Kaplan 



In a complete simulation study of the resultant motion of a 

 ship in which a dynamic positioning system is to be installed, all 

 three degrees of freedom (surge, sway and yaw) will be coupled and 

 the forces and moments will be dependent upon the relative orienta- 

 tion with respect to the incident wave system. This will be a some- 

 what complicated analysis, but the tools are generally available for 

 determining the various hydrodynaxnic parameters entering into such 

 a study. It will also be necessary to consider the type of signal 

 system that would inciate the position errors of the ship, together 

 with a signal processing operation (i.e. control system design) that 

 will be necessary in order to achieve the desired type of operation. 

 Similarly, some estimate of the response time of the thruster force 

 development must be included in determining ship response so that 

 a nneasure of positioning accuracy can be obtained as a result of the 

 analysis. 



In view of the complexity of this problem, a discussion of a 

 simple application will be given for the case of sway motion alone in 

 beam seas. In that case the equation of motion will be similar to 

 that given in Eq. (137), without the presence of the linear spring 

 term (that was due to the mooring in the previous case). The 

 response due to the linear wave forces will be generally the same for 

 this case as in the case of the moored ship, as shown in Fig. 15. 

 However, the effect of the drift forces will cause the ship to continu- 

 ally deviate in position within a very short time. The deviation will 

 be almost a quadratic growth with time since the response is similar 

 to that of a constant force acting on a system primarily represented 

 as a pure second derivative dynamic response. Thus a control force 

 is necessary, and the control rule should include terms proportional 

 to sway displacement and velocity, i.e. the control force will be of 

 the form 



Yc = - C,(y-yo) - Cgy (139) 



where y represents the lateral error displacement relative to the 

 desired position, y^, and this control force is Included in the basic 

 equation 



(m + A^S + V = Ywaves + Y,,,, + Y^ . (140) 



The lateral position error, which can be obtained from an 

 acoustic reference system placed on the ocean bottom, will contain 

 the Influence of the higher frequency response due to the linear wave 

 forces and in addition the control signal that Includes the lateral 

 velocity error will contain more "noise" In the resulting control 

 signal. This can be overcome by the inclusion of appropriate filter 

 circuits associated with the control signal processing, which Involves 

 the use of standard servomechanlsna techniques within the state-of- 

 the-art of control design. A closed loop feedback system using the 



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