A frequency-domain approach to bifurcations in control systems with saturation

Bifurcation analysis of nonlinear control systems supplies a global perspective of the system behaviour modes. In this paper, it is shown that this analysis can be implemented with very elementary and classical tools, such as frequency-domain graphical methods. The methodology proposed is illustrated analysing the e€ ects of a saturation nonlinearity on a system designed with a linear control law. The full morphology of qualitative behaviours and of polar plots for two-dimensional systems is displayed, pointing out how bifurcations give rise to the boundaries between regions with di€ erent qualitative behaviour modes. Also a case of a three-dimensional system is analysed.