9-6] TRACKING LOOP DESIGN 485 



of the peak transient errors will be maintained within acceptable levels. 

 The bandwidth specification will also affect the magnitude of the noise 

 in the output of the control loops. 



9-6 TRACKING LOOP DESIGN 



Solutions to most engineering problems are obtained as a result of 

 compromising between ideal but conflicting characteristics. The angle 

 track loop design problem is no exception. It would be desirable to have a 

 fast, accurate loop to keep the antenna pointed at the target during any 

 target or antenna platform motion in space. On the other hand, it is 

 necessary to have a relatively slow tracking system which will not respond 

 to the noise inherent in the radar receiver. A perfect solution to the problem 

 cannot be obtained; compromises are necessary: the fast loop response 

 needed to reduce antenna platform motion is obtained with a stabilization 

 loop, as discussed in Chapter 8, and a slow tracking loop is designed to 

 provide noise filtering without causing large dynamic errors while tracking 

 a moving target. 



The general configuration of the track loop was discussed and shown in 

 Fig. 9-4. The bandwidth may be expressed in several ways, ^° but in this 

 paragraph, it is the frequency coc in Fig. 9-4, where the open loop gain 

 magnitude is unity. Usually this is the same as the asymptotic gain plot 

 at unity gain. The velocity constant K^, reduces steady-state errors caused 

 by constant velocity inputs. Theoretically, it may be as large as desired, 

 but practically, it is usually between 100 and 500 sec~^ because higher gains 

 cause amplifier saturation during transients, and the resulting time response 

 is not satisfactory unless nonlinear networks are used. 



The corner frequency coi is used to reduce the high gain rapidly at higher 

 frequencies to realize a relatively low bandwidth. This is sometimes a 

 double corner to reduce the gain more rapidly as the frequency increases, 

 but the additional complexity is not often warranted. 



The lead corner frequency co2 is needed to provide stability or damping 

 for the tracking loop. The frequency is usually one-half to one-fifth of Wc. 

 If it is too low, the bandwidth will be excessive for the same low-frequency 

 gain; and although there will be little overshoot in the response to a step 

 input, the loop will not reach its steady-state operating levels very rapidly. 

 On the other hand, as co2 approaches ooc, the overshoot to a step input will 

 become undesirably large. An optimum choice for co2 is discussed in the 

 next paragraph. 



i"Other ways of expressing bandwidth: (a) The frequency where the phase angle of the 

 closed loop is 60°, (i) the frequency where the maximum value of the closed-loop response 

 occurs, (c) the frequency where the closed-loop response returns to unity, and (d) the frequency 

 where the closed-loop response is —3 db. 



