Dynamic output feedback stabilization of the 3 state Moore-Greitzer compressor model

Anton Shiriaev
Dept. of Applied Physics and Electronics
Umea University, SE-901 87 Umea, Sweden
Dept. of Engineering Cybernetics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway

Abstract: A three-state Moore-Greitzer (MG) model introduced in 1986 is a three-state system of ordinary differential equations, approximately describing a flow of gas through an axial compressor. The model is widely used for analysis and control of compressors due to its capabilities to cover qualitatively and quantitatively two limiting factors in performance of compressor systems: rotating stall and surge. The three-state MG-model is a heavily nonlinear system, whose linearization around any of operating points is not controllable, so that even full state feedback stabilization of such system is a challenge.

We suggest a new design of output feedback controllers for the three-state MG-model. The proposed approach is based of idea of parameterization of nonlinearities of the system via appropriate quadratic constraints, and re-use of such structural nonlinearities in the design of a dynamical output feedback controller. The overall stability of the closed loop system is further investigated exploiting classical results from quadratic stability theory. We show that stability is equivalent to solvability of a system of particular bilinear matrix inequalities. We derive conditions of solvability of such a system and, finally, propose a class of robustly stabilizing output feedback controllers