$H_∞$ control theory applied to xenon control for load follow operation of a nuclear reactor

Abstract

A robust controller is designed by applying the $H_∞$ optimal control theory to the xenon control for load follow operation of a nuclear reactor. The $H_∞$ optimal controller is developed for the automatic and simultaneous control of both reactor power and axial power distribution during the load follow operation. The reactor model for the controller design is established by use of the two-point kinetics equations with one delayed neutron group. For the controller design of robust multivariable control system, the two-point kinetics equations are derived from the nodal kinetics equations and applied to the development of $H_∞$ controller design. In this model, the coupling coefficients between two regions can be calculated exactly by dividing a core into two regions at the center of the reactor core. The two-point singly lumped thermal-hydraulic energy balance equations and the two-point xenon and iodine dynamics equations incorporate the temperature and xenon feedback effects. However, the set of reactor model equations for controller design is a stiff system. This singularly perturbed system arises from the interaction of slow dynamics modes (iodine and xenon concentrations) and fast dynamics modes (neutron and precursor densities, fuel and coolant temperatures). Therefore, in this study, the singular perturbation technique is used to overcome this stiffness problem. The design specifications are incorporated by the frequency weights using the mixed-sensitivity problem approach. The robustness of $H_∞$ control is demonstrated by comparing it with linear quadratic Gaussian (LQG) control for various load follow operation types such as 1) the typical daily load follow operation, 2) the load follow operation with external noises, 3) the load follow operation with external disturbances, 4) the load follow operation with delayed measurement, and 5) rapid load changes. The simulation results show that the $H_∞$ control has better stability robustness and performance...