The dynamics analysis and controller design for the PEM fuel cell under gas flowrate constraints

This paper is on the dynamics analysis and controller design for the PEM fuel cell under the flowrate constraints of the supplied hydrogen and oxygen. By linearization around the equilibrium trajectories defined by the quantities of hydrogen and oxygen input flowrate, the nonlinear dynamics of the PEM fuel cell can be expressed as a linear parameter varying system with the output current and temperature as the system parameters. The state-feedback controller design is performed based on the linear time-invariant model obtained from the derived linear parameter varying system evaluated at the half load operation condition. The control objective is to achieve a maximized relative stability or equivalently the maximum decay rate under the specified magnitude constraints on the input flowrate of hydrogen and oxygen. The convex linear matrix inequality algorithm is utilized for numerical construction of the state-feedback control law. Under the fixed load resistance corresponding to the half load condition, the time response simulations are conducted for both the cases of initial condition regulation and external command tracking. For the simulation of regulation, the initial deviation of state variables diminishes quickly that agrees with the obtained large delay rate during controller design. In the case of command tracking for the same amount of state variables, the controlled system can follow the issued command in the right direction but leave large tracking error, which is due to the weak controllability of the gas flowrates on the activation overvoltage for the PEM fuel cell system dynamics.