POD-DEIM Model Order Reduction Technique for Model Predictive Control in Continuous Chemical Processing

Abstract In this study, a model order reduction (MOR) technique is proposed to address the challenges of controlling large-scale problems for model predictive control (MPC) development in continuous chemical processing to meet the real-time control requirements. In particular, the proper orthogonal decomposition (POD) technique is employed to project the original large-scale full chemical process model onto a small system of a reduced model space, while the discrete empirical interpolation method is used to evaluate the nonlinear functions at a small set of the interpolation points. By using MOR, the original full chemical process model has been further represented by a much smaller number of state variables (about 2 to 3 orders of magnitude smaller in dimension). Thus, instead of solving the original full model, the MOR method solves the reduced sub-set model iteratively in the control process. In such a way, the MOR solution enables a much faster computational time and opens opportunities for various real-time control applications. In addition, an optimal snapshot selection algorithm is implemented to obtain the global basis vectors, which cover enough information of the model parameter(s) and input(s) in large control window(s) for an accurate MOR construction. For control demonstration, the in-silico control scenarios are performed for both applications (which are multiple scale chemical reactions and multiple pathway reactions), while onsite control is only performed for multiple pathway chemical reactions. Particularly, for soft-launch control demonstrations, the implemented framework is applied for multiple input (MI)/ multiple output (MO) and with the input disturbance and output noise control scenarios, while the onsite control demonstration is applied for SI/SO with input disturbance and MI/SO control scenarios. The obtained results show that the use of the developed MOR-MPC approach can significantly reduce the computational time of about two-orders of magnitude with the relative error of 1.0 × 10−3 compared to original full model. It implies that the MOR can be applied to the real-time control of certain applications, where it is impossible for the full original model.