458 REGULATORY CIRCUITS 



defined from a specified system error, the allowable miss distance, or hit 

 probability density.^" Actually, for an autopilot system, the criterion 

 involving the magnitude of the rate error due to aircraft motion may be less 

 important than a criterion concerning the amount of attenuation needed 

 from the stabilization loop to prevent system instability through the 

 coupling between the rate commands, autopilot, aircraft, and antenna. 



In the case of manual control of the aircraft flight path, the specification 

 of the allowable stabilization error is governed by the following basic 

 observations. 



(1) The stabilization error may be considered as a random error in the 

 measurement of angular rate. Thus the low-frequency component of the 

 stabilization error must be compatible with the specification for angular 

 rate measurement accuracy to avoid inaccuracies in the fire-control compu- 

 tation. 



(2) The high-frequency components of the stabilization error (greater 

 than 1—2 rad/sec) do not affect the fire-control problem directly because 

 the aircraft heading cannot change this rapidly. However, they do increase 

 the apparent amount of noise on the steering indication, and this does 

 degrade the pilot's ability to fly an accurate course (see Paragraph 12-7).'*^ 

 This degradation is proportional to the rms contribution of stabilization 

 error to the total apparent noise appearing on the pilot's indicator. 



An example using the basic AI radar problem presented in Chapter 2 is 

 informative in illustrating how these principles might be applied. The 

 applicable specification for the azimuth and elevation channels are (see 

 Paragraph 2-27) : 



Allowable random error in rate measurement 0.11° /sec rms 



Allowable magnitude of indicator noise 1° rms 



Allowable filtering 0.5 second. 



For purposes of analysis, we will assume that the contributions of the 

 stabilization error should be limited to the following: 



[Low frequency rate measurement] 7^ ^ ^ ^^n / 

 , , ... . \ Kl< 0.03 /sec rms 



error due to stabilization errors J 



[Indicator noise due to high 1 ,. ^ ■, ^ro / 

 c 1 -r • Al S 1.25 /sec rms 



frequency stabilization errors] 



''"For a detailed discussion of this problem see "Control System Optimization to Achieve 

 Maximum Hit or Accuracy Probability Density" by G. S. Axelby, Wescon Record of the IRE, 

 1957. 



''^The fact that the stabilization errors are actually correlated with the pilot-induced motions 

 does not seem to be important (as it is for autopilot applications where the correlation results 

 in degradation of system stability). Thus for analysis of manually flown systems, the rms 

 stabilization error must be combined with the rms noise errors from other sources to produce 

 an equivalent noise error. 



