To optimize the control of the pressurizer in nuclear power plants, this paper employs Model Predictive Control (MPC) for the optimization of pressure control in the pressurizer. MPC is an advanced control strategy that predicts the future behavior of a system through the establishment of a mathematical model and optimizes the control inputs based on these predictions. In MPC, an accurate system model is essential for predicting future system behavior, making model identification a critical step. This model needs to accurately reflect the dynamic characteristics of the process, including linear or nonlinear, time-varying or non-time-varying features. If the model is inaccurate, the effectiveness of predictive control may be significantly reduced. To enhance the accuracy of modeling, this paper utilizes Physics-Informed Neural Networks (PINNs) for model identification of the pressurizer in nuclear power plants, and then applies MPC on the established predictive model. Since the pressurizer is a nonlinear and time-varying model, using a transfer function for prediction, as in traditional predictive control methods, may not adequately capture its dynamics. The adoption of PINNs for modeling the pressurizer is expected to better reflect its changing process, achieving more precise control.