Limit cycle analysis of nonlinear sampled-data systems by gain-phase margin approach

Abstract

The main purpose of this work is to analyze the limit cycle phenomena of nonlinear sampled-data systems by applying the methods of gain-phase margin tester, the M-locus and the parameter plane. First, a sampled-data control system with nonlinear elements is linearized by the classical method of describing functions. According to stability equations and the parameter plane method, we can then analyze the stability of the equivalent linearized system with adjustable parameters. After adding the gain-phase margin tester in the forward open loop system, the relationship between the gain-phase margin and the characteristics of the limit cycle may be elucidated by finding the intersections of the M-locus and the constant gain and phase boundaries. A concise method is presented to solve this problem. In doing so, the minimum gain-phase margin of nonlinear sampled-data system at which a limit cycle can occur is conferred. This paper manifests that the procedure can be easily extended to analyze the limit cycles of a sampled-data system as compared with the continuous-data system cases in the literatures. Computer simulation results can verify its validity.