Design of optimized cascade fuzzy controller based on differential evolution: Simulation studies and practical insights

In this study, we discuss a design of an optimized cascade fuzzy controller for the rotary inverted pendulum system and ball & beam system by using an optimization vehicle of differential evolution (DE). The structure of the differential evolution optimization environment is simple and a convergence to optimal values realized here is very good in comparison to the convergence reported for other optimization algorithms. DE is easy to use given its mathematical operators. It also requires a limited computing overhead. The rotary inverted pendulum system and ball & beam system are nonlinear systems, which exhibit unstable motion. The performance of the proposed fuzzy controller is evaluated from the viewpoint of several performance criteria such as overshoot, steady-state error, and settling time. Their values are obtained through simulation studies and practical, real-world experiments. We evaluate and analyze the performance of the proposed optimal fuzzy controller optimized by Genetic Algorithm (GA), and DE. In this setting, we show the superiority of DE versus other methods being used here as well as highlight the characteristics of this optimization tool.

[1]  Seok-Beom Roh,et al.  Parameter estimation of fuzzy controller and its application to inverted pendulum , 2004, Eng. Appl. Artif. Intell..

[2]  Shaocheng Tong,et al.  Fuzzy robust tracking control for uncertain nonlinear systems , 2002, Int. J. Approx. Reason..

[3]  Li-Xin Wang Stable and optimal fuzzy control of linear systems , 1998, IEEE Trans. Fuzzy Syst..

[4]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[5]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[6]  P. Kokotovic,et al.  Nonlinear control via approximate input-output linearization: the ball and beam example , 1992 .

[7]  W. Chang PID control for chaotic synchronization using particle swarm optimization , 2009 .

[8]  Alfred C. Rufer,et al.  JOE: a mobile, inverted pendulum , 2002, IEEE Trans. Ind. Electron..

[9]  Arpita Sinha,et al.  Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets. , 2008, ISA transactions.

[10]  Sung-Kwun Oh,et al.  Structural and parametric design of fuzzy inference systems using hierarchical fair competition-based parallel genetic algorithms and information granulation , 2008, Int. J. Approx. Reason..

[11]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[12]  Romeo Ortega,et al.  Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment , 2002, IEEE Trans. Autom. Control..

[13]  Bor-Chin Chang,et al.  An application of robust feedback linearization to a ball and beam control problem , 1998, Proceedings of the 1998 IEEE International Conference on Control Applications (Cat. No.98CH36104).

[14]  Giancarlo Mauri,et al.  Learning fuzzy rules with tabu search-an application to control , 1999, IEEE Trans. Fuzzy Syst..

[15]  Sam Kwong,et al.  Genetic algorithms and their applications , 1996, IEEE Signal Process. Mag..

[16]  Juing-Shian Chiou,et al.  Numerical simulation for Fuzzy-PID controllers and helping EP reproduction with PSO hybrid algorithm , 2009, Simul. Model. Pract. Theory.

[17]  Robert Ivor John,et al.  Geometric Type-1 and Type-2 Fuzzy Logic Systems , 2007, IEEE Transactions on Fuzzy Systems.

[18]  Wooi Ping Hew,et al.  Development of a self-tuning fuzzy logic controller for intelligent control of elevator systems , 2009, Eng. Appl. Artif. Intell..

[19]  Reza Olfati-Saber,et al.  Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles , 2001 .

[20]  Jacob S. Glower,et al.  Designing fuzzy controllers from a variable structures standpoint , 1997, IEEE Trans. Fuzzy Syst..

[21]  Hani Hagras,et al.  A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots , 2004, IEEE Transactions on Fuzzy Systems.