### PID Controller Optimization for Rotational Inverted Pendulum System Using Particle Swarm Optimization and Differential Evolution Algorithms

#### Abstract

This paper presents stochastic search techniques, including Particle Swarm Optimization (PSO), Constriction Coefficient Particle Swarm Optimization (CPSO) and Differential Evolution (DE) algorithms for determining optimal Proportional-Integral-Derivative (PID) controller parameters attached to the Rotational Inverted Pendulum (RIP) system. This paper demonstrates in detail how to employ these proposed algorithms to optimize the performance index for balancing the pendulum in vertical-upright position. The efficiency of these intelligent strategies to tune PID gains is compared and evaluated based on the time response performance. The simulation results clearly demonstrate superior features of proposed tuning approaches, including easy implementation, and good computational efficiency. The overall results have validated that CPSO method yields better performance in control action compared to PSO and DE. The proposed approaches could generally be considered as an encouraging way for control of nonlinear industrial plants.

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#### References

Akhtaruzzaman, M., Shafie, A.A. (2010). Modeling and control of a rotary inverted pendulum using various methods, comparative assessment and result analysis. Proceedings of IEEE International Conference on Mechatronics and Automation, 2010 (pp. 1342-1347).

Bejarbaneh, E.Y. (2012). Multi-optimization of PID controller parameters using stochastic search techniques for rotary inverted pendulum system. Master. Thesis, Universiti Teknologi Malaysia.

Clerc, M. and Kennedy, J. (2002). The particle swarm - explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6, pp. 58-73.

Cong, S., and Liang, Y., (2009). PID-like neural network nonlinear adaptive control for uncertain multivariable motion control systems. IEEE Transactions on Industrial Electronics, 56, pp. 3872-3879.

Das, S., Abraham, A., and Konar, A. (2008). Particle Swarm Optimization and Differential Evolution Algorithms: Technical Analysis, Applications and Hybridization Perspectives. Advances of Computational Intelligence in Industrial Systems, 116, pp. 1-38.

Drof, R.C., and Bishop, R.H. B. (1995). Modern control systems. Reading, MA: Pearson (Addison Wesley).

Eibayomy, K.M., Jiao, Z. and Zhang, H. (2008). PID controller optimization by GA and its performance on the electro-hydraulic servo control system. Chinese Journal of Aeronautics, 21, pp. 378-384.

Gaing, Z.L. (2004). A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE Transactions on Energy Compensation, 19, pp. 384-391.

Haupt, R.L., S.E Haupt, S.E. (1998). Practical Genetic Algorithms. New York, John Wiley and Sons Inc.

Jones, B.P.A.H. (1992). Genetic tuning of digital PID control. Electronics Letters, 28, pp. 834-844.

Kennedy, J., and Eberhart, R.C. (1995). Particle swarm optimization. Proceedings of the International Conference on Neural Networks, Australia, 1995 (pp. 1942-1948).

Kwok, D.P., Leung, T.P,, and Sheng, F. (1993). Genetic algorithms for optimal dynamic control of robot arms. Proceedings of the International Conference on Industrial Electronics, Control and Instrumentation, San Francisco, Nov 1993 (pp.380-385)

Lei, C.W.J.F., and Kin, L.K. (1997). Fuzzy Logic Controller for an Inverted Pendulum System. Proceedings of IEEE International Conference on Intelligent Processing systems, 1, 1997 (pp. 185- 189).

Muskinja, N., Tovornik, B. (2006). Swinging up and stabilization of a real inverted pendulum. IEEE Transactions on Industrial Electronics, 53, pp. 631-639.

Nayak, M.R. (2011). Modified differential evolution optimization algorithm for multi-constraint optimal power. Proceedings of IEEE International Conference on Energy, Automation, and signal, 2011 (pp. 1-7).

Rani, M.R., Selamat, H., Zamzuri, H., Ahmad, F. (2011). PID controller optimization for a rotational inverted pendulum using genetic algorithm. Proceedings of IEEE International Conference on Modeling, Simulation and Applied Optimization, 2010 (pp. 1-6).

Stron, R., and Price, K. (1997). Differential Evolution, a simple and efficient heuristic strategy for global optimization over continuous spaces. Journal of global optimization, 11, pp. 341-359.

Subramanian, S., Bhuvaneswari, R. (2005). Optimization of Three-phase Induction Motor Design Using Simulated Annealing Algorithm. Electronic Power Components and Systems, 33, pp. 947-956.

Sukontanakarn, V., and Parnichkun, M., (2006). Real-Time optimal control for rotary inverted pendulum. American Journal of Applied Science, 6(6), pp. 1106-1115.

Uo-Huang, L. (2006). Implementation of Embedded Controller using SoPC Technology. Proceedings of IEEE International Conference on Robotics, Automations and Mechatronics, 2006 (pp. 1-6).

Van den berg, H.W.J. (2003). Introduction to the control of an inverted pendulum setup, Technische Universiteit Eindhoven.

Visioli, A. (2001). Tuning of PID controllers with fuzzy logic. Proceedings of the IEEE International Conference on Control Theory and Applications, 148, 2001 (pp. 1-8).

Yan, Q. (2003). Output tracking of undergraduate rotary inverted pendulum by nonlinear controller. Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, USA, 3, 2003 (pp. 2395-2400).

Zadeh, I.H., and Mobayen, S., (2008). PSO-based controller for rotary Inverted Pendulum. Journal of Applied Sciences, 8(16), pp. 2907-2912.

Zhou, G., and Birdwell, J. (1994). Fuzzy logic-based PID auto-tuner design using Simulated Annealing. Proceedings of the IEEE/IFAC Joint Symposium, Computer-Aided Control System Design, Tucson, Ariz, USA,1994 (pp. 67-72).

Zhong, W., and Rock. (2001). Energy and passive based control of double inverted pendulum on cart. Proceedings of the International IEEE Conference on Control Applications, Mexico, 2001 (pp. 896- 901).

Ziegler, J.G., and Nichols, N.B., (1942). Optimum setting for automatic controllers. ASMET Transactions, 64, pp. 756-768.

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