Distributed Parameter Optimum Control of a Nuclear Rocket With Thermal Stress Constraints

Abstract

The problem considered here is that of controlling the flow rate through a nuclear rocket such that temperature gradients in the fuel elements, and the corresponding thermal stresses produced, do not exceed specified values. The desired control program is that which takes the system from steady-state conditions at a given flow rate to a higher, specified flow rate in minimum time without violating the thermal stress constraints. The system equations here are a pair of coupled, first-order, bilinear, partial differential equations and the thermal stress constraint is proportional to a product of state and control variables. By analyzing both the solution for a step in control and the coupling between control level and time response in the bilinear system, the form of the optimal control is deduced. It is shown how the optimal control law can be generated using a digital computer. Numerical results are given.