Page 611 - Mechanical Engineers' Handbook (Volume 2)

602 Servoactuators for Closed-Loop Control

10.2 Electromechanical Servosystems
Only servosystems including dc servomotors are considered here. The reader should consult
Ref. 41 for a more comprehensive treatment of other types of electromechanical servosys-
tems.
Figure 44 shows a closed-loop servosystem that utilizes tachometer feedback around the
servoactuator discussed in the previous section. Through the use of velocity feedback, greater
accuracy can be achieved than with the open-loop system.

Mathematical Models
An approximate linearized model may be derived for the servosystem by combining the
open-loop system model [Eq. (73)] with the following equations:
Summation:
v v ref v ƒ (89)
i
Tachometer:
v K (90)
tm
ƒ
Amplifier:
v K v (91)
a
a i
Equation (90) assumes that the tachometer is mounted directly on the motor shaft, which is
normally the case. Reference 18 discusses cases where the tachometer is mounted in other
configurations. Also, Ref. 18 presents more accurate tachometer models to account for the
magnetic coupling of the tachometer to the motor field. The basic form of the tachometer
model in that case is that of a high-pass filter with a phase shift that is dependent on the
angular orientation of the tachometer to the motor.
Equations (73), (89), (90), and (91) may be combined to obtain the following closed-
loop servosystem model:
(s) G (s) V (s) G (s) T (s) (92)
4
e
i
m
3
where

Figure 44 Electromechanical servosystem with velocity feedback.