(463f) Reduced-Order Control Relevant Model for An On-Board Fuel Processing System
AIChE Annual Meeting
Wednesday, November 10, 2010 - 2:10pm to 2:30pm
The objective of the work is to develop a reduced order control oriented model of a Fuel processing system (FPS) for use in model-based control. Fuel processing system (FPS) consists of series of Autothermal reforming (ATR), Water gas shift (WGS) and Preferential Oxidation (PrOX) reactors. Model based control of these reactor system demands the need for dynamic model of the system. In literature there are wide varieties of models ranges from detailed CFD based models to simple lumped parameter models. Currently lumped models of these reactors are studied for model based control [1,2]. Since these models are obtained using simplifying assumptions, they can approximate only small region around the operating point. As the load demand on the FPS varies widely during a typical operation, model has to predict a broad region around the operating point. While complex CFD models have also been developed, these are too intractable to use in online control. For example, in our earlier work, CFD models took about 2-3 days for a transient simulations; in-house pseudo-2D codes were able to simulate the system in a couple of minutes . Still, while the distributed parameter models are more accurate for prediction of the FPS, these reactors models are nonlinear and infinite dimensional. The use of such models during online optimization will be computationally intensive.
In order to resolve this problem, suitable approximate methods have to be used to reduce it to finite dimensional order. The objective of this work is two-fold. First, we analyze the existing lumped parameter models and compare this performance in predicting input/output response of a FPS. Specifically, we use scaling and zero-parameter asymptote analyses to obtain simplified models. Second, we use model reduction techniques to develop reduced-order models. Specifically, Proper Orthogonal Decomposition (POD) and Differential Transform (DT) method will be tried [3,4]. In POD, the spatial variations are approximated along dominant Eigen modes, which results set of ordinary differential equations in time. The number of Eigen modes will determine the extent of approximation to the original solution. In DT, the transform applied to differential equation results in algebraic equation and gives series solution in terms of independent variables. The number of terms in this series will approximate the original solution.
1. Tsourapas, V., Stefanopoulou, A. G., 2007. Model-Based Control of an Integrated Fuel Cell and Fuel Processor with Exhaust Heat recirculation. IEEE Transactions on Control System Technology, 15. 233-245. 2. Lin, S.T., Chen, Y.H., Yu, C.C., Liu, Y.C., Lee, C.H., 2005. Dynamic Modeling and Control Structure design of an experimental Fuel Processor. International Journal of Hydrogen energy, 31. 413-426. 3. Chang, S.H., Chang, I.L., 2009. A new algorithm for calculating two ?dimensional differential of nonlinear functions. Applied Mathematics and Computation, 215. 2486-2494. 4. Park, H.M., Cho, D.H., 1995. The Use of Karhunen-loeve Decomposition for the Modeling of distributed parameter systems. Chemical Engineering Science, 51. 81-98.