An analytical approach to stability analysis of systems with two nonlinear elements

Stability analysis of systems with one nonlinear element is commonly performed by making use of the describing function principle and Nyquist or Nicholas diagrams. A procedure is described whereby the analysis method is extended to systems with two nonlinear elements. The proposed procedure is verified by stability analysis of a position control system with a saturation element and a dead zone as dominant nonlinearities. The limit cycle parameters predicted with the analysis procedure correspond very well with simulation results of the system. Using the results obtained from the analysis, a linear compensator is designed in order to suppress the limit cycle.<>