Bifurcation based quadratic feedback control for Moore-Greitzer model with surge and multiple stall modes

We consider the n-mode truncation of the Moore-Greitzer partial differential equation model for axial compressors with bleed valve as actuator. It is well known that all the rotating stall modes are linearly unstabilizable past the peak of the compressor characteristic. By using the center manifold and normal form reduction, we obtain a model describing the nonlinear interactions of rotating stall and surge modes when the compressor operates in a neighborhood of the peak pressure rise. The normal form is a special class of the the famous Lotka-Volterra system. Typically, there are 2(n) equilibria as the throttle coefficient varies. We analyze the stability of these equilibria for the normal form, and interpret their relevance to the robustness of the nominal equilibrium near the peak pressure rise. We also derive the necessary and sufficient conditions for stabilizing the peak of the characteristic using a quadratic feedback control law.