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4. SIMULATION VERIFICATION
 We verified the ship maneuvering control system by computer simulation. The target ship is assumed that it has six azimuth thrusters and they are fixed pitch propellers, which change the thrust by increasing or decreasing the propeller rotations. The thrust is limited up to 17 ton and the minimum thrust is 5.1 ton of the idle condition. Thruster's desired value is set to this idle thrust. We set turning angle commands of thrusters inner direction. Terminal time T of evaluation function (4) is 0.1 second.
 
 In the positioning controller, we assume that the controlled position is the stern point (xc=45m) and the terminal time T in the equations (8), (10) is 100 seconds. Also, this simulation has the following conditions: setting a route, which turn to right with 45 degrees by using the three WP, tracking at constant speed (0.5 m/s) and stopping automatically at the third WP. Hydrodynamic force functions shown in [4] are used in this simulation. Fig.5 and Fig.6 show the result of the tracking simulation.
 
Fig.5 WP setting and ship trajectory
 
Fig.6 Ship's position and heading
 
 Fig.6 shows that the ship began to turn after the Tp passed through the WP1(200,0) even before the controlled position (XG, YG) did not reach at the WP1. Fig.7 shows the speed and yawrate at the controlled position. Furthermore Fig.8 shows the result of optimal thrust allocation. Fig.9 shows thrust commands from route tracking controller and actual thrust calculated by feedback signals of thrusters. This figure indicates that the thrust allocation calculation was done properly by generating desired thrusts in spite that the thrust signals were enforced not to fall down under the idle thrusts.
 
Fig.7 Velocity and yaw rate at controlled point







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