Green's Functions and Optimal Systems. Necessary Conditions and Iterative Technique

Denn, Morton M.; Aris, Rutherford

doi:10.1021/i160013a002

Cited by 26 publications

(16 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should be clear, however, that the methods are quite general. Other performance criteria can be used, and the methods have been applied to more complicated processes, such as systems with bounds on state, as well as decision variables (7, 9, 33), discrete systems (8,12,13,18,22,23,27), systems with distributed parameters (16, 28), systems with complex interconnected structures (14,18,23), and randomly disturbed systems (30).…”

Section: Discussionmentioning

confidence: 99%

“…A number of other derivations, in varying degrees of generality and rigor are available (70, 77, 34). The most complete discussions of steep descent methods are probably those of Kelley (29), Denham and Bryson (9), and Denn and Aris (12). Applications of variational methods may be found throughout the engineering literature, and illustrations of chemical engineering problems are included in the annual reviews in Industrial and…”

Section: Discussionmentioning

confidence: 99%

“…The coefficients in the To demonstrate the use of the method of steep descent it is convenient to consider another of the "standard" optimization problems, the determination of the optimal temperature profile in a batch or plug flow tubular reactor in which consecutive reactions are taking place. This problem has been solved in a number of ways, including use of the maximum principle (2,5,12,14,21,31). This is clearly the first step only in an optimal design, determining the maximum profit which could be obtained if the temperature profile were completely at our disposal.…”

Section: Numerical Solutionsmentioning

confidence: 99%

“…equations do not yet completely specify Xi and X2, because no boundary conditions have been given. Equation 10 then becomes: , X2, Ml, M2)L = 8 50 d-0(e2)(12) …”

mentioning

confidence: 99%

See 3 more Smart Citations

Optimal Design and Control by Variational Methods

Douglas¹,

Denn²

1965

Ind. Eng. Chem.

View full text Add to dashboard Cite

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Numerical Solutionsmentioning

confidence: 99%

“…equations do not yet completely specify Xi and X2, because no boundary conditions have been given. Equation 10 then becomes: , X2, Ml, M2)L = 8 50 d-0(e2)(12) …”

mentioning

confidence: 99%

See 2 more Smart Citations

Optimal Design and Control by Variational Methods

Douglas¹,

Denn²

1965

Ind. Eng. Chem.

View full text Add to dashboard Cite

“…The scheme used in this study was developed by Goodman and Lance (1956). Use of their result was described first by Denn and Aris (1965). Fan (1966) outlined a step-by-step procedure to solve two point boundary value problems.…”

Section: Cocurrent and Countercurrent Flowmentioning

confidence: 99%

Analysis of equilibrium shift in isothermal reactors with a permselective wall

Mohan

Govind

1988

AIChE Journal

View full text Add to dashboard Cite

The objective of this study is to obtain a fundamental understanding of the behavior of reactors with a permselective wall (membrane reactors) in terms of: design parameters (reactor length, membrane thickness); operating variables (pressure ratio, feed flow rate): physical properties (rate constant, permeability of fast gas, permselectivity, equilibrium constant): and flow patterns (recycle, cocurrent, countercurrent). Pure feed reacts on the high-pressure side of the membrane, and the product(s) formed are continuously removed to the low-pressure side so that thermodynamic equilibrium is never reached. It is shown by simulation that equilibrium shift can be enhanced by: recycling unconverted reactant; shifting feed location to separate products; and maintaining high permeation rates to reduce backreaction. It is also shown that the choice between cocurrent flow and countercurrent flow depends on the system parameters.

show abstract

Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

2022

View full text Add to dashboard Cite

In the mid‐1950s, Pontryagin et al. published a principle that became a fundamental concept in optimal control (OC) theory. The principle provides theoretical and practical methods to find the solution of OC problems, in particular, open‐loop control problems. In chemical engineering, the principle has played an important role as a decision making framework for more than 60 years. This study gathers the main contributions on the application of the Pontryagin's principle to the dynamic optimization of chemical processes. A concise overview of the optimality conditions for a wide class of constrained OC problems is provided. Numerical methods to solve the necessary conditions and strategies to address inequality constraints are summarized. The information and illustrative case study presented in this work can be used as a guide to implement the principle in different settings. Opportunities for further application of the principle in relevant chemical engineering problems are also discussed.

show abstract

Green's Functions and Optimal Systems. Necessary Conditions and Iterative Technique

Cited by 26 publications

References 7 publications

Optimal Design and Control by Variational Methods

Optimal Design and Control by Variational Methods

Analysis of equilibrium shift in isothermal reactors with a permselective wall

Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

Contact Info

Product

Resources

About