Fig。 1。 A barge ship with a mooring winch system。

Fig。 3。 A schematics of mooring system for dynamic analysis with active cable。

mi  (i 1,。。。, p) : Particle mass of cable

ki (i 1,。。。, p) : Spring coefficient of each particle mass

di (i 1,。。。, p) : Damping coefficient of each particle mass

xi  (i 1,。。。, p) : Displacement of each particle mass。

The dynamic equations of the controlled system shown in Fig。 3 are described as follows:

Fig。 2。 Schematic diagram of a simplified mooring winch system。

Finally,  a  controller  is  designed  that  controls  the  mooring

winch system, and the effectiveness of the proposed method and the newly designed controller is tested through simula- tions and experiments。

2。 A basic model and system description

In this section, a vessel motion control system is designed by considering various cable motions。 Generally, the vessels with a mooring system have several winches on them。 For example, on the barge ship shown in Fig。 1 (10,000 [ton] class), 16 winches are installed。 The numbers of winches in- stalled depends on the vessel capacity。

For convenience, a mooring system with a single winch is considered as shown in Fig。 2 because it is possible to extend the result obtained from this study to the general mooring system。 Here, we assume that a single winch is installed on the right side (active cable) of the vessel and the cable on the op- posite side (passive cable) is just anchored to the seabed with- out a winch。 It means that the vessel is moved on the horizon- tal plane and controlled by a single winch operation。 Fig。 3 depicts a schematic diagram of the controlled system。

The parameters shown in Fig。 3 are defined as:

Ms  : Mass of the vessel

Ks : Spring coefficient

Ds  : Damping coefficient

x : Displacement of the vessel from the initial point

f : Input force to the vessel (disturbance force is included)

where Eq。 (1) describes the vessel dynamic equation and    Eq。

(2) is the active cable dynamics。 However, in Eq。 (1), the force is given as f fw fd , where, fw is the winding force of the winch and  fd is the cable tension variation due to winding and

unwinding of the winch。 Especially in fd , the environmental disturbance (wave and wind) forces are also included。

This description of the modeling method may be applied to the vessel motion analysis。 One of the problems in this ap- proach is that the dynamic characteristics depend on the pa- rameter definition process or methods。 Thus, the analyzing process becomes too complicated and difficult to be used as a practical approach。

Here, we introduce a useful control system design approach where the complex and precise cable model is not needed。 The proposed approach to identify the cable dynamics is summa- rized as follows:

(1st) setting the cable as a black box。

(2nd) winding and unwinding the winch in the considerable operating conditions (also changing the cable length)。

(3rd) measuring the cable tension variations using load cells installed on both end points of cable。

(4th)  analyzing  the frequency responses  of  tension  varia-

tions。

(5th) define the tension variations as the uncertainty。

(6th) design of a controller based on robust control theory。

3。 Modeling with experiment

3。1 Modeling strategy

First, we pide the controlled system into two parts: the vessel and the winch with cables, and then construct a model for the vessel and for the winch with cables, respectively。