Improved Robustness of Generalized Predictive Control for Uncertain Systems

Abstract

An off-line methodology has been developed to improve the robustness of an initial generalized predictive control (GPC) through convex optimization of the Youla parameter. However, this method is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and polytopic uncertainties. The basic idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a non convex quadratically constrained quadratic programming (QCQP) problem. Based on semidefinite programming (SDP), this problem is relaxed and solved. Therefore, the robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, we present a numerical example to demonstrate the proposed method.K e y w o r d s: generalized predictive control, quadratically constrained quadratic programming, polytopic uncertainties, relaxation, robust control, semidefinite programming, Youla parameterization

Robustified fractional-order controller based on adjustable fractional weights for a doubly fed induction generator

“…A disadvantage of the 2-DOF H ∞ LSC technique is observed in the implementation step, which leads to high cost, difficult commissioning, poor reliability and potential problems in maintenance. To avoid these problems, the 2-DOF controller based on Generalized Predictive Control (GPC) have been proposed to increase the robustness margin of a closed-loop system against plant uncertainties and sensor noises (Aidoud et al, 2015; Khelifa et al, 2015; Thomsen et al, 2011). The controller design follows a three-step procedure.…”