PEM fuel cell system identification and model order reduction for Hinfin; loop shaping controller design

Low order linear models are normally preferred over more complex ones particularly in the Hinfin control system framework. Controllers designed based on Hinfin linear control theory tend to exhibit orders higher than or equal to the order of the original system. In this contribution, two methods were utilized in order to obtain a low order linear MIMO state space model equivalent to the nonlinear automotive Proton Exchange Membrane Fuel Cell (PEMFC) power system developed in [2]. The principles of input-output system identification (prediction-error minimization) and balanced model order reduction were utilized. In the first method, a linear 8th order state space model was estimated to best reproduce the outputs of the nonlinear system. Model order was lowered one order at a time and a state space model was identified. The one step ahead prediction outputs of the linear modes (8th order through 4th order) were compared to the nonlinear model outputs of several input-output data sets. Outputs of the aforementioned linear models and the outputs of the nonlinear model were very closely matched. The identified 4th order linear model was deemed very suitable to represent the PEMFC system. In the second method, a balanced model order reduction technique was utilized to obtain a truncated 4th order linear model directly from the identified 8th order model obtained by the first method. The outputs of the truncated model and the outputs of the nonlinear model matched very well. Each of the 4th order models was capable of capturing the dynamics of the PEMFC system and each of their performances was deemed highly satisfactory. A simple yet effective Hinfin loop shaping power tracking controller was designed in order to set the net output power of the stack to its desired levels following dynamic changes in load demand by means of manipulating the input voltage of the compressor motor. The Hinfin compensated system exhibited faster transient response, less overshoot, higher robustness and lower sensitivity margins when compared to the results of basic feed forward controllers presented in [2], [4], and [10].