Robust mixed H 2 / H ∞ fuzzy tracking control of photovoltaic system subject to asymmetric actuator saturation

Abstract

This paper focuses on mixed ${\mathcal{H}}_2/{\mathcal{H}}_{\infty }$ fuzzy maximum power point tracking (MPPT) of photovoltaic (PV) system under asymmetric saturation and variations in climatic conditions. To maximize the power from the PV panel array, the DC–DC boost converter is controlled by its duty ratio which is practically saturated between 0 and 1. MPPT based on conventional control presents the problems of oscillations around maximum power point (MPP) and divergence under rapid climatic changes. In order to attenuate the effect of atmospheric condition variation and take into account asymmetric saturation of the duty ratio, we propose a novel robust saturated controller based on both ${\mathcal{H}}_2/{\mathcal{H}}_{\infty }$ performances and Takagi-Sugeno (T-S) representation of PV-boost nonlinear system. Within this approach, the nonlinear PV-boost system and its reference are first described by T-S fuzzy models. Second, the saturation effect is represented by a polytopic model. Then, a fuzzy integral state feedback controller is designed to achieve stable MPPT control. Based on Lyapunov function, the mixed ${\mathcal{H}}_2/{\mathcal{H}}_{\infty }$ stabilization conditions are derived in terms of linear matrix inequalities (LMIs). The optimization of the attraction domain of closed-loop system is solved as a convex optimization problem in LMI terms. Finally, the efficiency of the proposed controller under irradiance and temperature variations is demonstrated through the simulation results. The comparison with some existing controllers shows an improvement of MPPT control performance in terms of power extraction.