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

Aleksey Antipov, Svetlana Krasnova and Victor Utkin
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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

Mathematics, 2021, vol. 9, issue 23, 1-20

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.

Keywords: external disturbances; invariance; block control principle; decomposition; high-gain factors; sliding mode control; sigmoid function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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