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On the Use of Maximum Principle in Optimal Xenon Shutdown Problems

Seppo Salo

Nuclear Science and Engineering / Volume 50 / Number 1 / Pages 46-52

January 1973

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There have been some weak points in the use of modern control theory in xenon shutdown problems. The aim of this paper is to show how Pontryagin’s maximum principle should be applied to these problems. To do this, two special problems have been picked up and solved completely. It is shown that the solution to the energy optimal xenon shutdown problem of Rosztoczy is not a bang-bang control as proposed by Rosztoczy even when the xenon restraint is omitted. The actual optimum control includes a phase with continuously varying control. Further, numerical examples are given to show that the difference in the costs between the optimum control and the control proposed by Rosztoczy is negligible. The other problem considered is the energy optimal xenon shutdown of Lewins et al. It is shown that the solution can be found analytically which gives a slight improvement to their analysis.

 
 
 
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