Identification and Modeling of States and Parameters of Nuclear Reactor Systems

This paper presents the development and application of a method for on-line estimation of states and parameters in noisy nonlinear systems. Requisite data for the method consists of a sequence of measurements on system output variables which are, in general, nonlinear functions for one or more of the system state variables. The output variables may contain random instrument errors and the system itself may be subject to random input fluctuations. There is no need to introduce special test inputs as the normal operating system inputs and outputs suffice for the sequential identification and modeling method proposed here. A discrete version of the startup dynamics of a thermal nuclear reactor system is considered. It is desired to estimate output states and parameters such that a "best" linear model as well as a best nonlinear model for the reactor states and parameters may be determined. A discrete version of Pontryagin's Maximum Principle is employed to obtain the canonic equations of the least-squares optimal estimator for the kinetics equations. A discretized invariant imbedding technique is then applied to solve the resulting two-point boundary value problem. Finally, a system of sequential equations is obtained by application of variational methods to the optimal startup trajectory. The result is a sequential estimation scheme which has the advantage of direct applicability to discrete as well as continuous systems and which provides for the inclusion of certain higher-order terms not usually considered by other methods.