Cascaded Voltage-Current Control for Grid-Forming Inverters: Design of Multi-Resonant State-Feedback Controller Using LMI Approach

Grid-forming (GFM) inverters play a critical role in regulating voltage and frequency to ensure stable operation of isolated microgrids. Among the various control strategies, resonant controllers are recognized as one of the highest-performance solutions for AC current and voltage control. Traditionally, state feedback control implementations based on single loop control have been widely used for GFM inverters. However, these structures exhibit limitations in addressing key issues such as current reference tracking, and overcurrent conditions. To overcome these challenges, this paper proposes a discrete state feedback proportional multi-resonant control strategy implemented within a cascaded voltage-current loop for GFM inverters. This approach enables the controller to handle both current and voltage reference tracking simultaneously. A set of linear matrix inequality (LMI) constraints is employed to synthesize controller gains ensuring robust stability. Simulation results demonstrate the effectiveness of the proposed control strategy in achieving harmonic mitigation and precise reference tracking.