(b) By reducing down the block diagram, show that the transfer function, relating angular velocity, Nm, to input voltage, Va, of the motor will then be given by: Kt Sm (s) Va(s) Jm La JmRa+DmLa JmLa R,Dm+K¿Kµ JmLa s2 + where: La is the armature inductance, Ra is the armature resistance, Kt is the torque constant, Jm is the load inertia, Dm is the damping coefficient of the load and K, is the back emf constant.

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Author:Robert L. Boylestad
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(b) By reducing down the block diagram, show that the transfer function, relating
angular velocity, Nm, to input voltage, Va, of the motor will then be given by:
Kt
Sm (s)
Va(s)
Jm La
Jm Ra+DmLas +
Jm La
RaDm+K¢K,
JmLa
s2 +
т
where:
La is the armature inductance,
Ra is the armature resistance,
Kt is the torque constant,
Jm is the load inertia,
Dm is the damping coefficient of the load and
K, is the back emf constant.
Transcribed Image Text:(b) By reducing down the block diagram, show that the transfer function, relating angular velocity, Nm, to input voltage, Va, of the motor will then be given by: Kt Sm (s) Va(s) Jm La Jm Ra+DmLas + Jm La RaDm+K¢K, JmLa s2 + т where: La is the armature inductance, Ra is the armature resistance, Kt is the torque constant, Jm is the load inertia, Dm is the damping coefficient of the load and K, is the back emf constant.
T(s) Mechanical (s)
Subsystem
V,(s)
Electrical
|(s)
e(s)
Torque
Coupling
1/s
Subsystem
Va(s)
Back emf
Coupling
Figure 2: Sub-systems that can be identified in the electric motor.
Transcribed Image Text:T(s) Mechanical (s) Subsystem V,(s) Electrical |(s) e(s) Torque Coupling 1/s Subsystem Va(s) Back emf Coupling Figure 2: Sub-systems that can be identified in the electric motor.
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