Design and analysis of robustness of DLQR controllers applied to grid-connected inverters

This work deals with the design of a robust discrete-time quadratic controller applied to inverters connected to grid with uncertain inductance. First, the plant is modeled taking into account uncertain parameters and parasitic resistances, leading to a discrete-time polytopic model with two vertices. The control gains are computed by means of linear matrix inequality conditions. A design example including resonant controllers to ensure the tracking of sinusoidal reference for the grid injected current and attenuation of harmonics is detailed. As results, analysis of eigenvalues, frequency responses and time responses of the closed-loop system are shown, illustrating good performance for both extreme values of grid inductance.