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BELL SYSTEM TECHNICAL JOURNAL 



A logarithmic plot of | Fi(aj) | is shown in Fig. 13.* It may be seen that the 

 input signal spectrum fails at 6 db/octa.ve for oj « 0.5, at 12 db/octsive 

 forw = 0.524, and 30 db/octa,ve at co = 2.1. 



Assuming that the permissible dynamic error is 0.3 degree, a comparison 

 will be made between the type 1 and type 3 loop characteristics of the pre- 

 vious section. For the type 1 system, which will have essentially a pure 

 velocity error, (12.1) shows the required value of wo to be 30/0.3 or 100. 



-80 



■100 



04 0.6 08 10 



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Fig. 13 — Target frequency spectrum for constant velocity course. 



Thus ju = 100//co. Figure 14 shows a logarithmic plot of the corresponding 

 I fi |. This characteristic departs rapidly from the shape of input signal 

 spectrum given by Fig. 13, as w is increased above 0.1. 



The type 3 characteristic permits a considerably better match. Choosing 

 a compromise value for wi of 0.1, (12.3) may be used to calculate the neces- 

 sary value of ojo as 415. Thus the loop transmission becomes /z = 

 Al.S/jojijw -f- 0.1). Figure 14 shows a plot of the corresponding |/i|, 

 modified near the gain cross-over to satisfy the stability requirements. 

 This curve is a considerably better average match for the target frequency- 

 spectrum up to o) = 1. The resulting txpe 3 system has a predominant 

 acceleration error as judged from the ma.ximum velocity and acceleration 

 errors of .072 degree and 0.25 degree respectively. 



The total dynamic error curves for the constant-velocity course are given 



* I Fi(ci>) I = T has been taken as the zero db level. 



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