Exact determination of the limit cycles in relay control systems with additional nonlinearities in the feedback loops

The A-function method is extended to analyse a relay feedback control system with additional nonlinearities in the feedback loops. The situation considered is where the output of the plant and/or its successive derivatives are fed back to the input through nonlinearities that are assumed to be of polynomial type. An example is also given to show that, in some cases, the method can be used in systems with saturation or a linear segmented nonlinearity in the feedback path.