Analytic Parameterization of Stabilizing Controllers for the Moore-Greitzer Compressor Model

Sammanfattning: This work presents an extension, simplification and application of a design procedure for dynamic output feedback design for systems with nonlinearities satisfying quadratic constraints (QC). Our method was motivated by the challenges of output feedback control design for the three-state Moore-Greitzer (MG) compressor model. The classical three-state MG model is a nonlinear dynamical system that is widely used in stall/surge analysis and control design.

First, we find the parameter set of the stabilizing dynamic output feedback controllers for the surge subsystem by using conditions for stability of a transformed system and the associated matching conditions.

Second, we choose the optimal control parameters from the stabilizing set with respect to different desired criteria.

We show the set of parameters of the stabilizing controllers for the surge subsystem and the set of parameters of the stabilizing controllers with extended integral part for MG compressor.

We present simplified sufficient conditions for stabilization, new constraints for the corresponding parameters and examples of optimal problem for the surge subsystem of the Moore-Greitzer compressor model.

We discuss the degree of robustness and clarify an alternative proof of stability of the closed-loop system with the surge subsystem and the stabilizing dynamic output feedback controller without an integral state. In addition, we show the derivation of a quadratic function by using CVX.