ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)

12
Issue
vol 63 / December, 2020
Article

DOI 10.17586/0021-3454-2017-60-7-612-623

UDC 62-50

## STABILITY OF DESIRED STATIONARY REGIME OF CLOSED-LOOP SYSTEMS WITH PERIODICALLY CHANGING STRUCTURE

A. I. Korshunov

Abstract. Closed-loop automatic system with structure subject to high-frequency changes is considered. Systems of this class are widely applied in power electronics. Calculation of the system parameters is proposed to be performed by a limiting continuous model which does not account for current and voltage pulsations in actual system. The discrete nature of the control may cause in the real system negative effects such as oscillations distorting the desired stationary mode with pulsation frequency of the output signal equal to the switching frequency of the system structure. The reason of the effects is usually a violation of the conditions of stability of the desired mode. Taking into account different variants of mathematical description of power part of the system within the periods of switching, a difference equation governing the system component is derived as well as a difference equation of the integral controller. For a given ratio of the parts of the switching period, the stationary vector of the phase coordinates of the system and the matrix of the linearized differential equations of perturbed motion are defined. Location of the matrix eigenvalues inside the circle of the unit radius guarantees asymptotic stability of the stationary regime. Using this matrix in the case of the stability of the desired stationary mode it is possible to construct quadratic Lyapunov functions to guarantee separation of at least part of stability domain. An example of practical application of the results to a voltage regulator with parametric control is presented. The study of stability of desired stationary regime of the regulator carried out with the use of mathematical modeling in MatLab, confirmed the urgency of the problem under consideration and correctness of the proposed solution.
Keywords: linear system, periodic change of structure, desired stationary mode, stability, perturbed movement, matrix of the linearized equation of perturbed movement

References:
1. Korshunov A.I. Power electronics, 2005, no. 3, рp. 52–55.
2. Severns R.P., Bloom G.E. Modern DC-to-DC Switchmode Converter Circuits, 1985.
3. Belov G.A. Elektrichestvo, 2008, no. 4, рp. 40–49. (in Russ.)
4. Chetty P.R.K. Switch-Mode Power Supply Design, TAB Books Inc., 1986.
5. Korshunov A.I. Power electronics, 2016, no. 3, рp. 36–40. (in Russ.)
6. Rozanov Yu.K. Silovaya elektronika (Power Electronics), Moscow, 2007, 612 р. (in Russ.)
7. Korshunov A.I. Journal of Instrument Engineering, 2009, no. 9 (52), рp. 42–48.
8. Korzhavin O.A., Voronoy A.A. Practical Power Elecroincs, 2008, no. 30, рp. 29–35.
9. Bromberg P.V. Matrichnye metody v teorii releynogo i impul'snogo regulirovaniya (Matrix Methods in the Theory of Relay and Pulse Regulation), Moscow, 1967, 324 р. (in Russ.)
10. Korshunov A.I. Automation and Remote Control, 1990, no. 5, рp. 91–102.