The parameter model of nuclear reactor power distribution established based on the neutron diffusion equation involves three spatial dimensions and one time dimension. By simplifying for different spatial dimensions, the lumped parameter model of nuclear reactor power and the axial spatial distributed parameter model of nuclear reactor can be obtained. Infinite-dimensional controllers designed according to the distributed parameter control theory, with the nonlinear P-sD controller as an example, can be applied to the distributed parameter model to obtain the temporal variation of the axial power distribution, but the overall process is very complex. Controllers designed based on classical control theory, such as PID control, when applied to the lumped parameter model, can only obtain the temporal variation of power and cannot acquire information about the spatial distribution of power. Applying the lumped parameter controller to the distributed parameter model enables the acquisition of both the axial distribution and temporal variation of power, and the entire process is relatively simple. However, it lacks corresponding theoretical guidance, making it impossible to determine the controller parameters. Therefore, the Physics-Informed Neural Network (PINN) is introduced. The forward problem of PINN is used to obtain the results of applying the nonlinear P-sD controller to the distributed parameter model. After processing these results, they are applied to the inverse problem of a new PINN to obtain the corresponding parameters of the lumped parameter controller. Simulation results demonstrate that the PID controller designed with the controller parameters obtained by PINN, when applied to the distributed-parameter model, ensures both the overall power variation and spatial power distribution meet the desired requirements. Furthermore, the PINN-based PID parameter tuning method exhibits exceptional stability.

Physics-Informed Neural Network; Distributed Parameter Model; Neutron Dynamics; PID Controller; Parameter Tuning