Modeling, simulation & optimal control of non-linear PEM fuel cell with disturbance input

Fuel cell are considered to be one of the well- known developed green technologies among other renewable energy sources with high potential capability. In this paper, fifth order model of a PEM fuel cell has been considered which seems to be quite complex. The Jacobian linearization of the proposed system has been carried out around an operating point in non-coordinate standard form to take into consideration proper initial conditions well as equilibrium point. Conventional controllers like PID were used to regulate the pressure change of hydrogen and oxygen at the desired value despite of changes in the fuel cell current. Since it is known that large deviations in pressure can cause severe membrane damage in the fuel cell. As the equilibrium point at steady state becomes unique, hence Jacobian linearization of the original system has been done and the state space matrices of the linearized system were found using MATLAB Symbolic Tool Box. The linearized system is asymptotically stable as well as controllable and observable. During the optimal control design, hydrogen and oxygen partial flow rates are defined as the control variables and the hydrogen and oxygen pressure are appropriately defined as the control objectives. The simulation result shows that the linearized PEMFC model with conventional PID controller where the controller parameters are tuned using Genetic Algorithm with ISE and ISTE control strategies were having less tracking error.