Method for the theoretical analysis of relay feedback systems

A method is presented for accurately determining the operating conditions of relay feedback systems which is relatively simple to apply. The method is basically an extension of the sinusoidal describing function and can be explained by reference to an analogous system containing a modified plant with a sinusoidal output. It is exact for symmetrical oscillations in systems containing relays having either two or three possible states, for asymmetrical oscillations in the former and can give a good approximation for asymmetrical oscillations in the latter. Extension of the method to allow for determination of the frequency response of the system and also for the effect of high- and low-frequency disturbances on the performance is considered. In this connection, its use in calculating the approximate operating conditions for a system containing a nonlinearity in which the output is dependent on the input over part of the characteristic is investigated. This extends the usefulness of the method to other nonlinear systems. Details of practical simulator tests on several systems are given, and the results of these tests compared with the results obtained from theoretical calculations.