442 REGULATORY CIRCUITS 



8-28 STATIC AND DYNAMIC CONTROL LOOP ERRORS 



Perhaps the largest errors in the search-pattern stabilization are engen- 

 dered in the antenna control loops. These errors are reduced to satisfactory 

 limits by proper design of the control-loop gains and bandwidths or by 

 modification of the pattern command signals. Errors to be considered are: 

 (a) Static or steady-state errors due to aircraft motion 

 (i>) Static or steady-state errors due to search-pattern velocity 

 (c) Dynamic ierrors due to changes in search-pattern command signals 

 It may be considered that part of the total allowable search-pattern 

 errors may be allotted to the antenna control loops. For example, a 0.35° 

 steady-state error may be assumed and it may be divided equally between 

 aircraft motion and search-pattern velocity signals; i.e., the allowable error 

 contribution of each source is 0.25°.^^ 



To provide a means for translating the error requirements into a design 

 specification, a generic form muse be assumed for the search stabilization 

 and drive system transfer function. For the example to follow, the assumed 

 open-loop transfer function will have the form 



COl < Wo < CO3. lO-->^j 



s{\ + si^^){\ + .syco,,) 



The following analysis will demonstrate how the values of Ki,, wi, 0^2, and 

 C03 can be chosen to meet a set of system requirements. 



Aircraft Motion Errors. To reduce the steady-state errors caused by 

 aircraft motion to 0.25°, the nature of the aircraft motion must be known. 

 For example. Table 8-3 shows the amount of antenna movement that would 

 take place at large lead angles if the antenna were not stabilized. The 

 search stabilization loop generates position command signals which — if 

 computed correctly — are equal and opposite to the disturbance caused by 

 aircraft motion. However, the control loops that drive the antenna with 

 respect to the aircraft have finite gain and bandpass. Thus, the actual 

 position of the antenna will tend to lag the stabilization commands. As 

 shown in Fig. 8-30, the amount of lag depends upon the frequency and 

 magnitude of the input relative .to the open loop gain of the stabilization 

 loop at the input frequency. In order that the lag be kept below 0.25° at 

 all input frequencies, the minimum loop gain must be 



error specification 0.25- 



As an example, the input at 1.04 rad/sec is 33.6° peak-to-peak or Xi = 

 16.8°. Thus, the required open-loop gain of/= 1.04 is 67.2. Similar 



22Since aircraft motion is independent of the search pattern, the individual errors may be 

 added by taking the square root of the sum of the squares. 



