The power take-off (PTO) mechanism, a pivotal component in wave energy converters (WECs), holds significant importance in governing the motion and power conversion processes. This article delves deep into the intricate control mechanisms of the point-absorber wave energy converter, particularly focusing on the multifaceted constraints posed by damping and displacement. With the aim of elevating the energy capture efficiency of these devices, we crafted a Model Predictive Control (MPC) framework and subjected it to rigorous scrutiny. By skillfully transforming the lag function and deriving the state-space equation, we fashioned a predictive model and an objective function that powers our control algorithm. To accurately mimic the converters' behavior under varying sea conditions, a comprehensive model that seamlessly integrates theoretical analysis and numerical simulations was forged. This approach enables us to gain a profound understanding of optimal control strategies under diverse constraints and wave conditions, ultimately leading to an enhanced wave energy conversion ability. The simulation results are highly revealing and indicate that, in the absence of external constraints, the performance of MPC and optimal damping control in energy conversion optimization is nearly identical. However, when confronted with external constraints such as PTO damping force and displacement, MPC emerges as the superior choice, achieving better energy conversion performance compared to optimal damping control in both regular and irregular waves. This advantage is particularly evident near the natural frequency of the absorber.