A Method for Solving the Xenon Oscillation Control Problem

Large-size nuclear power reactors are subjected to dynamic problems that can be formulated using modern control theory. The problem considered here is a power oscillation caused by the presence of a fission product, ¹³⁵Xe, which is formed when the nuclear fuel undergoes fission. The application of control theory leads to a mixed boundary value problem. The presented method avoids the shooting by changing the direction of integration in the adjoint equations. Taking the steady state as the initial function, the method converges in a great parameter range. The method is formulated in general, but results are shown only for the one-dimensional case.