An Approach to State Signal Shaping by Limit Cycle Model Predictive Control

A novel nonlinear model predictive control approach for state signal shaping is proposed. The control strategy introduces a residual shape cost kernel based on the dynamics of circular limit cycles from a supercritical Neimark-Sacker bifurcation normal form. This allows the controller to impose a fundamental harmonic state signal shape with a specific frequency and amplitude. An application example for harmonic compensation in distribution grids integrated with renewable energies is presented. The controller is tasked with the calculation of the reference current for an active power filter used for load compensation. The results achieved are successful, reducing the harmonic distortion to satisfactory levels while ensuring the correct frequency and amplitude.