A describing function approach to limit cycle controller design

The design of robust limit cycle controllers introduced here can be used for autonomous systems with separable single-input-single-output nonlinearities. Considering a system with unavoidable limit cycle and an uncertain linear subsystem, the objective is to design a controller such that the variation in limit cycle amplitude and frequency due the uncertainty is as small as possible in the controlled system for the worst uncertainty considered. The method consists of quasi-linearization of the nonlinear element via a describing function (DF) approach and then shaping the loop to reach desired limit cycle characteristics. As the DF method is used, loop shaping takes place in the Nyquist plot