Parametric Model Order Reduction of Variable Parameter Axial Dispersion Model

IEEE Conference on Control Technology and Applications (CCTA), vol. 18, pp. 408–415

Abstract

Axial dispersion models are capable of delivering accurate predictions of non-ideal flow behavior, where the residence time distribution (RTD) of the flowing material is estimated. Such models are crucial for analysis, monitoring, and control purposes of processes appearing in a wide spectrum of applications, e.g. chemical, pharmaceutical. In the previous contribution [1] the problem of the variability of the residence time distribution due to its dependency on process variables is tackled using a grey-box approach. However, solving the grey-box model numerically including the varying model parameters requires a fine spatial discretization. In consequence, delivering a high-dimensional model unsuitable for control-oriented applications, e.g. model-based estimation/control, real-time monitoring. This work presents a solution to the problem by employing a projection-based Model Order Reduction (MOR) technique producing a computationally feasible Reduced Order Model (ROM) with acceptable accuracy. The exploitation of the Full Order Model (FOM) special structure along with a carefully selected input vector including the varying parameters allowed casting the model into a weak nonlinear form, i.e. bilinear. Hence permitting the investigation of two methods for parameter independent MOR, i.e. Proper Orthogonal Decomposition (POD) and bilinear $\mathcal{H}_{2}$ optimal. The latter method requirements are considered and treated within the FOM mathematical formulation. The ROMs produced by the two methods are evaluated against the FOM for selected simulation test scenarios showing the superiority of the latter. That is for a practical test case of a random biased input concentration and varying flow parameters, the ROM could predict the concentration output with a Normalized Mean Square Error (NMSE) lying below 4% for all tested Péclet number ranges. A computational speedup factor up to 32 is achieved using the ROM showing its potential for real-time applications even for sampling rates within milliseconds order of magnitude.

Authors 2

1. Ahmed Elkhashap Aachen Institute of Automatic Control (IRT)

   RWTH Aachen University

   Affiliation as printed

   Institute of Automatic Control, RWTH Aachen University,Aachen,Germany,52062

2. Dirk Abel Aachen Institute of Automatic Control (IRT)

   RWTH Aachen University

   Affiliation as printed

   Institute of Automatic Control, RWTH Aachen University,Aachen,Germany,52062