Passivity and robust PI control of the air supply system of a PEM fuel cell model

Fuel cells are electrochemical devices that convert the chemical energy of a gaseous fuel directly into electricity. They are widely regarded as potential future stationary and mobile power sources. The response of a fuel cell system depends on the air and hydrogen feed, flow and pressure regulation, and heat and water management. In this paper, the study is concentrated on the control of the air subsystem that feeds the fuel cell cathode with oxygen—whose dynamics is described with a widely accepted nonlinear model. Due to the complexity of this model, the model-based controllers that have been proposed for this application are designed using its linear approximation at a given equilibrium point, which might lead to conservative stability margin estimates for the usually wide operating ranges of the system. On the other hand, practitioners propose the use of simple proportional or proportional–integral controllers around the compressor flow, which ensures good performance in most applications. In this paper we provide the theoretical justification to this scheme, proving that this output variable has the remarkable property that the linearization (around any admissible equilibrium) of the input–output map is strictly passive. Hence, the controllers used in applications yield (locally) asymptotically stable loops—for any desired equilibrium point and all values of the controller gains. Ensuring stability for all tuning gains overcomes the inherent conservativeness of linearized dynamics analysis, and assures the designer on the current use of robust, high performance loops. Instrumental to prove the passivity property is the exploitation of some monotonicity characteristics of the system that stem from physical laws.