On boundedness of solutions of three-state Moore-Greitzer compressor model with nonlinear proportional-integral controller for the surge subsystem

TL;DR

This paper establishes explicit conditions for the boundedness of solutions in a three-state Moore-Greitzer compressor model with a nonlinear PI controller, ensuring stability and robustness despite system nonlinearities and uncertainties.

Contribution

It provides novel explicit stability conditions using a non-standard circle-criterion approach for a complex nonlinear compressor model with a nonlinear PI controller.

Findings

Solutions are proven to be bounded under specified controller parameters.

The stability conditions are robust to certain perturbations and model uncertainties.

The approach extends stability analysis techniques for nonlinear control systems.

Abstract

The work focuses on Lagrange stability of the origin for the three-state Moore-Greitzer compressor model in closed loop with a nonlinear PI controller, tuned only to stabilize a lower-dimensional invariant surge-dynamics subsystem.The linearization of the system is not stabilizable but the static nonlinearity satisfies a sector condition, and together with a structural property of the stall-dynamics subsystem, this plays an essential role in the analysis. The main contribution provides explicit conditions on the controller parameters together with analytical arguments that guarantee boundedness of all solutions of the closed-loop system. The analysis employs a non-standard application of circle-criterion-based arguments. Together with the additional arguments developed in the work, this stability test also shows that the closed-loop system is robust to certain perturbations and model uncertainties.