(453e) Modelling and Multi-Parametric Model Predictive Control of a Proton Exchange Membrane Fuel Cell

Fuel cell power systems have exceptional potential for both stationary and mobile applications due to their outstanding energy efficiency and environmental characteristics. Especially for mobile applications, such as automotive applications, Proton Exchange Membrane Fuel Cells (PEMFC) are a potential candidate for the replacement of traditional fossil fuel based propulsion technologies for reducing the emission of pollutants and greenhouse gases (Pukrushpan et al., 2004). The modelling and control of fuel cells poses great challenges due to the complex electrochemical reactions that take place in a fuel cell. Special effort is required for the development of detailed mathematical models, based on Partial Differential Algebraic Equations (PDAE), that capture all the physicochemical and electrical phenomena (Gerogiorgis et al., 2006; Golbert and Lewin, 2004). The complex fuel cell dynamics also dictate that advanced multivariable constrained control methods have to be used to ensure efficient power generation and temperature management in varying operating conditions such as load changes (Gerogiorgis et al., 2006; Golbert and Lewin, 2004). On the other hand the development of rigorous mathematical models, although it is ideal for the detailed simulation and optimization of the fuel cell, cannot be used with the current advanced model-based control methods (Pukrushpan et al., 2004).

Model Predictive Control (MPC) and specifically Explicit Model Predictive Control (Pistikopoulos et al., 2004, 2007a,b, 2008) have been proved a promising method for the voltage control of fuel cells. In Gerogiorgis et al., 2006 an explicit MPC controller was designed for the voltage control of Solid Oxide Fuel Cells (SOFC) while in Arce et al., 2007 an explicit MPC controller was designed for a PEM fuel cell. However, the design of explicit MPC for both the voltage and temperature control of a fuel cell has not yet been addressed in the existing literature. Since temperature control of a fuel cell system requires the use of cooling/heat-exchange systems, the complexity of the system model increases and hence the control design (Golbert and Lewin, 2004).

This work focuses on the development and validation of a high-fidelity mathematical model for a PEM fuel cell system and the design of an Explicit Model Predictive Controller (mp-MPC) for the voltage and temperature control of the PEM fuel cell stack in varying operating conditions. A unified framework for the design and validation of Explicit MPC controllers is described for the design of the explicit MPC controller for a PEM fuel cell system. This framework consists of the following four main steps:

1. Development of a high-fidelity dynamic model to provide a detailed description of the underlying process

2. Derivation of an approximating model that can be used to obtain a suitable MPC formulation that can be readily solved by multi-parametric programming techniques

3. Design of the Explicit Model Predictive Controller by solving the above MPC formulation with multi-parametric programming methods

4. Validation of the resulting Explicit MPC by directly incorporating it into the high-fidelity model and performing simulation and dynamic optimization studies

The most important feature of this framework is that all steps are performed off-line, before any real implementation and can be repeated until a satisfactory Explicit MPC design is achieved. The performance of the controller is studied by showing the results from the simulations of the implementation of the explicit MPC on the high-fidelity system model for a range of varying current loads.

References:

Arce, A., Ramirez, D.R., del Real, A.J. & Bordons, C. (2007). Proc. of the 46th IEEE Conf. Dec. Con., New Orleans, LA, USA.

Gerogiorgis, D.I., Kouramas, K., Bozinis, N. & Pistikopoulos, E.N. (2006). Proc. of the AIChE 2006 Annual Meeting, San Francisco, USA.

Golbert, J. & Lewin, D.R. (2004). J. of Power Sources, 135, 135.

Pistikopoulos, E.N., Bozinis, N., Dua, V., Perkins, J. & Sakizlis, V. (2004). Improved Process Control, European Patent EP1399784.

Pistikopoulos, E.N., Georgiadis, M. & Dua, V. (2007a). Multi-parametric Programming: Theory, Algorithms and Applications, Weinheim: Wiley-VCH.

Pistikopoulos, E.N., Georgiadis, M. & Dua, V. (2007b). Multi-parametric Model-based Control: Theory and Applications, Weinheim: Wiley-VCH.

Pistikopoulos, E.N., Bozinis, N., Dua, V., Perkins, J. & Sakizlis, V. (2008). Process Control Using Co-ordinate Space. United States Patent and Trademark Office Granted Patent No US7433743.

Pukrushpan, J.T., Stefanopoulou, A.G. & Peng, H. (2004). Control of Fuel Cell Power Systems: Principles, Modelling and Analysis and Feedback Design, Series in Advances in Industrial Control, Springer.