On an Extension of the Describing Function Method

A numerical method is presented for the local search of a limit cycle oscillation in multiloop nonlinear control systems with multiple nonlinearities. The nonlinearities may be asymmetric in nature. Dual inpuit Describing Functions have been used to model the bias and the first harmonic gains of the nonlinearities. Existence of a limit cycle is sought by solving a coupled set of eigenvalue problems. The evolution of the limit cycle is studied next as a function of a critical system-parameter. A Generalized Newton-Raphson method has been developed in this paper to solve for the active updates of the state variable amplitudes in a minimum norm sense. A case study involving a third order control system with an asymmetric nonlinearity is included to illustrate the application of the method.