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PID controller design of nonlinear systems using an improved particle swarm optimization approach. (English) Zbl 1222.90083
Summary: An improved particle swarm optimization is presented to search for the optimal PID controller gains for a class of nonlinear systems. The proposed algorithm is to modify the velocity formula of the general PSO systems in order for improving the searching efficiency. In the improved PSO-based nonlinear PID control system design, three PID control gains, i.e., the proportional gain \(K_{p}\), integral gain \(K_{i}\), and derivative gain \(K_{d}\) are required to form a parameter vector which is called a particle. It is the basic component of PSO systems and many such particles further constitute a population. To derive the optimal PID gains for nonlinear systems, two principle equations, the modified velocity updating and position updating equations, are employed to move the positions of all particles in the population. In the meanwhile, an objective function defined for PID controller optimization problems may be minimized. To validate the control performance of the proposed method, a typical nonlinear system control, the inverted pendulum tracking control, is illustrated. The results testify that the improved PSO algorithm can perform well in the nonlinear PID control system design.

90C59 Approximation methods and heuristics in mathematical programming
37N35 Dynamical systems in control
93C95 Application models in control theory
Full Text: DOI
[1] Kennedy J, Eberhart R. Particle swarm optimization. In: Proc IEEE int conf neural networks, vol. IV, Perth, Australia; 1995. p. 1942-48.
[2] Shi Y, Eberhart RC. Empirical study of particle swarm optimization. In: Proc IEEE int conf evol comput, Washington, DC; July 1999. p. 1945-50.
[3] Eberhart RC, Shi Y. Particle swarm optimization: development, applications and resources. In: Proc congress on evol comput, Seoul, Korea; 2001. p. 81-6.
[4] Hwang, K.C., Optimisation of broadband twist reflector for ku-band application, Electron lett, 44, 3, 210-211, (2008)
[5] Lin, Y.L.; Chang, W.D.; Hsieh, J.G., A particle swarm optimization approach to nonlinear rational filter modeling, Expert syst appl, 34, 1194-1199, (2008)
[6] Abido, M.A., Optimal design of power-system stabilizers using particle swarm optimization, IEEE trans energy conversion, 17, 406-413, (2002)
[7] Liu, B.; Wang, L.; Jin, Y.H.; Tang, F.; Huang, D.X., Improved particle swarm optimization combined with chaos, Chaos solitons fractals, 25, 1261-1271, (2005) · Zbl 1074.90564
[8] Wilkie, J.; Johnson, M.; Katebi, R., Control engineering, (2002), Palgrve New York
[9] Gaing, Z.L., A particle swarm optimization approach for optimum design of PID controller in AVR system, IEEE trans energy conversion, 19, 384-391, (2004)
[10] Karaboga, N.; Kalinli, A.; Karaboga, D., Designing digital IIR filters using ant colony optimization algorithm, Eng appl artif intell, 17, 301-309, (2004)
[11] Tutkun, N., Optimization of multimodal continuous functions using a new crossover for the real-coded genetic algorithms, Expert syst appl, 36, 8172-8177, (2009)
[12] Wang, L.X., Adaptive fuzzy systems and control: design and stability analysis, (1994), Prentice-Hall New Jersey
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