# Tutorial 8 - Ship Autopilot

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```					                         Tutorial 8 – Ship Autopilot
(JEE344 Applied Control Engineering)

Aim
•   To design and simulate an PID- based autopilot system
•   To use simulation as a diagnostic tool to improve autopilot performance and select
control gains

Learning Outcomes
• Simulate a ship’s steering dynamics with LabVIEW
• Simulate PID autopilot with Auto/Man switch mode for course keeping and changing

Ship 1: Autopilot system for Shioji Maru using Nomoto’s model

Problem Statement
Let’s consider the Nomotor’s first order manoeuvring model:
Tr + r = Kδ (or Tψ + ψ = Kδ )
&                && &                                             (1)
ψ=r
&                                                                   (2)
where ψ is yaw angle (rad) and δ is rudder angle (rad, −40π /180 to +40π /180 , T = 7.5
seconds and K = 0.11. Ship speed is constant, v = 15 knots (1 NM = 1,852.00 m). The
steering machine model is
&         δc − δ
δ=                                                                   (3)
δ c − δ TRUD + a
where TRUD is rudder constant, TRUD = 11.9 (sec), and a is constant chosen as 1 to avoid zero
dividing. The ship’s heading is control by a PID autopilot system with control gains of KP, KI
and KD. It is assumed that the rudder angle for the PID autopilot is in range of -10o (port) to
+10o (starboard), rudder rate in range of -5 deg/s to +5 deg/s, error (between the actual yaw
angle and set course) in range of -180o to +180o, and yaw angle in range of 0-360o. The
position of the ship is represented by the following model:
x = u sin ψ + v cos ψ
&                                                                    (4)
y = u cos ψ − v sin ψ
&                                                                    (5)
where u is surge velocity and v is sway velocity (assuming that v = 0). Make simulation
program/s with LabVIEW.

Solution

1. Ship’s open-loop system

U (knot)
x
δc        Steering       δ       Ship hull      ψ           Ship
y
machine                dynamics                trajectory
-40 to +40                                        0 to 360

Figure 1 Block diagram of the open-loop system

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2. Block diagram algorithm for the ship’s hull dynamics:
1 K
r=− + δ
&                                                                                  (6)
T T
ψ=r
&                                                                                 (7)
Sum
×                                     &
×
×                           ÷                    ∫                       ∫
δ [rad]      K                             T Divide         Integrator                 Integrator       Display ψ

Figure 2 Block diagram algorithm for ship’s hull dynamics

3. Block diagram algorithm for ship’s trajectory on the earth-fixed reference frame:
x = u sin ψ + v cos ψ
&                                                              (9)
y = u cos ψ − v sin ψ
&                                                              (9)

cos                 ×
+
×                    &
y                 y
∫          x
sin              ×
–              Integrator
×
u [m/s]                                                                                  (0,0)

×
+                                            XY-Chart
v [m/s]                              ×                    &
x                x
∫          y
×
+              Integrator
×

Figure 3 Block diagram for the ship’s trajectory (x – latitude, y – longitude)

4. Block diagram algorithm for the steering machine
&        δc − δ
δ=                                                                                 (10)
δ c − δ TRUD + a

δc
+                              δc − δ
&
δ                δ                                                                     ×
∫            –                  abs              ×              +
×                            ÷
Integrator                                                           +
Trud          a

Figure 4 Block diagram algorithm for the steering machine

2
5. Ship’s Closed-loop Control System (Autopilot with Auto/Man Switch)

U (knot)
SP ψ d                      -40 to +40                                 0 to 360
x
PID        δc      Steering           δ   Ship hull ψ          Ship
Autopilot            machine                dynamics          trajectory      y
GPS

ψm         Gyro-
compass

Figure 5 Block diagram of the closed-loop autopilot system

The block diagram algorithm for PID autopilot with Auto/Man mode is below:
PID Autopilot

Comparator                               Sum
(Compound
SP ψ d               Subtract                 Multiply    Arithmetic)
PV ψ                                                          +            Auto/Man
Kp               P
Multiply                          Select
Integral uin                                                         OP
+         Auto
I
KI                                                (Control signal)
Multiply                               Commanded
uin                                                      Man
+                       rudder angle
To Steering
Derivative                                    D
KD                                      Machine

Figure 6 Block diagram algorithm for PID autopilot with Auto/Man switch mode

Hands-on Exercise 1 (Save as ShipSimulator01.vi)
Open-loop system without the steering machine & trajectory: Refer to Figure 2 and the
following sample code:

Figure 7 Sample code for the open-loop system without SM & trajectory

3
•   Save the VI.
•   Do testing of its functionality.

Hands-on Exercise 2 (Save as ShipSimulator02.vi)
Open-loop system with the trajectory (without steering machine): Refer to Figure 3 and the
following sample code:

Figure 8 Sample code for the open-loop with trajectory (without the SM)

Hint: When using the XY Graph for ship’s trajectory, uncheck “Clear data on each call”:

Figure 9 Setting the Build XY Graph

•   Save the VI.
•   Do testing of its functionality.

Hands-on Exercise 3 (Save as ShipSimulator03.vi)
Open-loop system with steering machine and trajectory: Refer to Figure 4 and the following
sample code:

4
Figure 10 Sample code for the steering machine

•   Save the VI.
•   Do testing of its functionality.

Note: You can add indicator/s and/or a waveform chart to display the commanded rudder and
actual rudder.

Hands-on Exercise 4 (Save as ShipSimulator04.vi)
Program a gyrocompass and set limits for ship’s heading in range 0 to 360o.

Algorithm to set limits:
If psi >= 2 π then psi = psi – 2 π ,
Else if psi < 0 then psi = psi + 2 π
Else psi = psi

C language code (Formula Node):
If psi >= 2*pi
{ psi = psi – 2*pi;}
Else if (yaw < 0)
{ psi = psi + 2*pi;}
Else
{ psi = psi}

MATLAB language code (MathScripts Node):
if (psi >= 2*pi)
psi = psi – 2*pi;
elseif (psi < 0)
psi = psi + pi*2;
else
psi = psi;
end

Hands-on Exercise 5 (Save as ShipSimulator05.vi)
Closed-loop system (Autopilot with Auto/Man)
• Save the VI.
• Do testing of its functionality.

5
Conclusions
At this point the following LOs have been satisfied:
• Simulate a ship’s steering dynamics with LabVIEW
• Simulate PID autopilot with Auto/Man switch mode for course keeping and changing

Follow-up Exercise
Modify the above program for ship autopilot system in consideration of the trajectory with
initial latitude and longitude (the Control Lab’s latitude and longitude!):
x(0) = current latitude = 41o27.179’ S
y(0) = current longitude = 147o04.246’ E
such that the ship’s position is expressed with latitude and longitude. One nautical mile is
approximately 1852 m, and equivalent to one minute of arc.

Refer to Nautical mile: http://en.wikipedia.org/wiki/Nautical_mile

6

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