Solution of the Fuel Burnup Control Problem with a Controlling Neutron Equation and Walsh Functions

A burnup control problem during a reactor core life is considered and solved by making use of a neutron-governing equation that is particularly devised to fit power reactors. Space-dependent parameters are expanded using Walsh functions, and the burnup process is described in terms of the expansion coefficients. By applying the Walsh-function expansion to a newly devised neutron-governing equation, CUMULUS, the criticality condition is established through a more simplified approach, and the system structure of a two-region reactor can be illustrated graphically. Using the above burnup model, an optimal control problem to maximize the average burnup at the end of a core life is considered, and numerical test problems are solved.