ANALYSIS OF THE EFFECT OF UNCERTAINTY IN THE MATHEMATICAL MODEL OF MAGNETIC LEVITATION ON THE CHARACTERISTICS OF THE AUTOMATIC CONTROL SYSTEM

DOI: 10.47026/1810-1909-2023-2-102-111

УДК 004.896, 519.876.5

ББК 32.96

Anatoly G. KOROBEYNIKOV, Alexey Yu. GRISHENTSEV

Key words

Automatic Control System, magnetic levitation, transient function, robustness, uncertainty, MATLAB

Abstract

Stability in the design of automatic control systems is one of the main issues, because an unstable system has no practical significance. This is due to the fact that any control system is vulnerable to interference and noise in real working environment, and the effect caused by these signals will adversely affect the expected normal output in an unstable system.

The purpose of the study is the design and analysis of an automatic control system, taking into account the requirement of robustness based on the H_∞-norm.

Materials and methods. The construction of a robust automatic control system was carried out using methods based on the calculation of the corresponding H∞-norm with the involvement of methods for solving the matrix Riccati equation. MATLAB was used as a toolkit.

Research results. Under uncertainties, control algorithms are of great importance. They enable to achieve the goal of control with given requirements and possess the property of stability during the transformation of the parameters of the control object and the characteristics of the effects of various kinds of disturbances. Feedback control methods can reduce the impact of uncertainties and provide the desired performance. However, an inadequate feedback controller can result in an unstable closed system, although an initially open system is stable. In this paper, we consider the problem of designing a stabilizing controller for an automatic control system for a levitating body with uncertainties in the parameters. The initial mathematical model of magnetic levitation, which serves as an object of control, was derived on the basis of Newton’s second law and electromagnetic induction and is a second-order ordinary differential equation with parameters containing uncertainties due to exogenous or endogenous factors. According to the Earnshaw theorem, such a system, even with zero uncertainties in the parameters, is initially unstable. With the addition of uncertainties with non-zero values, the situation with achieving stability worsens significantly. Therefore, it is necessary to develop special automatic control systems. The results of studying the influence of uncertainties in the mathematical model of magnetic levitation on the characteristics of its continuous automatic control system with one input and one output (SISO-system) are presented in a graphical form.

Conclusions. The stable effect of magnetic levitation is achieved even with sufficiently large uncertainties in the mathematical model of the control object.

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Information about the authors

Anatoly G. Korobeynikov – Doctor of Technical Sciences, Professor, ITMO University; Deputy Director on a Science, Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio wave Propagation of the Russian Academy of Sciences St.-Petersburg Filial, Russia, St. Petersburg (Korobeynikov_A_G@mail.ru; ORCID: https://orcid.org/0000-0002-9968-0207).

Alexey Yu. Grishentsev – Doctor of Technical Sciences, Assistant Professor, ITMO University, Russia, St. Petersburg (agrishentsev@yandex.ru; ORCID: https://orcid.org/0000-0003-1373-0670).

For citations

Korobeynikov A.G., Grishentsev A.Yu. ANALYSIS OF THE EFFECT OF UNCERTAINTY IN THE MATHEMATICAL MODEL OF MAGNETIC LEVITATION ON THE CHARACTERISTICS OF THE AUTOMATIC CONTROL SYSTEM. Vestnik Chuvashskogo universiteta, 2023, no. 2, pp. 102–111. DOI: 10.47026/1810-1909-2023-2-102-111 (in Russian).

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