THE RATIONAL APPLICATION OF THE THEORY OF DISCRETE CHAINS IN THE DEVELOPMENT OF A GENERAL ANALYTICAL METHOD FOR EVALUATING THE STABILITY OF SELF-OSCILLATIONS IN RELAY SYSTEMS

This work is an extension of the previously developed analytical method for evaluating self-oscillations in relay systems, the basics of which are described in [1]. Relay systems have high speed, good noise immunity and easy to operate, and as a consequence, are common in control systems. The possibility of obtaining an analytical description of self-oscillations in a relay system required the development of new methods for assessing the stability of a solution. The stability analysis method for symmetric vibrations, when changes occur after half a period (Mτ), showed good results in comparison with known methods. Here we describe the further development of the method and its generalization to the case of asymmetric oscillations, when changes occur after a period (MT). In the case of an analytical study of high-order relay systems, sig-nificant difficulties may arise in the formation of a characteristic polynomial of equations that evaluate the stability of vari-ations in self-oscillations. The present work is devoted to the search for the optimal approach to composing the character-istic polynomial. The specificity of relay systems is such that the nature of the signal variations makes it possible to use the theory of discrete circuits for their analysis, on which the stability assessment method proposed by the authors is based.

Authors: A. G. Deripaska, M. V. Soklakova, E. P. Chernishev

Direction: Electrical Engineering

Keywords: Relay system, self-oscillations, characteristic polynomial, transfer function, stability, discrete chain

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