This paper presents a computational control algorithm for a vehicle to track a reference path within the automated lane centering system (ALC). The system aims to provide automatic lateral control by taking into account the physical and steering constraints imposed by the vehicle. A processing unit obtains the lateral error relative to the lane center and heading angle error from the center of its lane. To provide a smooth and continuous steering wheel angle as well as fast computation, the vehicle's kinematic and geometric models are unified and integrated with the controller of the system. The proposed control approach computes a steering wheel angle to track an ideal trajectory automatically. A proportional switching integral (PI) controller was implemented to control the vehicle speed. The path tracking algorithm is simulated for different vehicle speeds and curvy roads in TORCS (The Open Racing Car Simulator). The simulation results point out the effectiveness of the presented method, and indicate its wide practical application to self-steering and autonomous vehicles.