Robust Set-Based Predictive Control for Grid-Tied Inverter with LCL Filter

This paper presents a robust set-based model predictive current control algorithm for grid-tied inverter with an LCL filter. Taken into consideration are variations in grid frequency and grid impedance, as well as uncertainties in the LCL filter parameters which are modeled in polytopic linear parameter varying framework. A robust state feedback gain based on
$H_{\infty}$
and regional pole placement constraints is synthesized solving a linear matrix inequality (LMI) problem, using this gain robust positively invariant terminal set is computed. From the terminal set, a family of control invariant sets is computed offline. Optimization problem is solved online subject to invariant sets membership constraint steering the states of the system to terminal set in finite time. Control algorithm is tested in simulation under grid frequency disturbance and various power loads.