# Optimal Control of a Continuous Stirred-Tank Reactor

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Aris and Amundson [1–3] originally analyzed the design of a continuous stirred-tank reactor (CSTR) with a first-order, irreversible exothermic reaction. The reactor is controlled by varying the flow of a cooling fluid through a coil inside the reactor. The state equations for the CSTR are given by

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Contributed by: Housam Binous and Ahmed Bellagi (January 2016)

(King Fahd University of Petroleum & Minerals, KSA; University of Monastir, Tunisia)

Open content licensed under CC BY-NC-SA

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References

[1] R. Aris and N. R. Amundson, "An Analysis of Chemical Reactor Stability and Control—I: The Possibility of Local Control, with Perfect or Imperfect Control Mechanisms," *Chemical Engineering Science*, 7(3), 1958 pp. 121–131. doi:10.1016/0009-2509(58)80019-6.

[2] R. Aris and N. R. Amundson, "An Analysis of Chemical Reactor Stability and Control—II: The Evolution of Proportional Control", *Chemical Engineering Science*, 7(3), 1958 pp. 132–147. doi:10.1016/0009-2509(58)80020-2.

[3] R. Aris and N. R. Amundson, "An Analysis of Chemical Reactor Stability and Control—III: The Principles of Programming Reactor Calculations. Some Extensions", *Chemical Engineering Science*, 7(3), 1958 pp. 148–155. doi:10.1016/0009-2509(58)80021-4.

[4] R. Luus and L. Lapidus, "The Control of Nonlinear Systems. Part II: Convergence by Combined First and Second Variations," *AIChE Journal*, 13(1), 1967 pp. 108–113. doi:10.1002/aic.690130120.

[5] D. E. Kirk, *Optimal Control Theory: An Introduction*, Mineola, NY: Dover Publications, 2004.

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