Laser powder bed fusion (LPBF) process is one of popular additive manufacturing techniques for building metal parts through the layer-by-layer melting and solidification process. To date, there are plenty of successful product prototypes manufactured by the LPBF process. However, the lack of confidence in its quality and long-term reliability could be one of the major reasons prevent the LPBF process from being widely adopted in industry. The existing LPBF process is an open loop control system with some in situ monitoring capability. Hence, manufacturing quality and long-term reliability of the part cannot be guaranteed if there is any disturbance during the process. Such limitation can be overcome if a feedback control system can be implemented. This article studies the control effectiveness of the proportional-integral-derivative (PID) control and the model predictive control (MPC) for the LPBF process based on a physics-based machine learning model. The control objective is to maintain the melt pool width and depth at required level under process uncertainties from the powder and laser. A sampling-based dynamic control window approach is further proposed for MPC as a practical approach to approximate the optimal control actions within limited time constraint. Control effectiveness, pros, and cons of the PID control and the MPC for the LPBF process are investigated and compared through various control scenarios. It is demonstrated that the MPC is more effective than the PID control under the same conditions, but the MPC demands a valid digit twin of the LPBF process.