Enhancing linear quadratic regulator and proportional-integral linear quadratic regulator controllers for photovoltaic systems

Abstract

This article introduces the linear quadratic regulator (LQR) control and the hybrid linear quadratic regulator proportional-integral (LQR-PI) control, both applied to a photovoltaic system coupled with a DC-DC boost converter. The converter outputs direct current electrical energy to power direct loads. Two robust control correctors, based on the LQR and LQR-PI methods, are designed to enhance the static and dynamic performance of the PV DC-DC boost system. These controllers aim to minimize oscillations and overshoots while ensuring stability across varying solar conditions, thereby optimizing operation around the maximum power point. The disturb and observe maximum power point tracking (MPPT) technique, integrated with the LQR and LQR-PI controllers, ensures system functionality under disturbances. The novelty of this work lies in the development of a MATLAB control block diagram capable of regulating the reference voltage provided by the perturb and observe (P&O) MPPT algorithm. MATLAB simulations demonstrate the robustness and high performance of the LQR and LQR-PI controllers, validating the efficacy of this boost converter control strategy.