Automated design of a ship mooring system - Maplesoft Automated design of a ship mooring system ......

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Automated design of a ship mooring

system

The challenge: To investigate a mechanism to control and automate a mooring

system between two ships at sea

© Maplesoft, a division of Waterloo Maple Inc., 2009

Editor's Notes

Introduction

Problem Statement

1. Physical Model

Representation

2. Modeling Wave

Dynamics

3. Open-Loop Response

4. Closed-Loop Response

Results

** This application was developed using Maple and MapleSim


• •

• •

• •

Editor's NotesThe mooring of ships to harbors, terminals, and offshore structures is a common and essential procedure in

most seafaring operations. Inadequate mooring can result in significant structural damage to the berthing

vessel and moorings. To this day, most mooring operations are still performed in the same manner as they

were decades ago; they are dependent on heuristics, or in other words, the captain or mooring master’s

experience. Unfortunately, the effects of global warming and climate change are altering the hydrodynamics of

the sea, making manual mooring operations a very risky venture.

The challenge: To design a mechanism to control and automate a mooring system between two ships at sea.

MapleSim™ and Maple™ are used to:

Create a physical model of the two ships and mooring cables

Develop a realistic model of the external environmental forces and use the results to simulate conditions at

sea

Design and tune an appropriate controller to stabilize the system

Developing a realistic model of the external forces was critical to the design of the controller. This allowed the

engineer to tune the controller, eliminate vibrations, and stabilize the tension in the line. With the initial control

system complete, further improvements can be made to the disturbance model by including irregular waves

from multiple directions, wind gusts, wave drift forces, and the interaction effects from passing ships.

Introduction

The mooring of ships to harbors, marine terminals, floating terminals, and offshore structures is an essential

part of most seafaring operations. Inadequate mooring can severely jeopardize the success of most ship-to-

ship operations resulting in large operational downtimes. In addition, it can also result in significant structural

damage to the berthing vessel and/or the moorings. Consequently, optimizing and stabilizing the mooring

system is a high priority for most seafaring operations.

Mooring operations today are still performed in the same manner as they were decades ago. That is, they

depend on heuristics, that is, the captain or mooring master’s experience. Unfortunately, the effects of global

warming and climate change are altering the hydrodynamics of the sea, making un-mechanized mooring

operations a very risky venture.

This application investigates a preliminary design of a control system to automate the mooring process

between two large vessels, such as an oil tanker, in the open sea. The hydrodynamic interactions of the

waves and the presence of wind are modeled by a second-order linear partial differential wave equation. As

expected, the open-loop response of the system results in severe vibrations on the tension in the mooring line.

The incorporation of a PID controller to the open-loop system eliminates the vibrations on the line, and

stabilizes the tension at 70 N/m.

Problem Statement

To investigate the hydrodynamic interaction of a ship mooring system and develop a controller to ensure that

the mooring system can securely withstand external forces in the form of wind and waves.


As can be seen in the diagram, the physical model is made up of a controller and plant model. The controller

model adjusts the motor voltage driving the Mother Ship so that the tension in the mooring system remains at

72 N /m. The tension in the mooring line is fed back to the control system through a force sensor that is

connected between the Mother Ship and the Mooring Cable.

The Mother Ship submodel was modeled by a DC Motor and Gear submodel, where the DC Motor

was modeled as an equivalent electric circuit and an ideal gear. The mass of the Mother Ship was

assumed to be significantly larger than that of the Daughter Ship which is why it was modeled as a

fixed, non-moving surface.

•

The Mooring System which normally entails affixing the Daughter Ship to the Mother Ship with at

least 6 cables, was modeled by a single stiff spring.

•

The Daughter Ship submodel was modeled with a sliding mass component of 100 tons. For this

model, it was assumed that the engine driving the Daughter Ship was turned off.

•

The data used to model the Wave Dynamics submodel was derived in Maple. The details can be

found in the next section.

•

Each of these submodels, and the components that were used to model them can be seen in the .msim file.


(2)(2)

(1)(1)

2. Modeling Wave Dynamics

The wave equation that was used to derive a somewhat realistic model of the wave dynamics present in

rough, open waters is shown in (1).

WaveEquationdKv2

vt2 u x, t C

v2

vx2 u x, t = cos t $sin t

Kv2

vt2 u x, t C

v2

vx2 u x, t = cos t sin t

The initial conditions for the wave equation are defined as:

InitialConditionsd u x, 0 = sin 50$ π$x , u 0, t = sin 0.5$ t C sin 2$t , u 1, t = sin 0.5$ t

C sin 2$t , D2 u x, 0 = 50$π$cos π$x

u 0, t = sin 0.5 t Csin 2 t , u 1, t = sin 0.5 t Csin 2 t , u x, 0 = sin 50 π x ,

D2 u x, 0 = 50 π cos π x

The 3D plot shown below is obtained by solving the equation defined in (1) with the initial conditions in (2).

