Analysis of Limit Cycle Stability and Control for Nonlinear Systems

Authors:

Ashish Kumar Shakya (National Institute of Technology, Kurukshetra)

Lillie Dewan (National Institute of Technology, Kurukshetra)

Keywords: Lur’e Problem, Describing Function Method, Limit Cycle, Barkhausen characteristic polynomial, Robust limit cycle controller.

Abstract:

Describing function method is used for stability investigation and prediction of limit cycle in nonlinear systems. If there are uncertainties in the system then the frequency and amplitude of the limit cycle will change accordingly and describing function method can deal with these uncertainties. In this paper attempt has been made to study the stability and robustness of nonlinear systems in the presence of uncertainties in different forms. Barkhausen characteristic equation is used in this paper to determine the robustness of the limit cycle. A robust controller to control the amplitude and the frequency of limit cycle against the parametric perturbations is also explained in this paper.

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