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In harbor areas, precise ship steering is the most important operation. This requires a set of adequate thrust devices taking into account surge, sway and yaw motions precisely. However, the effectiveness of actuators during low-speed maneuvering is reduced, making it necessary to use tugboats to ensure safe berthing. In this paper, we present a mathematical model of a system describing the interaction between an unactuated ship and tugboats. Thrust allocation is solved by using the redistributed pseudo-inverse (RPI) algorithm to determine the thrust and direction of each individual tugboat. The main goal of this method is to minimize the power supplied to tugboats and increase their controllability. The constraints are twofold. First, the tugboat can only exert a limited pushing force, and second, it can only change directions slowly. Additionally, an adaptive control law is proposed to capture the draft coefficients of the ship, which are known as uncertainty parameters. The controller guarantees that the ship follows a given path (geometric task) with desired velocities (dynamic task). The specifications of Cybership I, a model ship, are used to evaluate the efficiency of the proposed method through Matlab simulations.

This paper presents an adaptive control approach using a model matching technique for 3-DOF nonlinear crane systems. The proposed control is linearly composed of two control frameworks: nominal PD control and corrective control. A nonlinear crane model is approximated by means of feedback linearization to design nominal PD control avoiding perturbation. We propose corrective control to compensate system error feasibly occurring due to perturbation, which is derived by using Lyapunov stability theory with bound of perturbation. Additionally, we achieve stability analysis for the proposed crane control system and analytically derive sufficient stability condition with respect to its perturbation. Numerical simulation is accomplished to evaluate our proposed control and demonstrate its reliability and superiority compared to traditional control method.

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