For Autonomous Underwater Vehicle (AUV), especially with reliable attitude control for trajectory tracking, an effective heading control is crucial. This work addresses the mathematical modelling of the considered vehicle, drafting closed loop control system design for the plant, and comparing germane control algorithms. In order to tackle the pith in trajectory tracking and heading control, the constructed equations of motion are inclusive of the time-variant properties such as added mass, vehicle drag and so on. The corresponding dynamics is constructed accordingly, to simulate the motion of the underwater vehicle without any environmental disturbance. Based on the model, error dynamics for the tracking controller is regulated, by estimating the deviation of the vehicle coordinates from predefined trajectory. This leitmotif is then scrutinized with the postulated equations, on the grounds of the conditions framed. The output produced is then compared between the algorithms to deduce the optimal one. © 2020 IEEE.