In the motor given in the figure, 0, is the motor angle; w(t) is the motor speed; ea(t) is the input voltage; ia(t) is the armature current; v(t) is a back-emf voltage; and Tm (t) is the mechanical torque. In this model, ignore the field as it is kept at a constant voltage. The Transfer Function G(p) wm(t) ea(t) N(p) D(P) when the armature inductance is negligible, that is, La ≈0, was developed from the Ra La field elle Rotor Armature v(t) circuit Tm(1) ia(1) - ed(1) 0m(1) block diagram: ea ia Tm 1 Kt Ra Kbwm Kb Gm(p)= wm(t) K₁ Rajm N(p) ea(t) P+ + P KK + D(p) m Ralm 1 Tm p+Tm Dm Wm Noticed a typo: β p+Tm ea(t) wm(t) G(p) B = 4 × 10-4 Nm/(rad/sec) P1. Use Laplace Transforms to find the motor speed wm (t) for a step input ea (t) = A us(t) Obtain a plot of ea(t) and wm (t) on the same graph. Select appropriate initial conditions and step magnitude.

Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter12: Power System Controls
Section: Chapter Questions
Problem 12.4P
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Wm(t)/ea(t)= 1838.41/(p+155.1)

In the motor given in the figure, 0, is the motor angle; w(t) is
the motor speed; ea(t) is the input voltage; ia(t) is the armature
current; v(t) is a back-emf voltage; and Tm (t) is the mechanical
torque. In this model, ignore the field as it is kept at a constant
voltage.
The Transfer Function G(p)
wm(t)
ea(t)
N(p)
D(P)
when the armature
inductance is negligible, that is, La ≈0, was developed from the
Ra
La
field
elle
Rotor
Armature v(t)
circuit
Tm(1)
ia(1)
-
ed(1)
0m(1)
block diagram:
ea
ia
Tm
1
Kt
Ra
Kbwm
Kb
Gm(p)=
wm(t)
K₁
Rajm
N(p)
ea(t)
P+
+ P
KK
+
D(p)
m
Ralm
1
Tm
p+Tm
Dm
Wm
Noticed a typo:
β
p+Tm
ea(t)
wm(t)
G(p)
B = 4 × 10-4 Nm/(rad/sec)
P1. Use Laplace Transforms to find the motor speed wm (t) for a step input ea (t) = A us(t) Obtain a plot of ea(t) and
wm (t) on the same graph. Select appropriate initial conditions and step magnitude.
Transcribed Image Text:In the motor given in the figure, 0, is the motor angle; w(t) is the motor speed; ea(t) is the input voltage; ia(t) is the armature current; v(t) is a back-emf voltage; and Tm (t) is the mechanical torque. In this model, ignore the field as it is kept at a constant voltage. The Transfer Function G(p) wm(t) ea(t) N(p) D(P) when the armature inductance is negligible, that is, La ≈0, was developed from the Ra La field elle Rotor Armature v(t) circuit Tm(1) ia(1) - ed(1) 0m(1) block diagram: ea ia Tm 1 Kt Ra Kbwm Kb Gm(p)= wm(t) K₁ Rajm N(p) ea(t) P+ + P KK + D(p) m Ralm 1 Tm p+Tm Dm Wm Noticed a typo: β p+Tm ea(t) wm(t) G(p) B = 4 × 10-4 Nm/(rad/sec) P1. Use Laplace Transforms to find the motor speed wm (t) for a step input ea (t) = A us(t) Obtain a plot of ea(t) and wm (t) on the same graph. Select appropriate initial conditions and step magnitude.
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