The fabrication of narrowband highly reflecting filters in single-mode step-index fibers was reported recently by Hill et al. [Appl. Phys. Lett. 32, 647 (1978)]. The underlying effect on which these filters are based is a photoinduced refractive-index change in the GeO(2) used as a core dopant in SiO(2) fibers. A study is reported aimed at the characterization of such optical fiber filters. A theoretical model is developed, and relevant fiber parameters are determined through intercomparison with experiment. In this way, both the magnitude of the photoinduced index change and its dependence on the writing power coupled into the fiber are determined.
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 ...
The anomalous dispersion characteristic of recently reported [Opt. Lett. 5, 476 (1980)] optical-fiber filters is proposed for use in equalization of material dispersion in optical-communication (OC) links employing single-mode fibers. Calculations show that, under appropriate circumstances, a fiber filter of length shorter than 2 cm can equalize dispersion from an OC link about 1 km long.
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