Page 871 - Mechanical Engineers' Handbook (Volume 2)

862 Mechatronics

Now, since
Ki t in (100)
in
substituting (100) into (99) yields
Ki I a ¨ KL 2

m
t
in
N 2 I m N 2 m (101)
Substituting (101) into (91) yields
V L I a ¨ KL 2
R I a ¨ KL 2
1
1
d
¨

in
m
m
dt K t N 2 I m N 2 m K t N 2 I m N 2 m
˙
K (102)
e motor
This differential equation relates to V . The Laplace transform can be used to obtain
m
in
the transfer function:
Output (s)
m
(103)
Input V (s)
in
Also, substituting (1/N) yields T(s) (s)/V (s).
a
m
a
in
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