Limit Cycle Bifurcation in SISO Control Systems with Saturation

Authors:	Ros Javier, Escuela Univ. Politecnica Univ. Sevilla, Spain Freire Emilio, Escuela Superior Ingenieros Univ. Sevilla, Spain Ponce Enrique, Escuela Superior Ingenieros Univ. Sevilla, Spain
Topic:	2.3 Non-Linear Control Systems
Session:	Nonlinear Stability and Structural Analysis
Keywords:	Piecewise linear systems, bifurcations, limit cycles, saturations

Abstract

The bifurcation of limit cycles in single-input single-outputcontrol systems with saturation is considered. Under somenon-degeneracy conditions, a theorem characterizing such bifurcationis stated for the cases of dimension two and three. In terms of thedeviation from the critical value of the bifurcation parameter,expressions in form of power series for the period, amplitude andthe characteristic multipliers of the bifurcating limit cycle areobtained. These results are similar to the Hopf bifurcation theoremfor differentiable systems, but they show some differences comingfrom the non-smooth character of the saturation characteristic.