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BELL SYSTEM TECHNICAL JOURNAL 



in Fig. 15. The velocity error of the type 1 system is always a lagging error 

 and is maximum at the point of nearest approach. The type 3 composite 

 of velocity and acceleration errors is lagging over about the first half of the 

 course and leading for the second half, having lead and lag maxima at points 

 closely grouped about the point of nearest approach. 



Although the two loop characteristics develop the same maximum dy- 

 namic error on the specified target course, their transient responses to an 

 input step differ widely, as may be seen from Fig. 16. The rise time for the 

 type 1 loop is about .03 second compared with an initial rise in 0.17 second 



1.2 



0.8 



> 0.6 



0.3 0.4 0.5 



TIME IN SECONDS - 



Fig. 16 — -Transient response of tracking servos. 



for the type 3 system. Also, because of the overshoot the type 3 system 

 requires about 0.7 second to settle within 5% of the equilibrium value. 



For a final comparison of the two systems the corresponding transfer 

 characteristics, y./{\ + n), are plotted in Fig. 17 on arithmetic amplitude 

 and frequency scales. It may be seen that the type 1 system is vulnerable 

 to noise and interfering signals over a far wider frequency range than the 

 type 3. Again assuming uniform input noise versus frequency, (14) may 

 be used to show that the ratio of output noise power for the two systems is 

 about 7.5:1. 



Thus the luxury of crisp transient response as obtained with the type 1 

 system may demand a heavy penalty in terms of output fluctuations due to 

 noise and other unwanted signal variations. This is a clear illustration of 



