8-32] ACCURACY REQUIREMENTS ON ANGLE TRACK STABILIZATION 459 



The problem now is to compute the stabilization loop attenuation Ks as 

 a function of frequency needed to achieve these levels of performance. 

 Table 8-3 will be used to provide aircraft input data. 



For the low-frequency (less than 2 rad) inputs 



where 0.7 Atl is the rms value of the sinusoidal inputs from Table 8-3, for 

 example, at co = 1.04, Jtl = 35/2 = 17.5°/sec and Kg < 0.00245'. 

 However, for the high-frequency inputs, the effects of filtering and error 

 sensitivity as a function of angular rate must be taken into account to 

 ascertain the amount of stabilization attenuation needed. The basic 

 expression may be written 



(J.1Atl\S^) {deHc/oATL)^f 



where dene Id At l = sensitivity of computed error signal to angular rate 

 inputs 



Gf = rate noise filter characteristic. 



From Table 2-3 the value of the angular rate sensitivity factor at the time 

 of firing on a head-on course is 14.2. 



If a 0.5-second filter is used, all sinusoidal signals above 3 rad /sec passing 

 through it are attenuated by a factor co//cos, where cos is any signal frequency 

 and CO/ is the filter corner frequency equal to 2 rad /sec. 



Therefore, if Kl is assumed to be equal to 1.25° rms for sinusoidal 

 frequencies and Gf equal to co//co£) for disturbance frequencies greater than 

 3 rad /sec, 



L25 ^ 0.125 



^' ^ (0.7)(^tl)(14.2)(co//co^) ~ Wcoz>)^rL' ^^'^^^ 



However, for sinusoidal motion Atl = Atl^d and 



,, . 0.125 0.0625 

 -'^'S S — -J— = —2 — 



Wf/lTL ^TL 



(8-44) 



Using the values for Atl in Table 8-3, the desired Ks is given in the 

 following table as a function of frequency. 



A plot of Ks is shown in Fig. 8-39. This is the minimum attenuation that 

 must be provided by the stabilization loop if rate signal errors caused by 

 aircraft motion are to be maintained below acceptable levels on the pilot's 

 indicator. The isolation required for the low-frequency inputs is also 

 indicated. The design of the stabilization loop characteristics to achieve 

 this attenuation is described in Paragraph 8-33. 



