Method A comprehensive control strategy based on a virtual reference model and a new type of sliding surface was proposed. By constructing a virtual ship system, the complex underactuated ship trajectory tracking problem was decoupled and transformed into an accurate tracking problem for the virtual ship speed command. In the design of the control loop, a new type of global fast terminal sliding surface was designed. To enhance the anti-disturbance ability, a nonlinear disturbance observer was designed and integrated to estimate the time-varying unknown environmental disturbances online and in real time, and the estimated value was introduced as a feedforward compensation term into the controller. In addition, for the saturation constraints of the actuator, a saturation function was introduced in the control law generation.

Results The simulation experiment results show that, even in the presence of unknown time-varying external disturbances, this controller still exhibits excellent robust stability and tracking accuracy, successfully avoiding the complex number calculation problems encountered in traditional methods. The comparative experiment analysis reveals that, compared with the advanced second-order sliding mode controller and the typical ordinary nonlinear sliding mode controller, the method proposed in this paper significantly improves the convergence performance: in position tracking, the convergence accuracy has increased by approximately 9.62% and 33.80% respectively; in longitudinal speed tracking, the error convergence accuracy has improved even more significantly, reaching approximately 49.43% and 51.11% respectively.

Conclusion The newly designed global fast terminal sliding mode trajectory tracking controller is superior to the second-order sliding mode controller and the ordinary nonlinear sliding mode controller, and it provides a new idea for the design of trajectory tracking controllers. The newly designed global fast terminal sliding mode trajectory tracking controller is superior to the second-order sliding mode controller and the ordinary nonlinear sliding mode controller, and it offers a new idea for the design of trajectory tracking controllers.