Determination of Self-Oscillations in Relay Control Systems

Some dynamical linear elements including on-off elements such as electro-mechanical relays and electronic components used in switching mode for some feedback control systems can present special features such as the capability to autonomously generate stable self-oscillations. This paper concerns the comparison of two approaches enabling to determine the frequency of self-oscillations in these systems. We examine Tsypkin’s approach which can provide analytical solutions to determining the frequency of existing self-oscillations. On the other hand, we examine the Describing Function (DF) approach which has been developed as an alternative to approximate these solutions.

We will compare these two approaches for nonlinear systems of first and second orders. We will examine particularly the possibilities and limits of each approach for calculating the self-oscillations. Simulation of these systems will be performed to visualizes their behaviors. An experimental feedback control system based on electronic circuits used in switching mode has been built as a setup enabling testing and envisioning some applications.