Page 104 - Modern Control Systems

78 Chapter 2 Mathematical Models of Systems

Table 2.5 Continued
Element or System G(s)

10. Gear train, rotational transformer
Gear I

Gear ratio = « = —

Gear 2
11. Potentiometer, voltage control

V 2 (J) = R 2 m R 2
Vi(s) R R^ + R 2
+ o-
R 2 _ e
V x(s) Rf* ° + R #«ax
R
2 V->(.v)

12. Potentiometer, error detector bridge
0-, V 2(s) = /:,,(0,(5)-02(5))
V 2(s) = Merror(^)
^Battery
* . -
"ma x
voltage
13. Tachometer, velocity sensor

V 2(s) = *,«(*) = #,s0(.y)
Shaft
C iv, = constant
*
0U), o>(.?)

14. DC amplifier
V\{S) ST + 1
- output resistance
R Q
C Q = output capacitance
T = R aC„,T « IS
and is often negligible for
controller amplifier
(continued)