(769f) Enhancing Real Time Optimization through Multiparametric Programming

Real time optimization is poised to provide significant improvements to the advanced control of chemical processes through enhanced performance and reduced operational costs. Though promising, widespread utilization has been limited to systems with slow dynamics to ensure an optimal solution can be determined under process time constraints. A salient feature of real time optimization is the iterative nature of solving a deterministic optimization problem at each sampling instance of the process. Improving any facet of the iterative procedure has been a core research focus of several researchers [1, 2, 3].

Multiparametric programming has shown to reduce the burden of iteratively solving a deterministic optimization problem [4]. In the context of real time optimization, multiparametric programming has been utilized to improve the computational performance through (i) directly solving the multiparametric nonlinear program [5], and by (ii) providing a warm start to the online optimizer [6]. Because of the potential for increased computational performance, real time optimization stands to benefit greatly through a direct strategy incorporating multiparametric optimization.

In this presentation, a novel strategy is presented to enhance the computational performance of real time optimization. Using fundamental properties of multiparametric programming, an `on the fly’ methodology is adopted to improve the performance of solving a detailed optimization based formulation in real time. The proposed strategy is designed to reduce the number of online optimization problems solved and reduce the computational burden of determining the optimal solution. The improved real time optimization scheme with multiparametric programming is implemented on problems of varying complexities.

References

[1] Gros, S; Zanon, M.; Quirynen, R.; Bemporad, A.; Diehl, M. From linear to nonlinear MPC: bridging the gap via the real-time iteration. International Journal of Control 2016, 1-19.

[2] Würth, L., Hannemann, R., Marquardt, W. Neighboring-extremal updates for nonlinear model-predictive control and dynamic real-time optimization. Journal of Process Control 2009, 19, 1277-1288.

[3] Zavala, V.M; Biegler, L.T. The advanced-step NMPC controller: Optimality, stability and robustness. Automatica 2009, 45, 86-93.

[4] Bemporad, A.; Morari, M.; Dua, V.; Pistikopoulos, E. N. The explicit linear quadratic regulator for constrained systems. Automatica 2002, 38, 3-20.

[5] Domínguez, L.F.; Pistikopoulos, E.N. A Novel mp-NLP Algorithm for Explicit/Multi-parametric NMPC. IFAC Proceedings Volumes 2010, 43, 539-544.

[6] Ziogou, C.; Pistikopoulos, E.N.; Georgiadis, M.C.; Voutetakis, S.; Papadopoulou, S. Empowering the Performance of Advanced NMPC by Multiparametric Programming—An Application to a PEM Fuel Cell System. Industrial & Engineering Chemistry Research 2013, 52, 4863-4873.