464 REGULATORY CIRCUITS 



A simplified block diagram of this positive feedback loop is shown in 

 Fig. 8-41. Since the gains of the autopilot, aircraft, and computer are 

 determined by the performance specifications, only one gain element in the 

 loop may be readily adjusted. This gain, or attenuation, from Aql to Atl 

 in Fig. 8-41 is the required stabilization loop attenuation Ks. If the gain 

 of the coupling loop is represented by KsGcl (where Gcl is the overall 

 characteristic of the' computer, autopilot, and aircraft) as indicated in 

 Fig. 8-41, the stabilization loop attenuation becomes 



l^sl < ,^- (8-45) 



|G, 



CL\ 



Since |Gcz,| is a function of frequency, \Ks\ may be determined as a 

 frequency function. 



Unfortunately, however, Gcl is not easily determined analytically.^* It 

 varies as a function of antenna elevation and azimuth angles as well as 

 the aircraft roll, pitch, and yaw angles in space because it involves the 

 conversion of three aircraft coordinates of motion into two antenna coordi- 

 nates including the dynamics of coordinated aircraft turns. Although the 

 magnitude of \Gcl\ may be estimated or approximated for various operating 

 conditions, the maximum value may be most easily and accurately found 

 using analog computer simulation. Of course, the magnitude of |i^s| should 

 provide adequate attenuation for the largest magnitudes of Gcl that are 

 likely to be encountered under normal operating conditions. In high- 

 performance autopilot systems, especially missiles, the necessary stabili- 

 zation loop accuracy or attenuation may be greater than that derived by 

 the criteria for manually controlled aircraft. 



8-33 DYNAMIC STABILITY REQUIREMENTS ON ANGLE 

 TRACK STABILIZATION 



In order to provide the necessary antenna isolation from aircraft motion, 

 the stabilization loop must have an attenuation characteristic similar to 

 that shown in Fig. 8-39. It must be stable, and it must provide a smooth, 

 constant antenna rate for a constant voltage input. Although it might be 

 desirable to have a transient response with negligible overshoot similar to 

 that produced by a critically damped quadratic system, this is not always 

 necessary or even possible in some cases. It is more important to achieve 

 the required attenuation characteristic even with some sacrifice in stability 

 margin. 



''^This function is not as complex in a cruciform missile configurat ion as it is in a conventional 

 aircraft which must roil to turn. 