WaveEquationSolnd pdsolve eval WaveEquation , InitialConditions, numeric, time = t, range = 0

.. 1 :

WaveEquationSoln:-plot3d t = 0.05 .. 20, x = 0 ..1, axes = boxed, orientation = 36, 42 , color = blue,

light = 145, 45, 0, 0, 10

0.0

0.25−260

5 0.5

−16

x10

0.75t

−6

15

1.020

4

14

24


The wave dynamics felt by the Daughter Ship when it is 0.5 m away from the Mother Ship can be seen in the

following plot.

WaveEquationSoln:-plot x = 0.5, t = 0.05 .. 20

t

2 4 6 8 10 12 14 16 18 20

K4

K3

K2

K1

0

1

2

3

According to research, the effects of wind on the wave dynamics defined above can be modeled by Gaussian

white noise.

WindRandomVariable d Statistics RandomVariable Normal 1, 0.15

2:

WindFunction d t/ Statistics Sample WindRandomVariable, 1 1 :WindSignald seq WindFunction t , t = 0.05 ..20, 0.05 :plot seq t, t = 0.05 ..20, 0.05 , WindSignal, title = "Wind Signal"


2 4 6 8 10 12 14 16 18 20

0.3

0.4

0.5

0.6

Wind Signal

The total wave dynamics, which take into account the effects of wind, can be seen below.

WaveDataProcdWaveEquationSoln:-value x = 0.5, t = 0.05 ..20 :

WaveDatadseq rhs WaveDataProc i 3 , i = 0.05 ..20, 0.05

8:

TimeDatad seq i, i = 0.05 ..20, 0.05 :TotalWaved zip x, y /x$ yC0.01 , WaveData, WindSignal :

plot TimeData, TotalWave, title = "Wave Input (wave C wind)"


(3)(3)

2 4 6 8 10 12 14 16 18 20

K0.2

K0.1

0

0.1

0.2

Wave Input (wave + wind)

WaveDynamicsd convert TimeData, Vector column convert TotalWave, Vector column

400 x 2 Matrix

Data Type: anything

Storage: rectangular

Order: Fortran_order


3. Open-Loop Response

As expected, the open-loop response to the system resulted in severe vibrations far surpassing the desired

line tension value.

# Without Controller

WaveWithoutController

Time5 10 15 20

Amplitude

K0.2

K0.1

0

0.1

0.2

Wave Input

OuptutWithoutController

Time

5 10 15 20

Tension N/m

K40000

K30000

K20000

K10000

0

10000

20000

30000

40000

50000

Cable Tension Output

Note: These plots were obtained by simulating the model with the parameter set defined in "OpenLoop.

params" file.


4. Closed-Loop Response

By adding a PID controller, the tension of the line was stabilized at around 70 N/m. The PID gain values were

obtained by tuning the model with a step pulse of 1m.

# With Controller

WaveWithController

Time5 10 15 20

Amplitude

K0.2

K0.1

0

0.1

0.2

Wave Input

OuptutWithController

Time

5 10 15 20

Tension N/m

K20

K10

0

10

20

30

40

50

60

70

Cable Tension Output

Note: These plots were obtained by simulating the model with the parameter set defined in "ClosedLoop.

params" file.


Results

This application illustrates the preliminary design of a controller to stabilize the mooring system of a ship on

the open sea. As mentioned previously, inadequate mooring could severely hamper ship-to-ship transfers of

cargo and other goods. Moreover, in the worst case, it could result in significant, and costly damage, to both

the mother and daughter ships.

Developing a realistic model of the external forces in the form of wind and waves is critical to the design of the

controller. That said, the next step towards improving the control system design is to make improvements on

the disturbance model by including irregular waves from multiple directions, wind gusts, wave drift forces, and

the interaction effects from passing ships. In this application, the wave dynamics are only applied to the

daughter vessel; however, in the future, the wave dynamics should also be applied to the mother vessel.

Legal Notice: © Maplesoft, a division of Waterloo Maple Inc. 2009. Maplesoft and Maple are trademarks of Waterloo Maple Inc. This application may contain errors and Maplesoft is not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact Maplesoft for permission if you wish to use this application in for-profit activities.

Automated design of a ship mooring system - Maplesoft Automated design of a ship mooring system ......

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