648 BELL SYSTEXf TECHNICAL JOURNAL 



For CO small compared with ccm , (21) becomes 



- (loop closed) c^ . ,„ , =-. , (w « com). 



E^ ^ MR + fxoRt) 



If the tachometer feedback is substantial (col » w„), this may be further 

 approximated as 



i (loop closed) ^J-, ( ^, f^'^^ ) . (21.2) 



and the corner frequency becomes 



/ HfsRt /" ' ^^^ . ^ 



COm ^=^ — f- 5 \^rn ^^ U>m) ' 



Thus for reasonably high feedback, the over-all transfer ratio (21.2) 

 depends only upon the tachometer characteristic, being substantially inde- 

 pendent of changes in the original mechanical resistance R or the amplifier- 

 motor factor MO- The corner frequency coL is similarly independent of 

 changes in R, although still a direct function of mo . Thus the principal 

 non-Unearity of two-phase induction motors, namely variation in electrical 

 damping with speed, is effectively suppressed by this type of local feed- 

 back, and systems employing such motors up to 80% of their synchronous 

 speed may be designed on a linear basis. 



The increase in mechanical impedance due to the feedback may be shown 

 by assuming a torque disturbance T applied at the output shaft. Without 

 feedback, the resulting speed disturbance is 



T T 



e (loop open) = -5- = p , • r • 



With feedback, the corresponding shaft speed disturbance becomes 



T \ 



6 (loop closed) = 7^ • ~ — , 



Zm I — firPT 



R -f fioRt + jioJ 



Thus the apparent mechanical resistance, and therefore the protec- 

 tion against frictional torques, has been multiplied by a factor 

 (1 + fJioRt/R) = ccL/wm . If the motor-drive system with tachometer feed- 

 back is employed in a simple follow-up system of the type of Fig. 5, 

 equation (16.3) shows that the resulting low-frequency output-shaft stiffness 

 will be o}o{R + noRt) or (col/co™)coo2?.^- Therefore the output stiffness has 

 ^^ The low-frequency loop transmission of the follow-up loop is again taken to be uo/joi. 



