• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.399-409
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• 2007

In this paper we use iterative dynamic programming in the discrete case to solve a wide range of the nonlinear equations systems. First, by defining an error function, we transform the problem to an optimal control problem in discrete case. In using iterative dynamic programming to solve optimal control problems up to now, we have broken up the problem into a number of stages and assumed that the performance index could always be expressed explicitly in terms of the state variables at the last stage. This provided a scheme where we could proceed backwards in a systematic way, carrying out optimization at each stage. Suppose that the performance index can not be expressed in terms of the variables at the last stage only. In other words, suppose the performance index is also a function of controls and variables at the other stages. Then we have a nonseparable optimal control problem. Furthermore, we obtain the path from the initial point up to the approximate solution.

• Korean Chemical Engineering Research
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• v.45 no.1
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• pp.73-80
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• 2007

This article aims to optimize the nitrogen removal of a sequencing batch reactor (SBR) through the use of the activated sludge model and iterative dynamic programming (IDP). Using a minimum batch time and a maximum nitrogen removal for minimum energy consumption, a performance index is developed on the basis of minimum area criteria for SBR optimization. Choosing area as the performance index makes the optimization problem simpler and a proper weighting in the performance index makes it possible to solve minimum time and energy problem of SBR simultaneously. The optimized results show that the optimal set-point of dissolved oxygen affects both the total batch time and total energy cost. For two different influent loadings, IDP-based SBR optimizations suggest each supervisory control of batch scheduling and set-point trajectory of dissolved oxygen (DO) concentration, and can save 20% of the total energy cost, while meeting the treatment requirements of COD and nitrogen. Moreover, it shows that the re-optimization of IDP within a batch can solve the modelling error problem due to the influent loading changes, or the process faults.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.248-251
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• 1999

The optimal reaction conditions are determined for a PET process, which consists of transesteriflcation, prepolymerization and polycondensation reactors in series. Based on the simulation results of the reactor system, we scrutinize the cause and effect between the reaction conditions and the final properties of the polymer product. We then select the process variables with significant influence on the properties of polymer as control variables and calculate the optimal reaction conditions by iterative dynamic programming (IDP) algorithm with constraints. A new reaction scheme incorporating reactions for by-products as well as three main reactions is considered in the constrained IDP method.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.451-451
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• 2000

This study aims for the optimization of process conditions in a fixed-bed catalytic reactor system with a circulating molten salt bath, in which partial oxidation of propylene to acrolein takes place. Two-dimensional pseudo-homogeneous model is adopted with estimation of suitable parameters and its validity is corroborated by comparing simulation result with experimental data. The temperature of the molten salt and the feed composition are found to exercise significant influence on the yield of acrolein and the magnitude of hot spot. The temperature of the molten salt is usually kept constant. This study, however, suggests that the temperature of the molten salt must be axially adjusted so that the abrupt peak of hot spot should not appear near the reactor entrance. The yield of acrolein is maximized and the position and the magnitude of hot spot are optimized by the method of the iterative dynamic programming (IDP).