Effects of magnitude saturation in control of bifurcations

Abstract

Motivated by problems such as active control of rotating stall in compression systems, an analysis of the effects of controller magnitude saturation in feedback stabilization of steady-state bifurcations is performed. In particular the region of attraction to the stabilized bifurcated equilibria is solved for feedback controllers with magnitude saturation limits using the technique of center manifold reduction and bifurcation analysis. It has been shown that the stability boundary is the saturation envelope formed by the unstable equilibria for the closed loop system when the controllers saturate. The framework allows the design of feedback control laws to achieve desirable size of region of attraction when the noise is modeled as a closed set of initial conditions in the phase space. Modular the phase of the limit cycles, the qualitative behavior in the Hopf bifurcation case is the same as some cases in the steady-state bifurcations.