# Research on a Support System for Automatic Ship Navigation in Fairway
## 5 Numerical Simulation and Result Discussion
### Automatic Ship Navigation in Fairway with the Proposed System  
The results of the numerical simulation of the proposed system are shown in Figure 10, and the time history of the ship control process is presented in Figure 11. The ship at the start is very far from the first waypoint (WP\({}_{1}\)), so the ship's heading was kept steady until the ship is at the first waypoint. For track-keeping via the proposed system, at the points (WP\({}_{1}\)), (WP\({}_{2}\)), the rudder was altered to port (\(-35^{\circ}\)) to keep the ship on the route while the rudder was also changed to (+35\({}^{\circ}\)) to starboard at (WP\({}_{5}\)) and (WP\({}_{7}\)). In the segment between (WP\({}_{3}\)) and (WP\({}_{4}\)), the rudder was steady kept amidships by the track-keeping function of the system. At the waypoints (WP\({}_{1}\)), (WP\({}_{2}\)), (WP\({}_{3}\)), and (WP\({}_{4}\)), the yaw rate had negative values at these waypoints. At three times between (WP\({}_{5}\)) and (WP\({}_{8}\)), the yaw rate had positive values. The track cross error is maximum at the waypoints because the ship's rudder is altered to the next waypoint when the ship is near to the current waypoint. With the ship is stable on the route, the track cross error converged to zero, (Figure 10). Meanwhile, for the function of speed reduction, from the sixth waypoint (at time = 1818 s), the propeller revolution was reduced to slow down the ships' speed, and the main engine of the ship was stopped at the ninth waypoint (WP\({}_{9}\)). At the ninth waypoint (WP\({}_{9}\)), because the ship's speed was low, the cross track error tended to increase even if the rudder was effective and was set to its maximum angle (\(-35^{\circ}\)). It was difficult to keep the ship on this track (from (WP\({}_{9}\) to WP\({}_{10}\)). In order to avoid a loss of control in this case, the bow thruster was activated by the heading stabilizing controller. The pushing force of the bow thruster was calculated based on the heading error and yaw rate. At time (2516 s), the heading error was a maximum (102\({}^{\circ}\)) to starboard, the yaw rate was \(-0.05\) (\({}^{\circ}\)/s), and the bow thruster force was set to \(-8000\) (N) to push the ship's bow from starboard to port until the heading error converged to zero.  
Figure 10: The track of ship controlled by an automatic navigation system under the wind disturbance (velocity 5 knots, direction from N to S).  
After completing the automatic navigation process, the ship is brought to (WP\({}_{10}\)). At this point, the ship control process is changed into automatic berthing mode with low speed ship motion. The berthing problem noted in researches [27; 28; 29; 30; 31] can adapt to the proposed navigation system. In Figure 12, the automatic berthing process described in References [27; 28; 29; 30; 31] uses a neural network controller to regulate the rudder angle and the propeller revolution simultaneously.  
Figure 11: The time history of ship motion controlled by the automatic ship navigation system.  
Figure 12: The automatic ship berthing system using neural network controller.