A coordinate‐transformation method for the numerical solution of nonlinear minimum‐time control problems

Kwon, Young Do; Evans, Lawrence B.

doi:10.1002/aic.690210616

Cited by 42 publications

(18 citation statements)

References 8 publications

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“…The initial value of the state is y 1 (0) = 0, y 2 (0) = 1 and y 3 (0)=1. Other parameters in Equations () to () can be found in References 27,34. It is noted that for the parameter A m , according to Reference 27, there is an additional parameter uncertainty, that is,

A_{m} (k) = A_{m 0} [1.2 - 0.25 \exp (- k / 3)],

where A m 0 is the nominal value of the parameter A m and the detailed value can be seen in Reference 27.…”

Section: Simulation On a Batch Polymerization Reactormentioning

confidence: 99%

Batch to batch optimal control based on multiinput multioutput adaptive hinging hyperplanes prediction and Kalman filter correction

Luo

Zhang

et al. 2020

Optim Control Appl Methods

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Summary A batch to batch optimal control strategy based on multiinput multioutput adaptive hinging hyperplanes (MIMO AHH) prediction and Kalman filter correction is proposed for the products quality control of the batch process. The model of AHH is one kind of piecewise linear models and is extended to the MIMO case in this article. The MIMO AHH is then used to develop the predictive model of the batch process. Due to the model‐plant mismatch and unknown disturbances, the optimal control policy calculated based on the MIMO AHH predictive model may not be optimal when applied to the true process. The Kalman filter is then utilized to correct the predictions of the current batch by considering the information of former batches. The effectiveness of the proposed strategy is verified through the simulation of a styrene batch polymerization reactor.

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A_{m} (k) = A_{m 0} [1.2 - 0.25 \exp (- k / 3)],

where A m 0 is the nominal value of the parameter A m and the detailed value can be seen in Reference 27.…”

Section: Simulation On a Batch Polymerization Reactormentioning

confidence: 99%

Batch to batch optimal control based on multiinput multioutput adaptive hinging hyperplanes prediction and Kalman filter correction

Luo

Zhang

et al. 2020

Optim Control Appl Methods

View full text Add to dashboard Cite

show abstract

“…The first-principle model for this polymerization process was proposed by Kwon and Evans (1975) through reaction mechanism analysis and laboratory testing as:…”

Section: Application To a Simulated Batch Polymerization Reactormentioning

confidence: 99%

Batch-to-Batch Optimal Control of Batch Processes Based on Recursively Updated Nonlinear Partial Least Squares Models

Zhang

Wang

2006

Chemical Engineering Communications

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A batch-to-batch optimal control approach for batch processes based on batch-wise updated nonlinear partial least squares (NLPLS) models is presented in this article. To overcome the difficulty in developing mechanistic models for batch=semi-batch processes, a NLPLS model is developed to predict the final product quality from the batch control profile. Mismatch between the NLPLS model and the actual plant often exists due to low-quality training data or variations in process operating conditions. Thus, the optimal control profile calculated from a fixed NLPLS model may not be optimal when applied to the actual plant. To address this problem, a recursive nonlinear PLS (RNPLS) algorithm is proposed to update the NLPLS model using the information newly obtained after each batch run. The proposed algorithm is computationally efficient in that it updates the model using the current model parameters and data from the current batch. Then the new optimal control profile is recalculated from the updated model and implemented on the next batch. The procedure is repeated from batch to batch and, usually after several batches, the control profile will converge to the optimal one. The effectiveness of this method is demonstrated on a simulated batch polymerization process. Simulation results show that the proposed method achieves good performance, and the optimization with the proposed NLPLS model is more effective and stable than that with a batch-wise updated linear PLS model.

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“…This example involves a thermally initiated bulk polymerization of styrene in a batch reactor. The differential equations describing the polymerization process are given by Kwon and Evans (1975) through reaction mechanism analysis and laboratory testing. Gattu and Zafiriou (1999) report the parameter values of the first principle model.…”

Section: Application To a Simulated Batch Polymerization Reactormentioning

confidence: 99%

Integrated Batch-to-Batch Iterative Learning Control and Within Batch Control of Product Quality for Batch Processes

Xiong

Zhang

Xiong

et al. 2005

IFAC Proceedings Volumes

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A coordinate‐transformation method for the numerical solution of nonlinear minimum‐time control problems

Cited by 42 publications

References 8 publications

Batch to batch optimal control based on multiinput multioutput adaptive hinging hyperplanes prediction and Kalman filter correction

Batch to batch optimal control based on multiinput multioutput adaptive hinging hyperplanes prediction and Kalman filter correction

Batch-to-Batch Optimal Control of Batch Processes Based on Recursively Updated Nonlinear Partial Least Squares Models

Integrated Batch-to-Batch Iterative Learning Control and Within Batch Control of Product Quality for Batch Processes

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