ANALYSIS OF SELF-OSCILLATIONS IN A SYSTEM WITH A LINEAR SPEED REGULATOR

Abstract

In electric drives of a direct current low-power, in which the speed is regulated without an internal current controller, it has been observed in practice that when the speed stabilizes, the linear regulator with increasing its gain can go into high-frequency mode while maintaining the stability of the control system. From a practical point of view, this mode of operation is almost a sliding or quasi-sliding mode. However, at low gain factors, the control remains linear. The paper carried out a theoretical analysis of these phenomena with the definition of the parameters of self-oscillations and the boundary value of the gain, above which the linear speed controller turns into a quasi-relay mode of operation. Thus, there is a transition from the control of a continuous signal to the control of non-linear high-frequency oscillations at the output of the regulator.The research of self-oscillations in the electric drive of direct current, which contains linear speed regulator with rigid and flexible feedback on the first derivative of the speed in its composition, was carried out by the method of harmonic linearization. It was found that a linear proportional speed regulator with a specified set of feedbacks at sufficiently small gains (about several tens) goes into a mode of high-frequency steady self-oscillations, which can be called a quasi-sliding mode. The dependences of the self-oscillation parameters on the parameters of the control system are determined, formulas are found for finding the frequency of self-oscillations and the boundary gain factor of the regulator, above which the regulator changes from linear to quasi-sliding mode. The methods of the theory of automatic control and the direct calculation of transients confirmed the stability of the electric drive in a quasi-sliding mode and the high quality of the speed control.