A Robust Model Predictive Control for a Photovoltaic Pumping System Subject to Actuator Saturation Nonlinearity

Abstract

In this paper, a new robust model predictive control (RMPC) for uncertain nonlinear systems subject to actuator saturation is designed to regulate the terminal voltage of a photovoltaic generator (PVG) that feeds a DC motor-pump via a buck DC–DC converter. The considered system is a combination of a PVG-converter and DC motor-pump, which possesses nonlinear behavior along with under a saturating control signal highly dependent on the operation point and climate conditions of solar radiation and temperature. As a result, the control task is complex due to the nonlinearity of the system and its dependence on climate conditions. Based on the dead-zone property, the presented paper introduces a new RMPC technique to provide an innovative and efficient solution to ensure the closed-loop system’s robust stability in the presence of actuator nonlinearity. In this paper, the nonlinear system is described in polytypic form, and an appropriate linear feedback control law is designed and used to minimize an infinite horizon cost function under the framework of linear matrix inequalities (LMIs). Furthermore, sufficient state-feedback control law conditions are synthesized to guarantee the robust stability of the closed-loop system in the presence of polytypic uncertainties. Simulation results are provided, in which the results illustrate the effectiveness of the proposed method.