Reference Trajectory Optimization Under Constrained Predictive Control

Abstract

Flores-Tlacuahuac et al., 2006;Asteasuain et al., 2006). A set of process variables is computed that minimizes a measure of the cost of the transition, subject to constraints on the inputs and possibly other specifi cation and/or operational constraints. The model states are related to the inputs through a dynamic model. The decision space in the above-cited studies includes the open-loop trajectories of certain inputs. McAuley and MacGregor (1992) show that plant/model mismatch could result in deviation of product quality variables from their desired values, and advocate the use of feedback control in the implementation of computed optimal transitions. In a subsequent paper (McAuley and MacGregor, 1993), they develop a non-linear model-based controller for a polymerization process, and apply it to track the profi les of output variables Chemical process systems often need to respond to frequently changing product demands. This motivates the determination of optimal transitions, subject to specifi cation 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 systèmes de procédés chimiques doivent souvent répondre à des changements de production fréquents. Ceci motive la détermination de transitions optimales, soumises à des contraintes de spécifi cation et de fonctionnement. Toutefois, l'implantation directe de trajectoires d'entrée optimales entraîne, en général, un décalage en présence de perturbations et d'une incompatibilité installation/modèle. Cet article porte sur l'optimisation des trajectoires pour des procédés contrôlés par le contrôle prédictif par modèle contraint (MPC). Le fait de considérer la dynamique en boucle fermée du procédé contrôlé par MPC dans l'optimisation des trajectoires de référence cause un problème d'optimisation à plusieurs niveaux. Une stratégie de solution est appliquée dans laquelle les sous-problèmes de programmation quadratique du MPC sont remplacés par des conditions d'optimalité de Karush-Kuhn-Tucker. On obtient ainsi un programme mathématique à niveau unique associé à des contraintes de complémentarité (MPCC). La performance de la méthode est illustrée par l'application de deux études de cas, le second considérant les transitions de grade optimales en ...

Dynamic real‐time optimization with closed‐loop prediction

“…Solving MPCC problems require reformulation of the complementarity constraints or alternative algorithm strategies that internally treat the constraints. Common approaches to handle complementarity constraints related to this work include: (1) regularization or constraint relaxation approach as implemented in Baker and Swartz and Lam et al, (2) mixed‐integer approach as implemented in Baker and Swartz and Soliman et al, and (3) exact penalty approach. An extensive review on MPCC problems is beyond the scope of this article, and readers are referred to more detailed and in‐depth discussions on MPCCs, inter alia, in Raghunathan and Biegler, Ralph and Wright, Baumrucker et al, and the references therein.…”

“…The multilevel programming formulation considered in this study was originally proposed in Baker and Swartz for optimal backoff calculations of steady‐state operating targets, while an extension of their work is presented in Lam et al for reference trajectory optimization of MPC‐controlled processes. Here we provide in‐depth analysis on the inclusion of MPC closed‐loop dynamics in the DRTO calculations, and identify conditions under of which the CL‐DRTO strategy most significantly outperforms the conventional open‐loop counterpart.…”

The utilization of closed‐loop prediction for dynamic real‐time optimization

“…A natural choice is to keep the reference trajectory constant over the DRTO execution interval, . This strategy is an effective mechanism for reducing excessive variation in the computed set‐point trajectories; it was applied in Lam et al in reference trajectory optimization in a supervisory control scheme, as well as in the CL‐DRTO strategies in Jamaludin and Swartz …”

“…Computing MPC set‐point trajectories that change with the MPC sample time could result in excessive variation in the set‐point trajectories due to the presence of multiple solutions or a relatively flat objective function surface at the optimum. We consider here two strategies for mitigating this: Set‐Point Hold (SPH) . This corresponds to the previously described strategy of maintaining the reference trajectories constant over the DRTO discretization intervals. Two‐Tiered Optimization .…”

“…A natural choice is to keep the reference trajectory constant over the DRTO execution interval, t DRTO . This strategy is an effective mechanism for reducing excessive variation in the computed set-point trajectories; it was applied in Lam et al [24] in reference trajectory optimization in a supervisory control scheme, as well as in the CL-DRTO strategies in Jamaludin and Swartz. [4][5][6][7] The resulting DRTO problem can in principle be solved using a sequential solution approach in which optimization iterations and closed-loop simulation are decoupled.…”