Application of Stable Adaptive Schemes to Nuclear Reactor Systems, (III)

Abstract

Stable parameter identification and adaptive control schemes are considered for a reactor model embodying two temperature feedbacks-slow and fast. This reactor model is liable to see its feedback coefficients change sign in the course of long periods of operation, resulting in nonlinear oscillations of neutron flux, which cannot be described by a linearized model. This nonlinear system is expressed in terms of memoryless nonlinear elements in the feedback loop of a linear system, with the aid of linear and nonlinear transformations, and the nonlinear elements are here treated without being linearized. A new system representation is introduced, using which, stable parameter identification and adaptive control schemes are developed in the pattern of the Model Reference Adaptive System (MRAS) with use made of the Lyapunov method. Both schemes are shown to be stable, and furthermore globally stable if the input has frequencies sufficiently varied to permit all the excited modes to be considered linearly independent. It is thus shown that the estimated parameters converge to the true values for the parameter identification, and that, for the adaptive control, the output error between the plant and the model tends toward zero.