• Journal of applied mathematics & informatics
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• 제24권1_2호
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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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• 제45권1호
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• pp.73-80
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• 2007

본 연구는 생물학적 폐수 처리 공정인 연속 회분식 반응기(sequencing batch reactor, SBR)에서 질소 제거 최적화를 위해 활성 오니 공정모델(activated sludge model, ASM No.1, ASM1)과 반복 동적 프로그래밍(iterative dynamic programming, IDP)을 이용하여 SBR의 처리 기준을 만족하면서 최적 운전 조건을 탐색하고 하는 것을 목적으로 하였다. 연속 회분식 반응기의 최적화를 위해 에너지 최소화와 최소 회분 시간이 질소 처리의 농도 그래프의 면적과 비례하는 점을 이용하여 이를 고려한 새로운 performance index를 제안하였다. 회분 시간과 에너지에 대항하는 면적에 적절한 비중(weight)을 줌으로써 최소 회분 시간과 최소 에너지 문제를 동시에 고려하였다. SBR에서 IDP를 이용한 최적 운전서 최적 용존 산소 농도의 설정치가 전체 회분 시간과 전체 에너지 비용에 동시에 영향을 미침을 알 수 있었고 최적 운전시 기존의 운전 방법과 같은 유기물과 질소 제거가 가능하고 동시에 전체 비용을 20％까지 줄일 수 있었다. 더 나아가 공정이상으로 실제 공정이 모델과 다른 모델링 에러에 의해 잘못된 모사의 경우에도 IDP를 이용하여 다시 재최적화할 수 있음을 보였다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1999년도 제14차 학술회의논문집
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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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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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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).