Heavy lift crane vessels play an important role in offshore installations. Previous studies have shown that position control systems for these vessels can cause unstable positioning behavior during offshore construction assignments under specific conditions, e.g., change of environmental loads. Some control methods, such as crane force feedforward to the controller or the estimator, have been developed to improve the stability of the position control systems. However, these methods depend on the accurate estimation of the crane force and fast reaction of thrusters, which are difficult to obtain under working conditions. To make the positioning system stable, and compensate the controller for the changing crane stiffness and the systems onboard, two methods will be provided. One is to increase the flexibility of the system, while the other one is to increase the robustness. Two control methods, adaptive PID and H-infinity, are adopted and the results are compared. During simulations, the two controllers can dispose of crane modeling error and time delay of thrusters. Adaptive PID has a smaller variance under higher wind and wave load, while H-infinity controller has a larger clearance with the platform.