Adaptive observer based adaptive control for P.W.R nuclear reactors during load following operation with bounded xenon oscillations using Lyapunov approach

Load-following is the most important operation in the nuclear reactors. In the nuclear reactors, imbalance of axial power distribution induces xenon oscillations. These oscillations must be maintained bounded within acceptable limits. Otherwise, the nuclear reactor could become unstable. Therefore, bounded imbalance of axial power distribution is considered to be a restriction for the load following operation. Also, in order to design the nuclear reactor control systems, xenon concentrations and delayed neutrons precursors densities must be available. But, physical measurement of these parameters is impossible. In this paper, for the first time, in order to estimate the xenon concentrations and delayed neutrons precursors densities and ensure imbalance of axial power distribution are kept bounded within acceptable limits during Load-following operation, an Adaptive Observer based Adaptive Sliding Mode Control based on the two-point kinetics reactor model is presented. The sliding mode method exhibits acceptable tracking performance in the presence of parametric uncertainty only at the expense of high gains and control chattering. Therefore, parameter uncertainties match envisaged by designing adaptive Algorithm for both the control and observer and high chattering authority is inhibited. The adaptation laws to online parameter adaptation and observer gains adaptation are generated using the Lyapunov approach. Also, the stability analysis is given by means of Lyapunov approach, thus the system is guaranteed to be stable within a large range. Simulation results are presented to demonstrate the effectiveness of the proposed controller for the load-following operation, in terms of the robustness and stability. Also, results show that the xenon oscillations kept bounded in the given region and the adaptive parameters are bounded during load following operation and observer follows the actual system variables accurately in the presence of the parameters uncertainties and external disturbances.