486 AUTOMATIC TRACKING CIRCUITS 



The corner frequency C03 is used to attenuate high frequency noise and 

 resonances. It is usually about three times greater than co^." 



It is the choice and physical realization of K^, co, coi, coz, and C03 that 

 constitute the tracking loop design and the consequent compromises. In 

 particular, K^, coi, and C02 determine the system tracking errors, and as 

 mentioned earlier, the errors which result from the design compromises may 

 be divided into two categories: random and bias errors. The relationship 

 between these errors and the track loop design parameters are discussed 

 in the next paragraphs. 



9-7 ANGLE TRACKING LOOP RATE ERRORS 



Usually the most important signals to be measured in the track loop are 

 the antenna rate signals, and the errors in these signals will be considered 

 first. 



Random Errors. The components of the random errors in the rate 

 signal and the methods of computing them are shown in Fig. 9-5. 



The principal random errors are caused {a) by gyro inaccuracies eg which 

 are assumed to be proportional to the rate being measured, {b) by the radar 

 noise e^ transmitted through the tracking loop to the gyro output, and {c) 

 by the antenna rates e^ caused by the platform motion which is attenuated 

 by the stabilization loop as discussed in Chapter 8. 



The gyro error is a function of the gyro construction. For a particular 

 gyro, this error is fixed; it cannot be influenced by the tracking loop design. 

 The noise in the filtered rate signal c„ is calculated as shown in Fig. 9-5. 

 It is a function of the track loop parameters C02 and coc,^^ the rate filter 

 corner w/r,'^ and the noise power density parameters oj, and co,,- 



The random rate error caused by platform motion e^ was discussed in 

 Chapter 8. Because it is the noise component most easily attenuated and 

 controlled by loop design, its allowable design value is derived from the 

 specified total rate error and the sums of the squares of the other two 

 principal errors as shown in the figure. 



Although a tracking loop bandwidth much lower than the 6.28 rad/sec 

 (1 cps) shown could be tolerated without making the steady-state bias 

 unduly large, it is usually not made much less because the system errors 

 caused by sudden input changes would be excessive for relatively long 

 periods of time. 



"A definite ratio can be determined by using approximate design equations relating gain, 

 phase, and frequency as shown in Chapter 8 where the search and stabilization loop charac- 

 teristics are derived. 



12/C„ is not an important parameter in these calculations if it is much larger than wc- 

 i^A simple lag corner is assumed here, but more complex filters may be used. 



