20 th European Symposium on Computer Aided Process Engineering – ESCAPE20 S. Pierucci and G. Buzzi Ferraris (Editors) © 2010 Elsevier B.V. All rights reserved. Modelling and Explicit MPC of PEM Fuel Cell Systems Christos Panos a , Konstantinos I. Kouramas a ,Michael C. Georgiadis b , Nigel Brandon a , Efstratios N. Pistikopoulos a a Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ, UK, E-mail: [christos.panos08,k.kouramas, e.pistikopoulos]@imperial.ac.uk b Department of Engineering Informatics and Telecommunications, University of Western Macedonia, 50100 Kozani, Greece E-mail: mgeorg@uowm.gr Abstract We present an analytical dynamic model and a general framework for the optimal design and control of a PEM fuel cell system. The mathematical model includes detailed model for the PEM fuel cell stack and simplified models for the compressor, humidifier and cooling system. The framework features (i) a detailed dynamic process model, and (ii) an explicit/multi-parametric model predictive controller design step. For the model based controller design, a reduced order approximate model is obtained from the dynamic simulation of the system. Keywords: PEM fuel cell, Explicit/Multi-Parametric Model Predictive Control, Multi- parametric programming, 1. Introduction Fuel cells are a promising technology for the electrical power generation, widely regarded as a potential alternative to internal combustion engines for the mobile applications. The electrical efficiency of the fuel cell is greater than the most conventional processes for electricity generation. The primary type of fuel cells under consideration for the automotive industry is Proton Exchange Membrane (PEM) fuel cells. They have the most suitable properties for vehicle applications such as fast start- up, low sensitivity to orientation and favorable power-to-weight ratio [2, 8]. However to compete with internal combustion engines, fuel cells must reach similar level of performance and life time. The main technical issue is that ground vehicle propulsion is a high challenging problem due to variety of transient behavior within the fuel cell system. The control system has to ensure that critical parameters are in their optimal values in order to optimize the operation of the system and avoid degradation that could damage the fuel cell stack. There are many published mathematical models of PEM fuel cell in the literature with various level of complexity and could be classified into three categories, (i) the steady state mathematical models based on empirical equations, (ii) one dimensional dynamical models and (iii) two and three dimensional models based on navier-stokes equations. Amphlett et al. (1996) proposed a simple dynamic model which given a set of feed and operating condition could predict fuel cell voltage and stack temperature. Del Real et al.(2007) [1] presented a semi-empirical one dimension mathematical model with novel algorithm to calculate empirical polarization curve. Pathapati et al.[4] concentrated in the electrochemical behavior trying to best model the start-up sequence. Some authors developed more detailed models considering a gradient in stack temperature, two phase effect or implemented a two or three dimensional model [3].