Robust LQG Controller Design by LMI Approach of a Doubly-Fed Induction Generator for Aero-Generator
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Date
2022-12-01
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Journal Européen des Systèmes Automatisés.Vol. 55, No. 6, December, 2022, pp. 803-816
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