Robust LQG Controller Design by LMI Approach of a Doubly-Fed Induction Generator for Aero-Generator

Abstract

This article presents a design method to improve the robustness in stability and performance of an LQG controller by the LMI approach applied to a multivariable system subject to parametric uncertainties, where its variations are known to have a direct impact on the degradation of the robustness margins of a classical LQG controller. The main of this work is to synthesize a robust Linear Quadratic Gaussian (LQG) controller reformulated by the Linear Matrix Inequality (LMI) approach and to apply it on an illconditioned system. Our choice fell on a doubly fed induction generator (DFIG) of the aero-generator to produce electrical energy, whose physical parameters are uncertain due to several factors: winding heating, magnetic saturation..., this makes it difficult to maintain the voltage at 220V and the frequency at 50Hz. First, the mathematical model of DFIG is written in a d-q reference frame. The singular values of the uncertainties are quantified and multiplied at the system output, and then the robustness conditions are determined. Secondly, the robust control law by the LQG synthesis based on the solution of the convex optimization problem under LMI Eigenvalue problem is elaborated and detailed. The simulation results of the stability and performance robustness of the LQG controller by the LMI approach with nominal and disturbed model of the DFIG are presented and discussed on the method efficiency.