolutionary computation algorithm[14]. DE has three main advantages (1) able to locate the accurate global optimum irrespective of the initial parameter values (2) has rapid convergence (3) utilizes few control parameters, thus easy and simple to use. This algorithm is similar to Genetic Algorithm (GA) and Particle Swarm optimization (PSO). During optimization step, mutation, crossover/recombination, and selection operators are involve in this computation. Initially, population is given randomly. DE utilize mutation operator as a search mechanism and selection operation to find directly based on prospective regions on search space. Implementation of DE-PID Controller Contribution of this paper is to apply the DE method in order to search an optimize configuration of PID parameters controller. A new control system optimization called DE-PID control system is proposed. Fig. 4 shows the proposed controller block diagram. Figure 4 DE-PID controller block diagram The Differential Evolution (DE) algorithm will be used to search an optimize parameters value in PID controller. At the first process, EDM model is controlled by initial PID parameters value. IAE is computed by Simulink software, it is used as an Objective target value in the DE algorithm.

4 Applied Mechanics and Materials Vols The DE will compute a new population based on this IAE value. In this work, DE is applied using matlab m.files coding. DE will propose a new population and then will be used as a new PID parameters value for the next generation. Simulation Results Simulation is conducted for several combinations. PID is configured to construct four types of controller, i.e. P, PD, PI and PID controller. The results can be seen in Table 1. Table 1 Experimental result for P, PI, PID and PD controller No Kp Ki Kd IAE Table 1 reveals value of each PID parameters for each type of controller. The values are achieved automatically using DE algorithm. PID controller has the lowest IAE value at Experimental results in Fig. 5 shows that all combination of PID parameters can be used to obtain optimum gap required in the EDM process. It is also shown zoomed graph from 450 until 650 mili seconds. It can be seen that gap response of P similar to PI controller whereas PD similar to PID controller. The excellent work of PID combination tuned by DE provides the best results in gap optimization Gap Response P PD PI PID Gap Response P PD PI PID Gap distance (micro meter) P and PI PD and PID Zoomed Gap distance (micro meter) time(mili seconds) time(mili seconds) Conclusion Figure 5 Result DE-PID In this paper, the PID controller parameters have been tuned by Differential Evolution. The simulation results reveal that determination of each parameter, K p, K i and K d, is achieved automatically. Gap between electrode and workpiece can be maintained satisfactory. Differential Evolution successfully tune all combination of P, I and D parameters. The response of all combination of PID shows that the optimum gap can be achieved. However every combination has different response and time to reach the setting value. PID controller shows the best performance to reach the setting with minimum IAE value. Acknowledgements The authors are grateful for the financial support from Research Management Centre (RMC) of Universiti Teknologi Malaysia.

5 2270 Innovation for Applied Science and Technology References [1] D. B. Ender, "Process control performance: Not as good as you think," Control. Eng., vol. 40 (10), pp , [2] W. Lv, D. Li, S. Cheng, S. Luo, X. Zhang, and L. Zhang, "Research on PID Control Parameters Tuning Based on Election-Survey Optimization Algorithm," in Computing, Control and Industrial Engineering (CCIE), 2010 International Conference on, pp [3] K. J. Åström and H. T., PID controllers: Theory, design and tuning, 2nd ed. Research Triangle Park, North Carolina, USA: Instrument Society of America, [4] K. J. Åström and T. Hägglund, "The future of PID control," Control Engineering Practice, vol. 9, pp , [5] P. Cominos and N. Munro, "PID controllers: recent tuning methods and design to specification," Control Theory and Applications, IEE Proceedings -, vol. 149, pp , [6] M.Saranya and D.Pamela, "A Real Time IMC Tuned PID Controller for DC Motor," International Journal of Recent Technology and Engineering, vol. 1, April [7] H. Pai-Yi and C. Yung-Yaw, "Design of PID controller for precision positioning table using genetic algorithms," in Decision and Control, 1997., Proceedings of the 36th IEEE Conference on, 1997, pp vol.3. [8] T. H. Kim, I. Maruta, and T. Sugie, "Robust PID controller tuning based on the constrained particle swarm optimization," Automatica, vol. 44, pp , [9] L. d. S. Coelho and D. L. d. A. Bernert, "PID control design for chaotic synchronization using a tribes optimization approach," Chaos, Solitons & Fractals, vol. 42, pp , [10] L. d. Santos Coelho and D. L. de Andrade Bernert, "An improved harmony search algorithm for synchronization of discrete-time chaotic systems," Chaos, Solitons & Fractals, vol. 41, pp , [11] L. D. S. Coelho and A. A. R. Coelho, "Automatic tuning of PID and gain scheduling PID controllers by a derandomized evolution strategy," Artificial Intelligence, for Engineering Design, and Manufacturing, vol. 13, pp , [12] H. b. Duan, D. b. Wang, and X. f. Yu, "Novel Approach to Nonlinear PID Parameter Optimization Using Ant Colony Optimization Algorithm," Journal of Bionic Engineering, vol. 3, pp , [13] Y. Chang, "VSS controller design for gap control of EDM," JSME International Journal, vol. 45(3), pp , [14] D. Ruijun, "Differential Evolution Versus Particle Swarm Optimization for PID Controller Design," in Natural Computation, ICNC '09. Fifth International Conference on, 2009, pp