Computation of multiple limit cycles in nonlinear control systems –
a describing function approach
doi: 10.5028/jatm.2011.03017010

Alexandro Garro Brito*
Institute of Aeronautics and Space
São José dos Campos – Brazil
alegbrito2@gmail.com

*author for correspondence

Abstract:

Limit cycles play an important role in nonlinear systems, provided that many control loops with common nonlinearities like relay, hysteresis, and saturation can present them. Thus, a proper description of this nonlinear phenomenon is highly desirable. A strategy for the linearized analysis is the describing function method, which is a frequency domain approach that allows the limit cycle prediction and stability analysis. Some papers had discussed the method for the simplified analysis; however, they are concentrated in the prediction of only one limit cycle even for systems with multiple conditions. This paper proposes a systematic way of multiple limit cycle determination, as well as the stability analysis of each one. All theoretical/computational issues involved in the approach are also discussed.

Keywords:

Limit cycle, Multimodal optimization, Describing functions.

J. Aerosp.Technol. Manag., São José dos Campos, Vol.3, No.1, pp. 21-28, Jan. - Apr., 2011
Received: 21/05/10
Accepted: 16/08/10