Parametric Robust Generalized Minimum Variance Control

Abstract

This work presents a hybridization of the Generalized Minimum Variance Control (GMVC) with Parametric Robust Control (RPC) for Linear Time-Invariant (LTI) Uncertain Systems. A linear parametric uncertainties model describes the system’s dynamic behavior. The controller synthesis is based on a PID controller with a low-pass filter and formulated as a convex optimization problem that considers the desired closed-loop performance and the uncertainties of the model parameters. The robust controller gains represent the best solution for all possible models and assign the closed-loop poles within the desired region in the s-plane and are transferred to GMVC by Tustin’s method, resulting in a parametric robust generalized minimum variance (PRGMV) controller. It was compared to two other approaches, carrying out several simulation essays in a Matlab environment. The performance index and sensitivity analysis highlight the controller’s performance and efficiency. The results confirmed that the proposed controller ensures better robustness and performance for reference tracking and disturbance rejection.

Keywords

• GMVC
• parametric uncertainties
• convex optimization
• PID control
• sensitivity analysis