Multi-loop linear resonant voltage source inverter controller design for distorted loads using the linear quadratic regulator method

In this study, an optimal multi-loop linear resonant control structure for a voltage source inverter (VSI) coupled to an inductor-capacitor (LC) filter is proposed for supplying nonlinear loads. A resonant controller ensures that sinusoidal voltage references are properly tracked and sinusoidal current disturbances are rejected without steady-state error under stable conditions. A desired transient response, on the other hand, can only be obtained by properly setting the controller coefficients. Further challenges include the reduction of output total harmonic distortion (THD), improving the damping of the LC resonance frequency and preventing the generation of fast closed-loop modes, which surpass the bandwidth of the inverter. The proposed technique is an extension of the classic linear quadratic regulator (LQR) that addresses the optimal tracking problem and provides a simple and step-by-step problem solving without stability or robustness issues. Additionally, the study also presents an improved controller to further reduce the voltage distortions for applications requiring acute accuracy. The designed controller is simulated and experimentally tested. The results are presented, discussed and confirmed against analytical derivations.