Dynamics of Naval Craft - System Identtficattion 
x, (0) = 1, and the estimated initial condition for x, and x, are 
x, (0). = 0; xy (Gy.= "0 (39) 
The rapid convergence of X57 x , and the value of x4 to the true 
value of a> = 0.3, ina time period of about 10 sec., shows an effec- 
tive technique for this simple case. 
The results obtained here indicate that the technique ap- 
plied to these test cases can provide valid parameter estimates ina 
relatively short computation time, and that performance is working 
properly. Similar performance using analog computers for the same 
type of problems, including noisy forcing functions, was shown by 
the results in [14] , and hence the present system identification 
technique is applicable to the case of naval craft in waves. 
No noisy forcing functions were applied in these test cases 
for the exercise of a digital computer program because of the exten- 
sive effort required to produce a forcing function (by digital means) 
within a prescribed bandwidth for the representative test systems, 
This is an important requirement for system identification, i.e. a 
proper input signal that would excite the system adequately, and that 
is obviously related to the effective response bandwidth of the system. 
In order to gain some insight into the effect of the forcing function 
bandwidth, some experiments were made with the simple second 
order system given by Equation (35) that was treated above. The 
forcing function in that case was obtained from a random number 
generator. With the sampling and integration step at every 0.01 
seconds, it was found that the identification would not be achieved in 
that case. The system never settled toward a convergent situation, 
and this was ascribed to the relatively high frequency of the forcing 
function relative to the system bandwidth. Thus it appears that, in 
any identification procedure, the excitation should not be unrealistic 
in comparison to the expected range of frequencies of the forcing 
functions for the system to be identified. This is a general guideline 
for all identification studies, and should be considered for various 
simulation procedures in generating actual data.Since the occurrences 
in nature for various systems often have natural limits consistent 
with system behavior, there does not appear to be a severe problem 
in that (more realistic) case. 
For the case of an SES craft, the basic linearized mathem- 
atical model for vertical plane motion is given by 
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