Consider a motor model that the load is modeled as an inertia connected to the motor by a torsional spring, k, instead of a load torque as shown in the figure. How should the equations of motion, Let K be the motor torque constant and also the motor's back emf constant. Select the correct set of equations of motion. + armature circuit V; R L 000 Motor eeee k Load T 0 di(1) dt L + Ri (1) + KO₁(1) =v, (1) 10₁(1) 1 ОР dt do₂(1) -=Ki(t) +k(0¸(t) − 0¸(1)) -=k(0₂(1) -0¸(1)) dt di(1) (1) or L ·+ Ri (1) + K- dt di d²0 (1) di² -=v₁(1) -=Ki(1) +k(0₂(1) − 0¸(1)) d²0₂(1) di² di(1) L dt ((1) 0-(1)³0)= · + Ri(t) − K- (1)'Orp do (1) di -=v₁(1) di² d20₂(1) 12 di² L di(1) dt == - Ki(t) +k (0₂(1)−0¸(1)) -=k(0₁(t) −0₂(1)) - + Ri (1) + KO₁(1)=v¸ (1) d²0 (1) ·=Ki(t) + k (0₂(t) −0¸(1)) di² d²0₂(1) di² -=k(0₁(1) -0₂(1))
Consider a motor model that the load is modeled as an inertia connected to the motor by a torsional spring, k, instead of a load torque as shown in the figure. How should the equations of motion, Let K be the motor torque constant and also the motor's back emf constant. Select the correct set of equations of motion. + armature circuit V; R L 000 Motor eeee k Load T 0 di(1) dt L + Ri (1) + KO₁(1) =v, (1) 10₁(1) 1 ОР dt do₂(1) -=Ki(t) +k(0¸(t) − 0¸(1)) -=k(0₂(1) -0¸(1)) dt di(1) (1) or L ·+ Ri (1) + K- dt di d²0 (1) di² -=v₁(1) -=Ki(1) +k(0₂(1) − 0¸(1)) d²0₂(1) di² di(1) L dt ((1) 0-(1)³0)= · + Ri(t) − K- (1)'Orp do (1) di -=v₁(1) di² d20₂(1) 12 di² L di(1) dt == - Ki(t) +k (0₂(1)−0¸(1)) -=k(0₁(t) −0₂(1)) - + Ri (1) + KO₁(1)=v¸ (1) d²0 (1) ·=Ki(t) + k (0₂(t) −0¸(1)) di² d²0₂(1) di² -=k(0₁(1) -0₂(1))
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Consider a motor model that the load is modeled as an inertia connected to the motor by a torsional spring, k, instead of a load torque as shown in the figure. How should the equations of motion,
Let K be the motor torque constant and also the motor's back emf constant.
Select the correct set of equations of motion.
+
armature
circuit
V;
R
L
000
Motor
eeee
k
Load
T 0
di(1)
dt
L + Ri (1) + KO₁(1) =v, (1)
10₁(1)
1
ОР
dt
do₂(1)
-=Ki(t) +k(0¸(t) − 0¸(1))
-=k(0₂(1) -0¸(1))
dt
di(1)
(1) or
L
·+ Ri (1) + K-
dt
di
d²0 (1)
di²
-=v₁(1)
-=Ki(1) +k(0₂(1) − 0¸(1))
d²0₂(1)
di²
di(1)
L
dt
((1) 0-(1)³0)=
· + Ri(t) − K-
(1)'Orp
do (1)
di
-=v₁(1)
di²
d20₂(1)
12
di²
L
di(1)
dt
==
- Ki(t) +k (0₂(1)−0¸(1))
-=k(0₁(t) −0₂(1))
- + Ri (1) + KO₁(1)=v¸ (1)
d²0 (1)
·=Ki(t) + k (0₂(t) −0¸(1))
di²
d²0₂(1)
di²
-=k(0₁(1) -0₂(1))
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