Nuances of the Analytical Method for Studying Stability in Relay Systems

摘要

Relay systems, like most non-linear systems, are mainly calculated by approximate methods. However, in the class of relay systems, in some cases, calculation by the analytical method is possible. The study of the stability of the obtained self-oscillations must also be carried out analytically, for example, using the apparatus of discrete circuits and signals. This method is quite simple to implement and allows one to study stability in theoretically important cases, for example, if the degrees of the numerator and denominator differ by 1 order or coincide. In the case of the integrator and the discontinuous transient response of the linear part, it is necessary to clarify the general methodology for studying stability, since the transition to discrete circuits by the method of full correspondence of impulse characteristics is incorrect, and in the case under consideration, the transition is carried out by the method of full correspondence of transient characteristics.