Effects of Magnitude Saturation in Control of Bifurcations
Yong Wang and Richard Murray
1999 IFAC World Congress
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 (or stable) 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. It is also possible to extend the techniques and results to Hopf bifurcations.
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