A describing function technique for multiple nonlinearities in a single-loop feedback system

A graphical technique for determining the existence of limit cycles, their amplitude, frequency, and stability when they exist, and the stability of a single-loop feedback system with memoryless nonlinear elements and one nonlinear element with memory is considered. The approach here is to assume an input to a nonlinear element and then apply the Nyquist stability condition to the linear system resulting after the nonlinear elements have been approximated by their describing functions. The method requires no trial and error procedure, is noniterative in nature, and is especially easy to apply. The method is subject to the usual errors and restrictions of the describing function method. An extension of the method to include non-linear elements with memory and nonlinear elements in parallel is also included. Three numerical examples are included to illustrate the method.