PID control design for the pressure regulation of PEM fuel cell

The well-known nonlinear fifth-order model of a proton exchange membrane (PEM, also known as polymer electrolyte membrane) fuel cell (PEMFC) seems to be quite complex. In this paper, we derived the linearized model of the original nonlinear system in non-coordinate standard form considering proper initial conditions and equilibrium point. Large deviations in pressure can cause severe membrane damage in the fuel cell. Conventional Proportional-Integralderivative (PID) controllers are used to regulate the pressure change of hydrogen and oxygen at the desired value despite of changes in the fuel cell current. As the equilibrium point at steady state becomes unique, Jacobian linearization of the original system has been done and the state space matrices of the linearized system were found using MATLAB Symbolic ToolBox. The linearized system is asymptotically stable as well as controllable and observable. During the control design, hydrogen and oxygen partial flow rates are defined as the control variables and the hydrogen and oxygen pressure difference are taken as the control objectives. The simulation result shows that the linearized PEMFC model with conventional PID controller where the controller parameters are tuned using Zeigler-Nichols (Z-N) having acceptable control performance.