Optimal Control Based on a Linear-Quadratic Regulator for Controlling a Nuclear Reactor

   Nuclear reactors are widely used in various fields of human activity, for example, for the production of electricity, the production of isotopes, for educational and research purposes, as well as in space engines. Despite their useful purpose, they pose a danger to humans and society due to hazardous radionuclides generated during operation. Therefore, it is imperative to perform actions that reduce the release of radionuclides into the environment. These activities include operating a nuclear reactor under stable conditions and complete control over the system. In this study, the control of the nuclear reactor using a linear-quadratic regulator of the optimal control method is carried out using a nonlinear model of the rigid-point kinetic equation with one group delayed neutron. First, it is shown that the nuclear reactor is asymptotically unstable. Moreover, there are unlimited input and limited output. As a result, a proportional gain compensator is applied to the system to form a closed loop system that stabilizes the system. In addition, the system takes into account reactivity feedback by combining the equations of point kinetics and additional equations of thermal hydraulics. The simulated equation is linearized and a linear quadratic control strategy is applied to achieve performance specifications such as minimum overshoot, settling time, and system stabilization. The simulation results have been confirmed by previous studies.

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