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Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization

Author

Listed:
  • Jiunn-Shiou Fang

    (Department of Electrical Engineering, National Cheng-Kung University, Tainan 701, Taiwan)

  • Jason Sheng-Hong Tsai

    (Department of Electrical Engineering, National Cheng-Kung University, Tainan 701, Taiwan)

  • Jun-Juh Yan

    (Department of Electronic Engineering, National Chin-Yi University of Technology, Taichung 41107, Taiwan)

  • Chang-He Tzou

    (Department of Electrical Engineering, National Cheng-Kung University, Tainan 701, Taiwan)

  • Shu-Mei Guo

    (Department of Computer Science and Information Engineering, National Cheng-Kung University, Tainan 701, Taiwan)

Abstract

A robust linear quadratic analog tracker (LQAT) consisting of proportional-integral-derivative (PID) controller, sliding mode control (SMC), and perturbation estimator is proposed for a class of nonlinear systems with unknown nonlinear perturbation and direct feed-through term. Since the derivative type (D-type) controller is very sensitive to the state varying, a new D-type controller design algorithm is developed to avoid an unreasonable large value of the controller gain. Moreover, the boundary of D-type controller is discussed. To cope with the unknown perturbation effect, SMC is utilized. Based on the fast response of SMC controlled systems, the proposed perturbation estimator can estimate unknown nonlinear perturbation and improve the tracking performance. Furthermore, in order to tune the PID controller gains in the designed tracker, the nonlinear perturbation is eliminated by the SMC-based perturbation estimator first, then a hybrid Taguchi real coded DNA (HTRDNA) algorithm is newly proposed for the PID controller optimization. Compared with traditional DNA, a new HTRDNA is developed to improve the convergence performance and effectiveness. Numerical simulations are given to demonstrate the performance of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1141-:d:289871
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    References listed on IDEAS

    as
    1. 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.
    2. Faezeh Ebrahimzadeh & Jason Sheng-Hong Tsai & Min-Ching Chung & Ying Ting Liao & Shu-Mei Guo & Leang-San Shieh & Li Wang, 2017. "A generalised optimal linear quadratic tracker with universal applications. Part 2: discrete-time systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(2), pages 397-416, January.
    3. Rongrong Qian & Minzhou Luo & Yao Zhao & Jianghai Zhao, 2016. "Novel Adaptive Sliding Mode Control with Nonlinear Disturbance Observer for SMT Assembly Machine," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-14, March.
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