LINEAR SERVO THEORY 639 



Again for the rapidly converging case, this system will have principally an 

 acctleration error. 



Type 3. —6, —12 db/octaie, fj, = ojocci/juiju + coi) 



This is perhaps the most commonly encountered characteristic in simple 

 servos. The corresponding error expansion is 



A(/) = -/i(0 + -^ /;(/) - -^- MO , (0)0 » coi). (12.3) 



and the principal error for this type system thus is a combination of velocity 

 and acceleration components. Either the velocity or the acceleration error 

 component may be predominant, depending upon the various parameters. 



3.3 Noise E,rrors 



The typical sinusoidal component of servo error due to noise (unwanted 

 signals or irregularities) in the input signal may be written as* 



A„ = -^ N, (13) 



1 + M 



where N represents the corresponding sinusoidal component of the input 

 noise. If the noise signal n{t) is known, the total noise error A„(/) may be 

 calculated from (13) in the ways described for the dynamic error. How- 

 ever, the noise input is seldom known in this sense, although certain out- 

 standing components sometimes may be estimated and their effects evalu- 

 ated. On the other hand the average disturbance due to random input 

 noise, of the kind described as "thermal noise" in electrical circuits, may 

 easily be calculated. This type of noise has constant amplitude versus 

 frequency, and the total power in the output noise error may be found from 



2 



Pn 





1+M 



do:, (14) 



where K is a. constant dependent upon the input noise power. 



Input noise also causes overloading of the power amplifier and overheat- 

 ing of the motor. These effects are aggravated by the falling transfer 

 characteristic versus frequency of the motor, as seen from the following dis- 

 cussion. The servo transfer characteristic is maintained approximately 

 at unity out to the cross-over frequency. However the transfer ratio of 

 the motor, equation (3.1), will be falling at least at 6 db/octa.\'e, usually 

 at 12 db/ociave, at frequencies below this point.-' Thus the transfer 



* Again assuming /3 = —1. 



23 Assuming that the mechanical load impedance is a series combination of resistance 

 and inertia. 



