Optimal Control of Steady State Neutron Flux Distribution in Slab Reactors

The algorithm is presented for seeking optimal control of the steady state neutron flux distribution making use of Pontryagin's Maximum Principle, for a one group model of the bare slab reactor as well as for a two group model of the reflected slab reactor, both of which are homogeneous except for the control material. The performance criterion to be minimized is the spatial square integral error between the thermal flux distribution and the desired flux shape, and the control variable is the cross section of the absorbing material.

A numerical example is given for the bare reactor where the desired shape is assumed to be uniformly flat. The non-linear nature of the problem imparts a complex aspect to the algorithm concerning the steepest descent method, as indicated by the numerical example. The results show that, as the bounds of the control variable are relaxed, the number of switchings is increased and a better performance criterion is obtained but this is accompanied by a higher hot spot factor.