Assignment 2, Part 3

Resources:

• Chapter 6, 9 in Fossen.

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Objective: In this assignment, you are going to implement a propulsion system and a controller to control the speed of the ship model you developed in the previous assignment. To solve this task, you will have to simulate additional states; do this by extending the state vector as needed.

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Problem 1: Propeller Revolution and Speed Control

a)

Implemented by using the function wagening()

% ...
Ja = 0;
z = 4;
PD = 1.5;
AEAO = 0.65;
 
[KT, KQ] = wageningen(Ja, PD, AEAO, z);
% ...

Where

• $K_T$ is the thrust coefficient.
• $K_Q$ is the torque coefficient.
• $J_a$ is the open-water advance coefficient.
• $P_D$ is the pitch/diameter ratio
• $AEAO$ is the blade area ratio
• $z$ is the number of propeller blades

b)

See Matlab

c)

Equation 9.8 is given by

$$Q=\rho D^5{K}_Q(J_a)|n|n$$

And implemented by

Q = rho * Dia^5 * KQ * abs(n) * n;

Where

• $\rho$ is the density of the water
• $D$ is the propeller diameter
• $n$ is the actual shaft velocity

d)

Equation 6.136 is given by

$$(m-X_{\dot{u}}){\dot{u}}_r-X_u{u}_r=-X_{\delta \delta }{\delta }^2+(1-t)T$$

This means that when $u_r=U$, ${\dot{u}}_r=0$ and $X_{\delta \delta }=0$ we can rewrite Eq. 6136 as

$$U=\frac{(t-1)T}{X_u}$$

e)

We achieve the desired speed when the heading angle is constant. This is due to the friction being zero.

f)

We need to change the open-loop controller to a closed-loop controller.