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Mekhatronika, Avtomatizatsiya, Upravlenie, 2017, vol. 18, no. 9, pp. 589—596
DOI: 10.17587/mau.18.589596
Current State and Prospects for Development of the Theory of Relay Feedback Systems
S. V. Feofilov, svfeofilov@mail.ru, A. V. Kozyr, Kozyr_A_V@mail.ru, Tula State University, Tula, 300012, Russian Federation

Corresponding author: Kozyr Andrew V., Postgraduate Student, Tula State University, Tula, 300012, Russian Federation, email: Kozyr_A_V@mail.ru
Received on March 02, 2017
Accepted on March 16, 2017
This paper presents a brief review of the theory of the relay feedback systems. Analysis and synthesis of the relay selfoscillating systems is currently a classical topic in the control theory. The main problems of the theory are analysis of the possible selfoscillations, stability, estimation of robustness, and regulator design. The first works devoted to the analysis of the relay feedback systems appeared in 1950s. However, many problems concerning this theory are still unresolved. Systematization of the theory of the relay control systems and the definition of possible directions for research in future are presented in this article. The main attention is paid to the method of studying of the selfoscillating systems for the phase locus method. This method was developed in the Department of Automatic Control Systems of Tula State University. Introduction contains a brief historical review of the problems and methods for their solution within the framework of the theory of the relay systems of automatic control. The second section provides a brief review of the methods for studying of the selfoscillations in the control systems in the frequency domain. The main attention in this section is given to the methods, based on the Tsypkin locus. The third section deals with the methods of analysis and synthesis of the relay systems of automatic control in the state space. The method of the phase locus is considered. This method is applicable to the study of the systems with a nonlinear control object. Within the framework of this method, a synthesis algorithm was generated. The recent work within the framework of this theory was devoted to the synthesis of stable selfoscillating control systems. An analysis of the global asymptotic orbital stability of the selfoscillations in the systems with a linear control object in the form of linear matrix inequalities is considered, as well as the problems of designing of the digital relay controllers.
Keywords: selfoscillating relay control systems, Tsypkin locus, phase locus 
For citation:
Feofilov S. V., Kozyr A. V. Current State and Prospects for Development of the Theory of Relay Feedback Systems, Mekhatronika, Avtomatizatsiya, Upravlenie, 2017, vol. 18, no. 9, pp. 589—596.
DOI: 10.17587/mau.18.589596
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