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A Novel Predefined Time PD-Type ILC Paradigm for Nonlinear Systems

Author

Listed:
  • Chun-Wu Yin

    (School of Information and Control Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China)

  • Saleem Riaz

    (School of Automation, Northwestern Polytechnical University, Xi’an 710129, China)

  • Haider Zaman

    (Electronics Engineering Department, University of Engineering and Technology Peshawar, Peshawar 25000, Pakistan)

  • Nasim Ullah

    (Department of Electrical Engineering, College of Engineering, Taif University, Taif 11099, Saudi Arabia)

  • Vojtech Blazek

    (ENET Centre, VSB—Technical University of Ostrava, 708 00 Ostrava, Czech Republic)

  • Lukas Prokop

    (ENET Centre, VSB—Technical University of Ostrava, 708 00 Ostrava, Czech Republic)

  • Stanislav Misak

    (ENET Centre, VSB—Technical University of Ostrava, 708 00 Ostrava, Czech Republic)

Abstract

Intelligent robotics has drawn a great deal of attention due to its high precision, stability, and reliability, which are the basic key factors for industrial automation. This paper proposes an iterative learning control (ILC) technique with predefined-time convergence as a solution to an applied engineering problem, namely, that local time cannot be preset when a second-order nonlinear system undertakes control of the accurate tracking of local time under any initial iterative value. A time-varying sliding surface with an initial value of zero was designed, and it was theoretically proven that the trajectory tracking error in the sliding surface could converge to zero within a predefined time. The iterative control problem of trajectory tracking was thus changed to an iterative control problem of time-varying sliding-mode surface tracing with a starting value of zero. A PD-type closed-loop ILC with a time-varying sliding mode surface was designed such that the trajectory tracking error converged and stabilized on the sliding mode surface after a finite number of learning iterations. The control goal for the system’s output was the ability to track the desired trajectory accurately within a predefined time interval, and it was achieved by combining this with the predefined time convergence characteristics of the time-varying sliding mode surface. Numerical simulation of trajectory tracking control of a repetitive motion manipulator was used to verify the effectiveness of the proposed controller and its robustness in the face of external disturbances.

Suggested Citation

  • Chun-Wu Yin & Saleem Riaz & Haider Zaman & Nasim Ullah & Vojtech Blazek & Lukas Prokop & Stanislav Misak, 2022. "A Novel Predefined Time PD-Type ILC Paradigm for Nonlinear Systems," Mathematics, MDPI, vol. 11(1), pages 1-19, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:56-:d:1013188
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    References listed on IDEAS

    as
    1. Saleem Riaz & Hui Lin & Muhammad Waqas & Farkhanda Afzal & Kai Wang & Nasir Saeed, 2021. "An Accelerated Error Convergence Design Criterion and Implementation of Lebesgue-p Norm ILC Control Topology for Linear Position Control Systems," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-12, November.
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