On boundedness of solutions of three-state Moore-Greitzer compressor model with nonlinear proportional-integral controller for the surge subsystem
A team proves bounded stability for a 3-state compressor model using a nonlinear PI controller, despite the system being non-stabilizable via linear methods.
A team of researchers from Umeå University and Lund University has published a significant theoretical advance in control systems engineering, providing a formal proof of stability for a critical industrial model. Their paper, 'On boundedness of solutions of three-state Moore-Greitzer compressor model with nonlinear proportional-integral controller for the surge subsystem,' tackles the challenge of stabilizing compressor surge—a dangerous instability in jet engines and gas turbines—using a nonlinear PI controller. The work is notable because the system's linearization is not stabilizable, forcing the team to develop new analytical methods to prove that all closed-loop solutions remain bounded, a property known as Lagrange stability.
The technical contribution lies in the explicit conditions provided for controller parameters and the novel application of circle-criterion-based arguments. The analysis leverages a structural property of the stall-dynamics subsystem and a sector condition satisfied by the static nonlinearity. This approach not only guarantees boundedness but also demonstrates the closed-loop system's robustness to specific perturbations and model uncertainties. For engineers deploying AI and advanced control systems in safety-critical applications, this research provides a rigorous mathematical foundation for designing controllers that can prevent catastrophic failures in turbomachinery, moving beyond heuristic tuning to provably safe operation.
- Proves Lagrange stability for the 3-state Moore-Greitzer model with a nonlinear PI controller, providing explicit parameter conditions.
- Employs a non-standard application of circle-criterion arguments to handle a system whose linearization is not stabilizable.
- Demonstrates robustness to certain perturbations, a key requirement for real-world industrial control systems in jet engines and power plants.
Why It Matters
Provides a mathematical foundation for safe, AI-driven control of critical infrastructure like jet engines, preventing catastrophic surge events.