Active Stabilization of Rotating Stall: A Bifurcation-Theoretic Approach

Abstract

Active control of the onset of stall instabilities in axial flow compressors is pursued using bifurcation analysis of a dynamical model proposed by Moore and Greitzer (1986). This model consists of three ordinary differential equations with state variables being the mass flow rate, pressure rise, and the amplitude of the first harmonic mode of the asymmetric component of the flow. The model is found to exhibit a stationary (pitchfork) bifurcation at the inception of stall, resulting in hysteresis. Using throttle opening as a control, analysis of the linearized system at stall shows that the critical mode (zero eigenvalue) is unaffected by linear feedback. Hence, nonlinear tools must be used to achieve stabilization. A quadratic feedback control law using the measurement of asymmetric dynamics is proposed which stabilizes the bifurcation and eliminates the undesirable hysteretic behavior.