JEE506: Modelling and Simulation of Container Ship Steering System

This report presents a comprehensive Simulink model for simulating the steering dynamics of a container vessel. The model incorporates factors such as rudder angle, propeller forces, thruster forces, and yaw rate to determine the vessel's trajectory. Equations of motion are derived based on established theories, and the model is implemented in Simulink using parameters defined in the modelparam.m file. The report includes plots of rudder angle, yaw rate, yaw position, and trajectory, demonstrating the vessel's response to different rudder angles. The analysis reveals that larger rudder angles result in greater hull displacement, while smaller angles lead to circular trajectories with minimal displacement. The MMG model of the Hoorn vessel is constructed and simulated, providing insights into the vessel's manoeuvring characteristics under various operational conditions. Desklib provides access to similar solved assignments and study tools for students.

Problem 1: Steering Dynamics of a Container Vessel Model - Ship Manoeuvring System
1.1: The modelling of the ship hull manoeuvring dynamics is designed in Simulink as given
below. The physical model of the vessel is shown in figure 1.
The mathematical model for relating the inputs and the outputs of the hull dynamics is given
below.
δ = rudder angle [in radian] (from -60 degrees to +60 degrees)
F1 and F2 drag forces generated by twin propellers [N]
F3 and F4 thrust forces generated by the thrusters [N]

r yaw rate [rad/sec]
ψ yaw angle [rad]
The equation for the trajectory can be represented using a state space model which is
˙x=usinψ +vcosψ
˙y=usinψ + vcosψ
Here, u is the velocity of surge and v is the sway velocity. The co-ordinate of hull is
represented by x and y axis.
Now, given that the inertia moment about the z axis = 22.5 kgm^2.
G to rudder distance is 1085 mm
The distance between the twin propellers = 118 mm.
The distance from the bow thruster to G = 852 mm.
The distance from G to stern thruster = 338 mm.
Vessel total length = 2570 mm
Vessel mass = 63.4 kgs.
Propeller maximum speed = 1000 RPM.
The maximum amount of generated drag force = 50 N.
The torque coefficient of water resistance between the hull and water = 6.75 Nm/rad/s.
The moment of rudder constant = 2.5 Nm/rad.
The maximum ladder thrust force = 25 N.
Now, the Yaw rate ˙ψ=r
Now, the equation of rudder angle is
˙❑=❑− ¿
¿ ¿ ¿
The pitch angle is given by,
˙= p− p
|p− p|Tcpp+a
Where,
❑ = Commanded rudder angle
p = Commanded pitch angle
Trud = time constant of the rudder
Tcpp = time constant of the pitch
a = constant

Now, the steering equation of the hull is
Surge m( ˙u – vr )=Xh+ Xp+ Xr
Sway m( ˙v+ur )=Yh+Yt +Yr
Yaw Izz∗˙r=Nh+ Nt +Nr
Here, m = mass of the vessel = 63.4 kg.
Xr, Yr = hydrodynamic forces acting on ship’s rudder
Xh, Yh = hydrodynamic forces acting on the ship’s hull
Izz = moment of inertia about z axis = 22.5 kgm^2
˙u, ˙v is the acceleration in the x and y direction.
Yt = hydrodynamic force by thruster = 25 N.
Nt = hydrodynamic moment by the thruster
Simulink model of the steering mechanism and ship hull:
Rudder angle plot:

Yawrate plot:
Yaw position plot:

Trajectory plot (XY co-ordinate):
Now, the MMG model of Hoorn vessel is constructed in Simulink from the numerical values
of the variables as given above. The values of the different variables are calculated given in
the file modelparam.m file.

Simulink model:
Initially the rudder angle is taken as 60 degrees and then the angle is gradually reduced in
large steps. The model is simulated for 100 secs and the hull position in XY co-ordinate is
obtained as given below.
XY position plot of the hull for rudder angle of 60 degrees:

XY position plot of hull for the rudder angle of 15 degrees:
XY position plot of hull for the rudder angle of -15 degrees:

XY position plot of hull for the rudder angle of -60 degrees:
Hence, it is seen that when the magnitude of the rudder angle is large then the hull
displacement is large from its initial position as the locus is spiral but with low magnitude of
the rudder angle the locus tends to complete circle and hence the displacement of the hull
from its initial position is small.