An algebraic approach to the design of robust limit cycle controllers

The design of robust limit cycle controllers introduced here can be used for autonomous systems with separable single-input-single-output nonlinearities and unavoidable limit cycles. The objective is to design a controller to secure specified oscillation amplitude and frequency. 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.