Third-generation PWRs, tasked with increasing grid peaking responsibilities, demand enhanced load-following capabilities in reactor control systems. Model predictive control (MPC) algorithms offer dynamic controller updates based on operational parameters, in comparison to traditional PID control. An asymptotic identification method-based MPC algorithm is thus employed to PWR control studies. Initially, the paper performs identification experiments utilizing an asymptotic identification method tailored to PWR characteristics, yielding an accurate model with small variance. The identified model demonstrates good performance in the frequency domain according to the model validation theory of asymptotic method. In time domain validation, the fitting degree are all higher than 80%. Subsequently, a model predictive controller is designed based on the identification model, and simulation analysis is conducted for four working conditions respectively. The simulation results indicate that the MPC controller has advantages in control precision and settling time than the original controller. However, when encountering a larger step, the MPC controller shows a larger overshoot due to the more intense output of the controller during the control process. To address this issue, a new MPC controller is designed that integrates reference trajectories and model predictions for the G-rod. The analysis of the performance reveals that the MPC controller with reference trajectories mitigates overshoot in the control process, while maintaining enough control precision and short settling time.