Globally stabilizing controllers for multi-mode axial flow compressors via equilibria-dependent Lyapunov functions

Compressor aerodynamic instabilities can have adverse effects on compression system performance. In this paper we develop a multimode model for rotating stall and surge in axial flow compression systems that lends itself to the application of nonlinear control design. Using Lyapunov stability theory, a novel nonlinear globally stabilizing control law based on equilibria-dependent Lyapunov functions with converging domains of attraction is developed. The multimode model is used to show that the second and higher-order disturbance velocity potential harmonics in the flow equations strongly interact with the first harmonic during stall inception and must be accounted for in the control-system design processes