Bifurcation analysis and control for surge model via the projection method

A bifurcation approach is adopted to analyze and control the surge model for axial flow compressors. An explicit expression is obtained for the first nonzero coefficient of the characteristic exponents of the periodic solutions born from the Hopf bifurcation associated with surge. The sign of this coefficient determines stability of the surge model at the criticality. Local nonlinear feedback control laws are then developed to stabilize the Hopf bifurcation associated with surge. Both quadratic and cubic state feedback control laws are investigated. Feedback stabilization using output measurement such as pressure rise is also studied where stabilizing gains are characterized that can be used for synthesis of surge control laws.