mT K, i-Bep)Kinductance, Lm, is low comparedUsually theto the resistance, Rm, and can be neglected. Also assume friction in the motor bearings can be neglected (B= 0). Assume theinertia, J, includes the motor armature inertia, Jm, and the load inertia, Ji,. Simplify the transfer function and determine the motortime constant, 7, and the motor gain constant, K.2.

Question
Asked Nov 1, 2019
m
T K, i-
B
ep)K
inductance, Lm, is low compared
Usually the
to the resistance, Rm, and can be neglected. Also assume friction in the motor bearings can be neglected (B= 0). Assume the
inertia, J, includes the motor armature inertia, Jm, and the load inertia, Ji,. Simplify the transfer function and determine the motor
time constant, 7, and the motor gain constant, K.
2.
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m T K, i- B ep)K inductance, Lm, is low compared Usually the to the resistance, Rm, and can be neglected. Also assume friction in the motor bearings can be neglected (B= 0). Assume the inertia, J, includes the motor armature inertia, Jm, and the load inertia, Ji,. Simplify the transfer function and determine the motor time constant, 7, and the motor gain constant, K. 2.

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Expert Answer

Step 1

The transfer function is the ratio of the Laplace transform of output to the input into the system.

In a series motor, the terminal voltage is the input and the shaft displacement is the output.

 

Solving the electrical circuit in the Laplace domain-

Applying KVL-

V()I(s) R+L]+E, (s)
..41)
m
m
Also, as we know-
de
dt
de
dt
E,(s)=sK (s)
.(2)
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V()I(s) R+L]+E, (s) ..41) m m Also, as we know- de dt de dt E,(s)=sK (s) .(2)

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Step 2

At the shaft-

,&O(t)
d()de(t)
T J
B
dt
dt
Taking laplace of the above equation-
T (s)-[sJ+sB]0(s)
..(3)
Given that
T Ki
(4)
or, T(s) K,I (s)
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,&O(t) d()de(t) T J B dt dt Taking laplace of the above equation- T (s)-[sJ+sB]0(s) ..(3) Given that T Ki (4) or, T(s) K,I (s)

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Step 3

From equation (3)...

s(5J+B)
..(5)
e(s)
I(s)
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s(5J+B) ..(5) e(s) I(s)

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