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Processes 2016, 4(3), 20; doi:10.3390/pr4030020

Parallel Solution of Robust Nonlinear Model Predictive Control Problems in Batch Crystallization

1
School of Chemical Engineering, Purdue University, 480 Stadium Mall Drive, West Lafayette, IN 47907, USA
2
Department of Chemical Engineering, Texas A&M University, 3122 TAMU, College Station, TX 77843, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Michael Henson
Received: 6 May 2016 / Revised: 20 June 2016 / Accepted: 22 June 2016 / Published: 30 June 2016
(This article belongs to the Special Issue Algorithms and Applications in Dynamic Optimization)
View Full-Text   |   Download PDF [271 KB, uploaded 30 June 2016]   |  

Abstract

Representing the uncertainties with a set of scenarios, the optimization problem resulting from a robust nonlinear model predictive control (NMPC) strategy at each sampling instance can be viewed as a large-scale stochastic program. This paper solves these optimization problems using the parallel Schur complement method developed to solve stochastic programs on distributed and shared memory machines. The control strategy is illustrated with a case study of a multidimensional unseeded batch crystallization process. For this application, a robust NMPC based on min–max optimization guarantees satisfaction of all state and input constraints for a set of uncertainty realizations, and also provides better robust performance compared with open-loop optimal control, nominal NMPC, and robust NMPC minimizing the expected performance at each sampling instance. The performance of robust NMPC can be improved by generating optimization scenarios using Bayesian inference. With the efficient parallel solver, the solution time of one optimization problem is reduced from 6.7 min to 0.5 min, allowing for real-time application. View Full-Text
Keywords: dynamic optimization; robust NMPC; parallel NLP; batch crystallization dynamic optimization; robust NMPC; parallel NLP; batch crystallization
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Cao, Y.; Kang, J.; Nagy, Z.K.; Laird, C.D. Parallel Solution of Robust Nonlinear Model Predictive Control Problems in Batch Crystallization. Processes 2016, 4, 20.

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