RETRACTED: Interval-based LQR strategy for optimal control of proton exchange membrane fuel cell system with interval uncertainties

Abstract

Proton exchange membrane fuel cells (PEMFC) are a type of the increasingly developed sustainable energy systems which have been turned into one of the most popular of them in the last decade. The performance of these types of fuel cells is the best among the others; however, they can be better by an authentic control to maintain in the maximum efficiency in the operative points during the current ripples. To do this and also to improve the value of the output voltage, the two-phase interleaved boost converter is utilized. Since boost converter has uncertain parameters and disturbances in their essence, using the ordinary methods for the control of them can ignore some of the principal parameters. In this study, a new technique is utilized for optimal control of the proton exchange membrane fuel cells with interval uncertain parameters. Here, we consider the uncertainties in the converter inherent. Because of considering the uncertainties in the system, controllability of the system is first testified based on interval arithmetic. Then, an extended version of the linear quadratic regulator strategy using interval analysis is employed for achieving a reliable and optimal solution. Chebyshev inclusion method is utilized for solving the Pontryagins problem of the LQR problem. Eventually, by solving the interval version of the Riccati equations, the robust range for optimal control of the PEMFC is obtained. The results of the proposed system are finally compared with Monte Carlo method for showing the efficiency of the presented technique.