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Methods of Ensuring Invariance with Respect to External Disturbances: Overview and New Advances

Author

Listed:
  • Aleksey Antipov

    (Laboratory of Systems with Discontinuous Control, V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Science, 117997 Moscow, Russia)

  • Svetlana Krasnova

    (Laboratory of Systems with Discontinuous Control, V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Science, 117997 Moscow, Russia)

  • Victor Utkin

    (E.S. Pyatnitskiy Laboratory of Dynamics of Nonlinear Control Processes, V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Science, 117997 Moscow, Russia)

Abstract

In this paper, we carry out a demonstration and comparative analysis of known methods of the synthesis of various control laws ensuring the invariance of the output (controlled) variable with respect to external disturbances under various assumptions about their type and channels of acting on the control plant. Methods of the synthesis are presented on the example of a third-order nonlinear system with single input and single output (SISO-systems), dynamic feedback synthesis is presented at a descriptive level and the focus is on procedures of static feedback synthesis. For the systems in which the matching conditions are not satisfied, it is concluded that it is expedient to introduce smooth and bounded nonlinear local feedbacks. Within the framework of the block control principle, we developed an iterative procedure of synthesis of S-shaped sigmoid feedbacks for such systems. Nonlinear local feedbacks ensure stabilization of the output variable with the given accuracy and settling time as in a system with traditionally used linear local feedbacks with high gains. However, in contrast to it, sigmoid functions do not lead to a large overshoot of state variables and control actions.

Suggested Citation

  • Aleksey Antipov & Svetlana Krasnova & Victor Utkin, 2021. "Methods of Ensuring Invariance with Respect to External Disturbances: Overview and New Advances," Mathematics, MDPI, vol. 9(23), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3140-:d:695945
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    Citations

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    Cited by:

    1. Yaqiong Ding & Hanguang Jia & Yunong Zhang & Binbin Qiu, 2023. "High-Order Modeling, Zeroing Dynamics Control, and Perturbations Rejection for Non-Linear Double-Holding Water Tank," Mathematics, MDPI, vol. 11(13), pages 1-18, July.
    2. Natalia Bakhtadze, 2023. "Preface to the Special Issue on “Identification, Knowledge Engineering and Digital Modeling for Adaptive and Intelligent Control”—Special Issue Book," Mathematics, MDPI, vol. 11(8), pages 1-3, April.
    3. Anton V. Utkin & Victor A. Utkin & Svetlana A. Krasnova, 2022. "Synthesis of a Control System for a Waste Heat Boiler with Forced Circulation under Restrictions on Control Actions," Mathematics, MDPI, vol. 10(14), pages 1-24, July.

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