Analysis of asymmetrical nonlinear oscillations in the parameter plane

This paper presents the analysis of asymmetrical non-linear oscillations by the parameter plane method and the describing function technique. The asymmetrical oscillations, which refer to the case when a limit cycle is superimposed on a constant or slow-varying signal, are investigated in control systems having either asymmetrical nonlinear characteristics or slow-varying input signals. It is shown how the presence of a limit cycle can modify the nonlinear characteristic for the slow-varying signal. A procedure is presented by which the modified characteristic is calculated. The application of the procedure to limit cycling control and adaptive systems is straightforward. The proposed method is illustrated by examples in which the asymmetrical oscillations are investigated in multiloop feedback structures with several adjustable parameters and different non-linear characteristics. The obtained results are checked by computer simulations.