A novel controller based on the sum of squares relaxation for the uncertain model of the PEMFC considering external disturbances and actuator saturation

Abstract

The current paper aims to model the uncertainties of the proton exchange membrane fuel cell system and control its main parameters, such as compressor speed and oxygen excess ratio, in the presence of external disturbances and actuator saturation using the improved controller, which is designed based on the sum of squares relaxation for nonlinear models. The open-loop nonlinear system is considered in state-dependent polynomial equations. The state feedback method is used to obtain the appropriate control responses. To numerically solve the state-dependent Linear Matrix Inequalities, semi-definite programming based on the sum of squares decomposition is also used. First, the transient response of the system is improved in the design phase of the controller. Then, the actuator saturation problem of PEMFC is considered for the state feedback controller proposed in polynomial systems, and the obtained results are expanded for the uncertain system. Results are also validated in the presence of external disturbances. The results are compared with those of the robust and adaptive control methods. The proposed controller not only has good agreement with the results of robust and adaptive control methods but also outperforms the previous controllers in terms of accuracy, rise time, fluctuation, and overshoot.