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In situ adaptive tabulation for real-time control

This paper outlines a method to implement nonlinear model predictive control (NMPC) in real-time control applications. Nonlinear model identification is generally seen as a major obstacle to implementing NMPC. However, once an accurate nonlinear model is identified the computational effort is often too great to implement the model in a real-time application. The approach in this paper is a two step process, model reduction followed by computational reduction. Model reduction is accomplished by computing balanced empirical gramians. Computational reduction is accomplished by using the method of in situ adaptive tabulation (ISAT) which was previously developed for computational reduction of turbulent flame direct numerical simulations and is extended to the sequential NMPC framework in this work. A case study is performed with a binary distillation column model with 32 states. By computing balanced empirical gramians the number of states is reduced to five. With ISAT, the computational speed is 85 times faster than the original NMPC while maintaining the accuracy of the nonlinear model. Since ISAT is a storage and retrieval method, it is compared to artificial neural networks in another case study. This case study is performed with a dual CSTR model with 6 states. Open loop and closed loop step tests are performed to demonstrate the superior quality of ISAT in extrapolating outside of the training domain.