An isoperimetric optimal control problem for a non-isothermal chemical reactor with periodic inputs

Zuyev, Alexander; Seidel‐Morgenstern, Andreas; Benner, Peter

doi:10.1016/j.ces.2016.12.025

Cited by 26 publications

(48 citation statements)

References 16 publications

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“…A short overview of the previously suggested theoretical methods for evaluating possible performance enhancement can also be found in our previous publications ,. Recently, an approach based on optimal control problem formulation was also suggested …”

Section: Introductionmentioning

confidence: 99%

Nonlinear Frequency Response Method for Evaluating Forced Periodic Operations of Chemical Reactors

Petkovska

Nikolić

Seidel‐Morgenstern

2018

Israel Journal of Chemistry

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Nonlinear Frequency Response (NFR) method is a relatively new method which can be used for fast evaluation of possible process improvements through periodic operations. The method is analytical and approximate. Its main task is to give an answer whether periodic modulation of one or more process inputs can result in improved process performance. The method is explained in brief and an overview of the existing applications is given. The review covers simple reactions performed in isothermal and non‐isothermal stirred tank reactors exposed to different modulated inputs (inlet concentration, flow‐rate, inlet temperature, temperature of the heating/cooling medium). Processes with two simultaneously modulated inputs and different shapes of the periodic input are also considered. The results of the NFR method are compared with the results of numerical simulation and a critical evaluation of the method is given.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Frequency Response Method for Evaluating Forced Periodic Operations of Chemical Reactors

Petkovska

Nikolić

Seidel‐Morgenstern

2018

Israel Journal of Chemistry

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“…Here the controls are v 1 = C Ai /C Ai and v 2 = F/F , and the vector fields depend on physical parameters k 1 , k 2 ,n, St, γ, δ, [3,7]:…”

Section: Nonlinear Chemical Reactions With Flow-rate Modulationmentioning

confidence: 99%

“…On the other hand, the integrand of the cost function depends on both the state and the control (in contrast to the pure state-dependent cost considered previously in [1,7]). This problem brings the following theoretical challenges: on the one hand, the system of governing equations is not control-affine as it contains the product of the two controls.…”

Section: Introductionmentioning

confidence: 95%

“…Some recent advances in this area are summarized in the book [5] and survey paper [4]. The task of maximizing the mean product of non-isothermal reactions over a given time period t ∈ [0, τ ] is treated in [7] as an isoperimetric optimal control problem with two independent inputs: the inlet concentration and the inlet temperature. It is proved in [7] that the optimal controls are bang-bang, and an upper estimate of the number of switchings is proposed based on the linearization procedure.…”

Section: Introductionmentioning

confidence: 99%

“…The task of maximizing the mean product of non-isothermal reactions over a given time period t ∈ [0, τ ] is treated in [7] as an isoperimetric optimal control problem with two independent inputs: the inlet concentration and the inlet temperature. It is proved in [7] that the optimal controls are bang-bang, and an upper estimate of the number of switchings is proposed based on the linearization procedure. Switching controls for the considered isoperimetric problem are analysed in [1] with the use of the Chen-Fliess series.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal periodic control of nonlinear chemical reactions with a time‐varying flow rate

Zuyev

Seidel‐Morgenstern

Benner

2019

Proc Appl Math and Mech

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This paper deals with a mathematical model of a non-isothermal chemical reaction described by nonlinear ordinary differential equations with two-dimensional control. The control variables correspond to the possibility of manipulating the concentration of the input reactant and the total flow rate. We consider the task of maximizing the reactor performance as an isoperimetric optimal control problem with periodic boundary conditions. Necessary optimality conditions are derived by the Pontryagin maximum principle with Lagrange multipliers corresponding to the isoperimetric constraints.

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

2022

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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.

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An isoperimetric optimal control problem for a non-isothermal chemical reactor with periodic inputs

Cited by 26 publications

References 16 publications

Nonlinear Frequency Response Method for Evaluating Forced Periodic Operations of Chemical Reactors

Nonlinear Frequency Response Method for Evaluating Forced Periodic Operations of Chemical Reactors

Optimal periodic control of nonlinear chemical reactions with a time‐varying flow rate

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

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