Reference Trajectory Optimization Under Constrained Predictive Control

Chemical process systems often need to respond to frequently changing product demands. This motivates the determination of optimal transitions, subject to specification and operational constraints. However, direct implementation of optimal input trajectories would, in general, result in offset in the presence of disturbances and plant/model mismatch. This paper considers reference trajectory optimization of processes controlled by constrained model predictive control (MPC). Consideration of the closed-loop dynamics of the MPC-controlled process in the reference trajectory optimization results in a multi-level optimization problem. A solution strategy is applied in which the MPC quadratic programming subproblems are replaced by their Karush-Kuhn-Tucker optimality conditions, resulting in a single-level mathematical program with complementarity constraints (MPCC). The performance of the method is illustrated through application to two case studies, the second of which considers economically optimal grade transitions in a polymerization process. Les systemes de procedes chimiques doivent souvent repondre a des changements de production frequents. Ceci motive la determination de transitions optimales, soumises a des contraintes de specification et de fonctionnement. Toutefois, l'implantation directe de trajectoires d'entree optimales entraine, en general, un decalage en presence de perturbations et d'une incompatibilite installation/modele. Cet article porte sur l'optimisation des trajectoires pour des procedes controles par le controle predictif par modele contraint (MPC). Le fait de considerer la dynamique en boucle fermee du procede controle par MPC dans l'optimisation des trajectoires de reference cause un probleme d'optimisation a plusieurs niveaux. Une strategie de solution est appliquee dans laquelle les sous-problemes de programmation quadratique du MPC sont remplaces par des conditions d'optimalite de Karush-Kuhn-Tucker. On obtient ainsi un programme mathematique a niveau unique associe a des contraintes de complementarite (MPCC). La performance de la methode est illustree par l'application de deux etudes de cas, le second considerant les transitions de grade optimales en termes economiques dans un procede de polymerisation.

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