Page 608 - Mechanical Engineers' Handbook (Volume 2)

10 Steady-State and Dynamic Behavior of Servoactuators and Servosystems 599

Figure 42 Coulomb friction characteristic.

in gaining an understanding of the general behavior of a system and the sensitivity of the
performance to parameter changes.
Equations (67)–(72) can be linearized by assuming small variations of all variables about
an initial steady-state operating point. For the system considered here, the linearized dynamic
model in the Laplace domain is given by
(s) G (s) V (s) G (s) T (s) (73)
i
1
m
2
e
where the transfer functions G (s) and G (s) are
2
1
KK
G (s) a T (74)
1
RB ( s 1)( s 1) KK
at e m T E
(R /n( s 1)
G (s) a e (75)
2
RB ( s 1)( s 1) KK E
T
e
m
at
and where
L J
a t
e
R a m B t
J B
J J L B B L
m
t
n 2 t m n 2
A block diagram of Eq. (73) is given in Fig. 43.
In most cases the mechanical time constant ( ) is much greater than the electrical time
m
constant ( ). In this case, the transfer functions of Eqs. (74) and (75) simplify to first-order
e
forms as follows:
K
G (s) 1 (76)
1
s 1
1
K
G (s) 2 (77)
2
s 1
2
where