An effective computational algorithm for suboptimal singular and/or bang‐bang control I. Theoretical developments and applications to linear lumped systems

Nishida, Naoki; Liu, Y. A.; Lapidus, Leon; Hiratsuka, S.

doi:10.1002/aic.690220314

Cited by 24 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is a well‐known DOP for the chemical engineering process taken from Nishida et al The dynamic equations of the DOP are described as follows:

\min J = \sum_{i = 1}^{8} x_{i}^{2} ((), t_{f})

…”

Section: Numerical Applicationsmentioning

confidence: 99%

A novel analytical second‐order sensitivity calculation approach using the finite element method for chemical engineering problems

Xiao

Ma³

et al. 2019

Can J Chem Eng

View full text Add to dashboard Cite

This paper presents an effective orthogonal collocation approach to approximate dynamic optimization problems into nonlinear programming problems, where the resulting problems can then be usually solved by first‐order sensitivity based algorithms. However, the results obtained fail to satisfy the timeliness and accuracy requirements of some dynamic optimization problems. A novel collocation approach with second‐order sensitivity information is therefore first proposed to improve the efficiency of the method. The resulting nonlinear programming problem is obtained through the orthogonal collocation on finite element combined with a single shooting approach. Three benchmark optimal control problems are considered to demonstrate the performance of the presented approach. Comparisons among the proposed approach, the BFGS method, and other literature solutions are also carried out in detail. Numerical results validate the effectiveness of the proposed method and the time saving benefit.

show abstract

“…This is a well‐known DOP for the chemical engineering process taken from Nishida et al The dynamic equations of the DOP are described as follows:

\min J = \sum_{i = 1}^{8} x_{i}^{2} ((), t_{f})

…”

Section: Numerical Applicationsmentioning

confidence: 99%

A novel analytical second‐order sensitivity calculation approach using the finite element method for chemical engineering problems

Xiao

Ma³

et al. 2019

Can J Chem Eng

View full text Add to dashboard Cite

show abstract

“…(Xm, Um, Ym) < H(Xm, U. Ym) (8) is used t o modify the non-optimum control obtained from the (m-1)th iteration, Um-l. Outside this subinterval, that is, for tET-m where T~U T-m = (0,tf) and r m n T'm=O, the previously obtained non-optimum control Urn-1 is to be used. Further details can be found in(23).…”

mentioning

confidence: 99%

Optimization of continuous polymerization reactors: Start‐up and change of specification

Farber¹,

Laurence²

1986

Makromolekulare Chemie. Macromolecular Symposia

View full text Add to dashboard Cite

show abstract

Studies in chemical process design and synthesis II. Optimal synthesis of dynamic process systems with uncertainty

1976

View full text Add to dashboard Cite

The concept of the optimal synthesis of dynamic process systems with uncertain parameters is introduced. A structure parameter approach is used to theoretically derive the necessary condition for the optimal performance system structure, and an effective algorithm for implementing the synthesis method is presented. The results are applied to the optimal synthesis of a reactor-separator system for the dynamic start-up of two reaction systems. SCOPESignificant progress has been made in the past few years on the synthesis of chemical process systems. The determination of the optimal type and design of processing units, as well as their optimal interconnections within a process flowsheet, can now be done with some success by many synthesis techniques. A good description of the useful techniques has been given by Hendry, Rudd, and Seader (1973), and a latest review of the state of the art of process synthesis can be found in a report by Mah (1975).One serious limitation with most recent studies of process synthesis is that they are mainly concerned with the synthesis of steady state process systems. A wide variety of important chemical process operations, such as the start-up or shutdown of equipment, the batch or semibatch operation of processing units, etc., however, fall into the category of dynamic process systems. Furthermore, a large number of recent studies in chemical engineering have shown that certain types of processing units, such as the parametric pumping and the cycling zone absorption, etc., can give better performance by periodic (dynamic) operations. Therefore, it is of practical interest in many situations to consider the problems of dynamics and control at the stage of process synthesis (Mah, 1975;Henley and Motard, 1972) rather than merely synthesizing the process by assuming a steady state operation and then compensating the effect of dynamics by means of control after the synthesis is completed. Unfortunately, except for the recent studies by the authors (Nishida and Ichikawa, 1975; Nishida, Liu, and Ichikawa, 1975a), this important aspect of including the dynamics and control considerations in the process synthesis problem has been neglected in the literature. Another important aspect of process synthesis which has not been given sufficient attention is the effect of uncertainty in process parameters. In the literature, only the optimal synthesis of steady state process systems with uncertainty has been studied recently (Nishida, Tazaki, and Ichikawa, 1974).The objective of this work is to extend the recent results on the optimal synthesis of dynamic process systems (Nishida and Ichikawa, 1975; Nishida, Liu, and Ichikawa, 1975n) to include the effect of process parameter uncertainty. The problem considered may be stated briefly as: "Given the process dynamics, how to synthesize the process flow sheet and to specify the process design and control variables subject to the uncertainty in process parameters so as to achieve an optimal dynamic operation of the process?" The approach taken is to co...

show abstract

An effective computational algorithm for suboptimal singular and/or bang‐bang control I. Theoretical developments and applications to linear lumped systems

Cited by 24 publications

References 0 publications

A novel analytical second‐order sensitivity calculation approach using the finite element method for chemical engineering problems

A novel analytical second‐order sensitivity calculation approach using the finite element method for chemical engineering problems

Optimization of continuous polymerization reactors: Start‐up and change of specification

Studies in chemical process design and synthesis II. Optimal synthesis of dynamic process systems with uncertainty

Contact Info

Product

Resources

About