Particle Swarm Optimization of the Multioscillatory LQR for a Three-Phase Four-Wire Voltage-Source Inverter With an $LC$ Output Filter

This paper presents evolutionary optimization of the linear quadratic regulator (LQR) for a voltage-source inverter with an LC output filter. The procedure involves particle-swarm-based search for the best weighting factors in the quadratic cost function. It is common practice that the weights in the cost function are set using the guess-and-check method. However, it becomes quite challenging, and usually very time-consuming, if there are many auxiliary states added to the system. In order to immunize the system against unbalanced and nonlinear loads, oscillatory terms are incorporated into the control scheme, and this significantly increases the number of weights to be guessed. All controller gains are determined altogether in one LQR procedure call, and the originality reported here refers to evolutionary tuning of the weighting matrix. There is only one penalty factor to be set by the designer during the controller synthesis procedure. This coefficient enables shaping the dynamics of the closed-loop system by penalizing the dynamics of control signals instead of selecting individual weighting factors for augmented state vector components. Simulational tuning and experimental verification (the physical converter at the level of 21 kVA) are included.