Kaplan, Sargent and Goodman 
supposed to represent the wave-induced vertical force and pitch 
moment due to waves. In addition to the excitations due to random 
waves, various step changes in commanded height were made at 
different times in the trajectory records. 
For the present application, the elevator and flap angles 
were generated in accordance with the transfer function relations 
given in Equations (18) - (20) but their time histories were assumed 
to be known (i.e. as measured input) and hence inserted into the 
identification equation system. This procedure is sensible, and also 
serves to reduce the order of the equations to be treated by a signi- 
ficant amount, thereby reducing the required computation time. In 
the present hydrofoil case the magnitude of the 'noisy'' excitation, 
which was generated by filtering the output of digital random number 
generators, was very small as supplied by the sponsoring agency 
who provided such trajectory data. Thus there was little to ''drive"' 
the system by means of this noise and the identification depended 
upon use of the larger disturbances provided by the commanded step 
changes due to the controls. 
The generated trajectory data used in the identification 
was that of pitch angle @, pitch rate 6 » and the CG heave dis- 
placement h which was obtained from combining signals involving 
the height sensor, pitch angle, etc. As mentioned above, the eleva- 
tor and flap deflection 6, and 46¢ were also used as known input 
data, and all of this trajectory information was sampled every 0.05 
sec. for use in the identification equations. With 10 unknown coef- 
ficients and 4 state variable equations, a total of 210 differential 
equations must be solved for this problem (by use of symmetry 
considerations in the Pj; matrix elements, this can be reduced to 
119 equations). Different runs were made for the trajectories 
representing the same craft, starting with an initial guess for each 
of the 10 unknown parameters. Typical outputs illustrate the man- 
ner in which the various coefficients evolve as functions of time, as 
shown in Figure 8. Those values that appear to approach a limit 
after a period of time are then used as initial values for another run 
with the recorded trajectory data (since the continuous "noisy" 
forcing functions were not sufficiently large to excite the main dy- 
namic responses), and a comparison of the predicted trajectory 
(using the estimated coefficients in the equations) with the recorded 
(i.e. generated) trajectory illustrates how well the estimated para- 
meters produce adequate ''tracking'' of the actual system responses. 
An illustration of these results, where the final values of the es- 
timated parameters are established since they do not change signi- 
ficantly throughout the time period of the experiment, is shown in 
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