Stability Analysis of a Nonlinear Compressor System Using an Active Adaptive Controller and Reliable MPC Against Surge with an Anti-Surge Valve

This paper analyzes a nonlinear compressor system to characterize its dynamic behavior and develop a control scheme that improves operational efficiency. A mathematical approach based on the Greitzer–Moore (GM) model is employed to predict the onset of surge and instability. Using phase-plane analysis and Jacobian linearization, the method identifies stable and unstable regions and captures the limit cycle within the unstable domain. The system is formulated in state-space form using the nonlinear GM model, and validation is performed using experimental data from a previously studied compressor. Because fixed-gain PID controllers exhibit limited robustness, an adaptive PD controller based on a Model Reference Adaptive System (MRAS) is designed. In addition, a reliable Model Predictive Control (MPC) controller is developed to enhance disturbance rejection. Simulation results demonstrate that both the adaptive PD and MPC controllers achieve stable operation under challenging conditions.