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Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems

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  • Chang, Wei-Der
  • Yan, Jun-Juh

Abstract

A robust adaptive PID controller design motivated from the sliding mode control is proposed for a class of uncertain chaotic systems in this paper. Three PID control gains, Kp, Ki, and Kd, are adjustable parameters and will be updated online with an adequate adaptation mechanism to minimize a previously designed sliding condition. By introducing a supervisory controller, the stability of the closed-loop PID control system under with the plant uncertainty and external disturbance can be guaranteed. Finally, a well-known Duffing–Holmes chaotic system is used as an illustrative to show the effectiveness of the proposed robust adaptive PID controller.

Suggested Citation

  • Chang, Wei-Der & Yan, Jun-Juh, 2005. "Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 167-175.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:1:p:167-175
    DOI: 10.1016/j.chaos.2004.12.013
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    Cited by:

    1. Lee, Keum W. & Singh, Sahjendra N., 2007. "Robust control of chaos in Chua’s circuit based on internal model principle," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1095-1107.
    2. Dadras, Sara & Momeni, Hamid Reza, 2009. "Control uncertain Genesio–Tesi chaotic system: Adaptive sliding mode approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3140-3146.
    3. Sharma, B.B. & Kar, I.N., 2009. "Parametric convergence and control of chaotic system using adaptive feedback linearization," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1475-1483.
    4. Lin, Chih-Min & Chen, Chiu-Hsiung, 2008. "CMAC-based supervisory control for nonlinear chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 40-58.
    5. Peng, Ya-Fu, 2009. "Robust intelligent backstepping tracking control for uncertain non-linear chaotic systems using H∞ control technique," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2081-2096.
    6. Dadras, Sara & Momeni, Hamid Reza, 2010. "Adaptive sliding mode control of chaotic dynamical systems with application to synchronization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2245-2257.
    7. Jiunn-Shiou Fang & Jason Sheng-Hong Tsai & Jun-Juh Yan & Chang-He Tzou & Shu-Mei Guo, 2019. "Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization," Mathematics, MDPI, vol. 7(12), pages 1-20, November.
    8. Maganti, Ganesh B. & Singh, Sahjendra N., 2006. "Output feedback form of Chua’s circuit and modular adaptive control of chaos using single measurement," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 724-738.

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