Model Approximation in Multiparametric Optimization and Control – A Computational Study
Justin Katz (1,2) , Nikolaos A. Diangelakis (2), Efstratios N. Pistikopoulos (1,2)
1. Artie McFerrin Department of Chemical Engineering, Texas A&M University 100 Spence St., College Station, TX 77843, United States
2.Texas A&M Energy Institute, Texas A&M University 1617 Research Pkwy, College Station, TX 77845, United States
The development of a high fidelity model to accurately describe a dynamical system can lead to a complex structure of (partial) differential algebraic equations. Incorporating these highly complex, coupled, and nonlinear systems into optimization and control studies may often lead to an intractable problem. Reduction of such large scale systems into more tractable forms is typically done via model approximation; for example in control studies some form of linearization or complexity reduction is performed. Such model approximations are also at the heart of the PARameteric Optimization and Control (PAROC) framework for the derivation of explicit/multiparametric controllers and/or online (e.g. MPC) explicit strategies. A key question that remains open within the PAROC framework is what constitutes a suitable approximate model for the derivation of explicit control strategies with multiparametric programming?".
In this work, we present a computational study towards addressing this question. In particular, we study system identification, and piece-wise linearization, in order to gain fundamental insights on the impact of the model approximation on (i) the solution of the multiparametric optimization problem, and (ii) the derived explicit control strategies. A computation study which features a detailed comparison based on error metrics is proposed in the following steps. Open loop dynamic optimization is first performed on a variety of high fidelity models of increasing complexity to ascertain the `desired' optimal trajectories. These optimal trajectories are then compared to the trajectories determined from advanced control strategies, including explicit/multiparametric MPC, which are based on model approximations. Key error metrics include model accuracy, controller accuracy, and deviations from the `desired' optimal trajectory. Two systems are used as a basis for this computational study: (i) a linear tank system with minimal complexity utilized to highlight the main principles of this approach, and (ii) a CSTR system where the reaction mechanisms are manipulated to increase the model complexity.
Keywords: Multiparametric programming, Model reduction, Model predictive control