Analysis and Design of Photovoltaic Nonlinear System: A Delta Operator Fuzzy Control Scheme

Abstract

Aims: The paper is concerned with the problem of robust H∞ output feedback control for photovoltaic nonlinear system. Background: The PV systems are built to transform sun irradiance into electrical power. The dc-dc converters, such as buck type, boost type, and buck-boost type, have been widely implemented in the PV systems. Linear controllers for dc-dc converters are often designed based on mathematical models. To get a desired performance objective, an accurate model is essential. Objective: There has been increasing interest in the scheme of digital controller design for dc-dc converters. However, most of the research efforts are focused on the representation based on the standard forward-shift operator approach, which are of inherently ill-conditioned when datum are taken at high sampling rates. Compared with the forward-shift operator, the delta operator has many virtues which can be applied as a better representation of the underlying physical model under high sampling rates. Despite the delta operator possessing the superior high sample rate performance has been recognized in the past two decades, there exists little literature discussing the analysis and synthesis of photovoltaic nonlinear systems by using delta operator fuzzy control method, which motivates us to make an effort in this topic. Methods: We propose a Fuzzy Dynamic Output Feedback (FDOF) controller, and introduce a novel Lyapunov-Krasovskii Functional (LKF) in delta domain, the framework of robust H∞ output feedback control is investigated. Results: Sufficient conditions are derived for the existence of the desired FDOF controllers in terms of Linear-Matrix Inequalities (LMIs). A numerical example is used to illustrate the design procedure of the present method. Conclusion: This paper has studied the problems of robust H∞ output feedback control for photovoltaic nonlinear system with interval time-varying delay and parametric uncertainties. Based on the formulated fuzzy system and the FDOF controller, we introduced a Lyapunov-Krasovskii function in delta domain, the scheme of FDOF was proposed. Sufficient conditions for the existence of the FDOF controller were derived in terms of LMIs. A numerical example was used to demonstrate the effectiveness of our proposed methods.