Virtual tracking control of underwater vehicles based on error injection and adaptive gain

An improved virtual tracking control scheme is proposed based on error injection and adaptive gain for underwater vehicles in the presence of a large initial tracking error and external disturbances. To relieve the effect caused by a large initial tracking error, the developed control scheme is achieved based on two closed-loop systems. Specifically, a virtual closed-loop system is constructed based on an approximate dynamic model of an underwater vehicle, while an actual closed-loop system is built with a real underwater vehicle. Firstly, in order to improve the tracking precision of the virtual tracking control scheme, an auxiliary variable produced by a first-order filter is injected into a virtual tracking error in the virtual closed-loop system. And then, the virtual trajectory provided by the virtual closed-loop system is followed by the actual closed-loop system. In the actual closed-loop system, a modified sliding mode surface is designed to achieve the finite-time stability, while the control gains can be on-line adjusted based on the tracking performance. Finally, the effectiveness and feasibility of the proposed control scheme are demonstrated by case studies on an underwater vehicle subject to different external disturbances.