# Control Strategy of In-Port U-Turn for Ships Based on Arctangent Function Nonlinear Feedback
###### Abstract
The authors of [PERSON] et al. [14] proposed a fuzzy logic-based human-like decision-making method for ultra-large ship berthing, validated with pilotage data, offering insights for autonomous navigation in port waters. The authors of [PERSON] et al. [15] examined the impact of shallow water on vessel steering models using system identification methods and compared parameter estimation accuracy among different modeling techniques, demonstrating that shallow water significantly impairs ship maneuverability. The authors of [PERSON] et al. [16] presented a mathematical model to analyze the motion of moored ships in harbors, incorporating strategies like porous breakwaters and wave absorbers to mitigate resonance and enhance safety in maritime navigation. The authors of [PERSON] et al. [17] introduced a nonlinear feedback-based controller design that enhances system robustness, reduces energy consumption, and demonstrated significant practical engineering value through simulations with the training ship \"Yupeng\". The authors of [PERSON] and [PERSON] [18] outlined a method for autonomous ship operation in ports, utilizing the ant colony optimization algorithm for safe trajectory calculation and a combination of trajectory and low-speed controllers to maneuver a very large crude carrier model. The aforementioned methods have proposed various research and evaluation approaches in the domain of shallow water navigation analysis and ship motion control, showing promising results in simulations and experiments. They face issues related to model complexity and high computational costs. These challenges necessitate more advanced hardware support and meticulous parameter tuning, increasing the difficulty and cost of implementation. Moreover, the increasing complexity of algorithms often relies on accurate models and parameters, making the system difficult to adapt quickly to un known or changing environments. Building on the aforementioned research, this paper proposes a simple and robust control strategy for the automatic U-turn of ships in the port. By employing the closed-loop gain-shaping algorithm to design the controller and integrating nonlinear feedback techniques for error processing, this approach achieves effective automatic U-turn control for ships within port environments. In addition, the controller was further optimized to reduce the variation of the system output, reduce the wear of the rudder, and extend its service life. Reducing the wear of rudder can ensure that the rudder is in good working condition, preventing the generation of more wear particles. These wear particles can enter the hydraulic and lubrication systems of the ship, causing system contamination and further exacerbating wear. At the same time, reducing rudder motor wear can also lower fuel consumption, reduce noise and vibration, and decrease waste oil emissions. This can reduce the negative impact of the ship on the environment and improve the environmental performance of the ship, embracing the concept of green shipbuilding. The main innovations of this paper include:  
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2. third-order Nomoto model, it is rewritten into state-space form; the wind and wave interference models are added in the ship model to design the ship U-turn controller. 3. Nonlinear feedback technology is used to improve the controller, reducing the energy consumption of ship U-turns with low speed in the port and reducing the wear of the steering gear, which can prolong its service life.