Precise Trajectory Tracking Control of Ship Towing Systems via a Dynamical Tracking Target
Abstract
:1. Introduction
- An appropriate passive steering angle is introduced to make the towed ship track well the trajectory of the tugboat.
- A dynamical tracking target, sliding mode control, and inverse dynamics adaptive control methods are introduced to design two robust torque controllers for the STS, so that the tugboat and the towed ship can move along the same target trajectory curve accurately under uncertainties.
2. System Modeling
- A1.
- The motion of the STS is in a horizontal plane. The ship roll, pitch, heave, and lateral drift motions are negligibly small.
- A2.
- The motion of the towed ship is achieved by the system coupling action.
- A3.
- The nonlinear force is ignored, since the STS commonly does not make large maneuvers.
- A4.
- The rudder cannot be controlled directly, and the motion of the towed ship is controlled indirectly by the coupling action of nonholonomic constraints.
- A5.
- The resistance force of the towline is ignored.
2.1. Kinematics Modeling
2.2. Dynamics Modeling of a Single Ship
2.3. Dynamics Modeling
3. Trajectory Tracking Control of the Ship Towing System
3.1. Dynamical Tracking Target
3.2. Control Design
3.2.1. Forward Speed Control Subsystem
3.2.2. Yaw Rotation Speed Control Subsystem
4. Simulation Results
4.1. A Comparison between the Dynamical Target and Statical Target
4.2. Actual Trajectories of the Towed Ship with Different Steering Coefficients
4.3. Robustness of the Proposed Controller
5. Conclusions
- The towed ship is able to move along the trajectory of the tugboat by introducing an appropriate passive steering angle. Then, the original motion control problem is transformed into the tugboat tracking the target trajectory curve.
- The target trajectory curve is converted into a dynamical tracking target by using the relative curvature of the target curve, which can fundamentally solve the problem of accurate tracking for the ship towing system.
- By combining dynamical tracking target, sliding mode control and inverse dynamic adaptive control, the torque controller has strong robustness. Even if the error speed subsystem is unstable affected by an uncertain factor, all bodies can still track the target trajectory curve accurately.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Notation | Definition |
---|---|
, | Torques provided by the propeller and rudder of the tugboat |
, | Yaw angles of the tugboat and the towed ship |
, | Yaw rotation speeds of the tugboat and the towed ship, and |
, | The coordinates of the midpoint of the tugboat |
, | The coordinates of the midpoint of the towed ship |
Angular difference of yaw angles between the tugboat and the towed ship, and | |
, | Forward speeds of the tugboat and the towed ship |
The forward speed of the stern midpoint of the tugboat | |
The forward speed of the bow midpoint of the towed ship | |
Steering angle of the towed ship, and | |
Steering coefficient of the steering angle | |
a | Length of the rigid towline |
Masses of the tugboat and the towed ship | |
Additional lateral masses of the tugboat and the towed ship | |
Moment of inertia of the tugboat and the towed ship about Z-axis through the center point | |
Additional moments of inertia of the tugboat and the towed ship about Z-axis through the center point |
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Li, O.; Zhou, Y. Precise Trajectory Tracking Control of Ship Towing Systems via a Dynamical Tracking Target. Mathematics 2021, 9, 974. https://doi.org/10.3390/math9090974
Li O, Zhou Y. Precise Trajectory Tracking Control of Ship Towing Systems via a Dynamical Tracking Target. Mathematics. 2021; 9(9):974. https://doi.org/10.3390/math9090974
Chicago/Turabian StyleLi, Ouxue, and Yusheng Zhou. 2021. "Precise Trajectory Tracking Control of Ship Towing Systems via a Dynamical Tracking Target" Mathematics 9, no. 9: 974. https://doi.org/10.3390/math9090974