LINEAR SERVO THEORY 



641 



and the apparent low-frequency stiffness is oiaR, being the ratio of the 

 mechanical resistance to the velocity error coefficient. It may be noted 

 that the static error will vanish if the loop transmission approaches infinity 

 more rapidly than 1/w as co approaches zero. 



3.4 Cofnparison of n Characteristics for a Particular Input Signal 



In order to illustrate the advantages of shaping the loop characteristic 

 for a particular input signal, a brief discussion will be given of the design of 

 an automatic radar loop to track an airplane in azimuth over a constant 

 linear- velocity course. The servo configuration is that given by Fig. 5b, 

 di being the azimuth angle of the target and 6-2 the corresponding antenna 

 angle. The lobing radar antenna has been assumed to take the place of the 



Fig. 12 — .\zimuth angle for constant linear velocity course. 



synchro pair. Thus /3 = — 1, and an error signal proportional to ^i — Oz is 

 developed." 



Assuming a constant linear-velocity course having a ma.\imum azimuth 

 rate of 30 degrees/sec, the target azimuth angle is given by '^^ 



di{t) = tan-' .524/, (17) 



which is plotted in Fig. 12. 



This course will develop a maximum azimuth acceleration di of ±10.3 

 degrees/sec^ and a maximum di of -16.4 degrees/secl The continuous 

 frequency spectrum of di{t) may be found from (10.1) to be 



Fi(u) = T 



-1.9lul 



J'^ 



(18) 



?fi Assuming a low elevation course. . , • j . ■ ^ c 



2«The azimuth angle has been so taken that zero azimuth is obtained at the point ot 

 nearest approach. 



