Analysis and Control of Limit Cycle Bifurcations

The chapter addresses bifurcations of limit cycles for a general class of nonlinear control systems depending on parameters. A set of simple approximate analytical conditions characterizing all generic limit cycle bifurcations is determined via a first order harmonic balance analysis in a suitable frequency band. Moreover, due to the existing connection between limit cycle bifurcations and routes to chaos, the obtained predictions can also give a rough indication of possible regions of chaotic dynamics. Based on these analysis results, an approach to limit cycle bifurcation control is then proposed. The control design is based on a frequency interpretation of the bifurcation conditions obtained via harmonic balance approach. Examples of the control technique for a number of important bifurcations are reported.