Suboptimal Control of Nuclear Reactors with Distributed Parameters Using Singular Perturbation Theory

Abstract

A new method based on the singular perturbation theory is presented for synthesizing suboptimal control of nuclear reactors with spatially distributed parameters. The inverse of the neutron velocity is regarded as a small perturbing parameter, and the model, adopted for simplicity, is an infinite slab reactor described by the one-group diffusion equation. A control is found for the problem of transferring a given distributed neutron flux to the desired one assuming the deviation is small.It is shown that the Helmholtz mode is suited for the singular perturbation technique when one carries out the modal expansion, and the mode controllability is then determined in view of the asymptotic stability of solutions, which depends on the criticality condition. The theoretical estimation of the error of solution is also attached. A numerical example is given showing a large saving of computation time in the present method.