Robust optimal tracking control for a three phase inverter

This paper proposes a robust nonlinear optimal control to regulate the active and reactive power in a three-phase inverter connected to the utility grid. The inverter includes an LCL filter to reduce the total harmonics distortion of the current injected to the grid. The optimal controller is derived from the Hamilton-Jacobi-Bellman equation, whose solution can be obtained for a class of disturbed nonlinear systems, named state-dependent coefficient factorized nonlinear systems, which include disturbances. The resulting control law minimizes a quadratic cost functional, which evaluates the tracking error and the control effort. Simulation results are presented to assess the performance of the proposed controller.