Design of an adaptive backstepping controller for auto-berthing a cruise ship under wind loads

International Journal of Naval Architecture and Ocean Engineering.
2014.
Jun,
6(2):
347-360

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial us e, distribution, and reproduction in any medium, provided the original work is properly cited.

- Published : June 30, 2014

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INTRODUCTION

Berthing is the process of positioning and mooring a ship beside a quay, jetty, or floating dock, usually for the purpose of loading or unloading. For large ships such as a container or a cruise ship, berthing is done with the aid of tug boats. When the ship approaches the berthing position, forward tug boats are used to hold the bow to prevent the ship from contacting the quay. Aft tug boats are then used to push the ship towards the quay. If the lateral speed of the ship is higher than the desired speed, the tug boats would be used to retard it. By careful operation of the propellers and rudder, the ship is positioned a few meters away from the quay, and thereafter brought nearer by means of tug boats and mooring ropes. The entire operation is actually very complex and time consuming.
Crabbing is the pure sway motion of a ship without surge velocity, and is induced by a peculiar operation method known as the push-pull mode. The push-pull mode is induced by the combined manipulation of the main propeller and side thrusters. The two propellers are made to generate the same amount of thrust while rotating in opposite directions, thereby exerting a yawing moment on the vessel without inducing longitudinal motion. By the simultaneous operation of the side thrusters, the push-pull mode is implemented, resulting in the generation a large lateral force. When a ship is in the push-pull mode, an interaction force is induced by complex turbulent flow around the ship generated by the propellers and side thrusters. Crabbing is a slow sway motion and can thus be applied to berthing if the ship is equipped with propellers and the thrusters are close to the berthing position. Some requirements for effective crabbing and berthing were presented by
Quadvlieg (1998)
, namely the maintenance of a lateral speed of 0.25(
MATHEMATICAL MODEL

- Overview

The coordinate system used in this study is shown in
Fig. 1
. It consists of the body-fixed coordinate
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- Hull force

The hull force consists of the added mass term, hydrodynamic damping term, and restoring term. The added mass is the pressure-induced force due to the motion of the ship, and it is proportional to the acceleration. The restoring term is the hydrostatic force due to the weight and buoyancy of the ship, and does not have a horizontal component. The added mass is determined by the empirical formula of
Motora (1959)
. The hydrodynamic damping is produced by the wave, drag, and vortex shedding effect. During the crabbing motion for berthing, the surge velocity is nearly zero and the sway velocity is increased by the side thrusters and propellers in the push-pull mode. The sway velocity is also very small, which makes the wave-making damping effect negligible. The inclusion of these terms in a mathematical model for predicting the lateral force affords greater accuracy than the conventional model. A static sway test, dynamic sway test, static yaw test, and dynamic yaw test without forward speed were conducted by
Yoo (2006)
and the results were used to develop a mathematical model of the force acting on the hull during crabbing. The equations of the model are as follows:
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- Propeller force

The thrust of the propeller is a function of its thrust coefficient, rotational speed, and diameter. The sign function is adopted to consider the direction of the thrust of the propeller:
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- Side thruster force

The side thruster is used when the rudder is incapable of generating sufficient lateral force and yaw moment at low speeds. In the push-pull mode, the propellers produce a large yaw moment, and the side thruster is therefore used to compensate for the yaw moment. The thrust of the thruster is a function of its thrust coefficient, rotational speed, and diameter. The direction of the thrust of the side thruster during berthing is different from that during unberthing; hence, a sign function is adopted:
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- Interacting force

In the push-pull mode, the fluid particles accelerated by the reverse rotation of the propeller impact the stern of the ship, whereas those accelerated by the side thruster change the flow field on the lateral side of the ship.
Quadvlieg (2011)
conducted a push-pull mode model test and observed a difference between the measured force and the sum of the forces of the propeller and the side thruster. The difference is defined as the interaction force, which is expressed as follows:
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- Wind force

The wind force is considered as an environmental disturbance. The wind force is considered in the berthing problem because it has been suggested that the requirements for effective berthing are dependent on the wind conditions
Quadvlieg (1998)
. The equations of the wind force can be obtained as expressed by Eq. (10).
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CONTROLLER DESIGN

A backstepping controller can deal with the system nonlinearity of the berthing maneuver. An adaptive controller can also be used to compensate for the unknown disturbance. Based on the work of
Fossen (1994)
, an adaptive backstepping controller for the vector system is designed in this section.
- Adaptive backstepping controller

Three degrees of freedom nonlinear equations of the planar motion can be expressed as
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- Control allocation

The determined control force vector is allocated to the propellers and side thrusters. The rudder is incapable of generating sufficient lateral force and yaw moment during crabbing and is therefore excluded from the control allocation. The relationship between the control force vector and the thruster forces can be expressed as follows:
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- Reference model

A reference model is used to prevent wastage of control effort as a result of excessive position error in the initial phase. In this study, a second order dynamic system is established for use in referencing the model dynamics. The reference model dynamics can thus be written as
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SIMULATIONS

A cruise ship equipped with twin propellers and two side thrusters is used for the simulation. The principal dimensions of the ship are given in
Table 1
.
Principal dimensions of cruise ship.

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Components of control gain matrices.

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- Performance criteria 1

The simulation of crabbing in wind is used to check whether the cruise ship satisfies performance criteria 1 given by Hooren (1985), namely that a lateral speed of 0.25
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- Performance criteria 2

The simulation of auto-berthing in wind is used to verify whether the ship satisfies performance criterion 2, namely the ability to berth and unberth under a wind speed corresponding to Beaufort 7 without the aid of tug boats. The initial position vector of the ship is [0
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- Auto-unberthing simulation

The simulation of auto-unberthing is used to verify the control allocation algorithm. If the control allocation is not designed properly, inappropriate results may be obtained depending on the direction of the lateral motion. The wind condition is the same as that of scenario 2. The initial position vector and initial reference model position vector are both [0
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CONCLUSIONS

The equations of the crabbing maneuver of a ship were derived in this paper. The hull force, propeller force, side thruster force, interaction force, and wind force were considered as external forces acting on the ship. Because crabbing is an extremely low speed maneuver, the rudder was excluded from the control algorithm. Errors may be present in the model of the interaction force and the wind force of actual berthing. The interaction and wind forces were thus defined as uncertainty terms in the design of the controller. The terms were estimated by the adaptive law and compensated for by a control input. The other terms were controlled by the backstepping control method. The results of auto-berthing simulations that were performed to verify the derived control law confirmed the effectiveness of the designed controller.
Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2012R1A1A2008633).

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Citing 'Design of an adaptive backstepping controller for auto-berthing a cruise ship under wind loads
'

@article{ E1JSE6_2014_v6n2_347}
,title={Design of an adaptive backstepping controller for auto-berthing a cruise ship under wind loads}
,volume={2}
, url={http://dx.doi.org/10.2478/IJNAOE-2013-0184}, DOI={10.2478/IJNAOE-2013-0184}
, number= {2}
, journal={International Journal of Naval Architecture and Ocean Engineering}
, publisher={The Society of Naval Architects of Korea}
, author={Park, Jong-Yong
and
Kim, Nakwan}
, year={2014}
, month={Jun}