QUESTION 2 va(t) ia(t) Ra La w(t) A DC motor is a electro-mechanical system, where mechanical motor is coupled with an electrical circuit. The motor shows up in the circuit equation as a voltage loss proportional to the motor speed, and the electrical system shows up as the input torque proportional to the armature current. DC motor equations are given by do (1) J -+bw (t) − Ki¸(t) = −T di friction -To load (1) di (1) a L a +R_i_(t) +Kw(t) = v. (1), di in where J is the mass moment of inertia in kg-m2, b is the damping coefficient in N-m-s, K is the motor constant N-m/A, Tfriction is the torque caused by static friction, L is the inductance in H, and R is the resistance in ohm. The inputs to this system is the input voltage, vin(t), and the load torque, Tload(t). The outputs may be the motor speed, w(t) in rad/s, and the armature current i(t) in A. What is the transfer function, 2(s)/T(S)? Let Tfriction be zero. R L Js²+(R_J+L_b)s+ (R_b+K²) a a K L Js²+(R_J+L_b)s+ (R_b+K²) L s a L Js²+(R_J+L_b)s+ (R_b+K²) b L Js²+(RJ+L b)s+ (R_b+K²) Js+b L_Js²+(R_J+L_b)s+ (R_b+K²) a а Ls + R₂ a L Js²+(R_J+L_b)s+ (R_b+K²)
QUESTION 2 va(t) ia(t) Ra La w(t) A DC motor is a electro-mechanical system, where mechanical motor is coupled with an electrical circuit. The motor shows up in the circuit equation as a voltage loss proportional to the motor speed, and the electrical system shows up as the input torque proportional to the armature current. DC motor equations are given by do (1) J -+bw (t) − Ki¸(t) = −T di friction -To load (1) di (1) a L a +R_i_(t) +Kw(t) = v. (1), di in where J is the mass moment of inertia in kg-m2, b is the damping coefficient in N-m-s, K is the motor constant N-m/A, Tfriction is the torque caused by static friction, L is the inductance in H, and R is the resistance in ohm. The inputs to this system is the input voltage, vin(t), and the load torque, Tload(t). The outputs may be the motor speed, w(t) in rad/s, and the armature current i(t) in A. What is the transfer function, 2(s)/T(S)? Let Tfriction be zero. R L Js²+(R_J+L_b)s+ (R_b+K²) a a K L Js²+(R_J+L_b)s+ (R_b+K²) L s a L Js²+(R_J+L_b)s+ (R_b+K²) b L Js²+(RJ+L b)s+ (R_b+K²) Js+b L_Js²+(R_J+L_b)s+ (R_b+K²) a а Ls + R₂ a L Js²+(R_J+L_b)s+ (R_b+K²)
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:QUESTION 2
va(t)
ia(t)
Ra
La
w(t)
A DC motor is a electro-mechanical system, where mechanical motor is coupled with an electrical circuit. The motor shows up in the circuit equation as a voltage loss proportional to the motor speed, and the electrical system shows up as the input torque
proportional to the armature current. DC motor equations are given by
do (1)
J
-+bw (t) − Ki¸(t) = −T
di
friction
-To
load (1)
di (1)
a
L
a
+R_i_(t) +Kw(t) = v. (1),
di
in
where J is the mass moment of inertia in kg-m2, b is the damping coefficient in N-m-s, K is the motor constant N-m/A, Tfriction is the torque caused by static friction, L is the inductance in H, and R is the resistance in ohm.
The inputs to this system is the input voltage, vin(t), and the load torque, Tload(t). The outputs may be the motor speed, w(t) in rad/s, and the armature current i(t) in A.
What is the transfer function, 2(s)/T(S)? Let Tfriction be zero.
R
L Js²+(R_J+L_b)s+ (R_b+K²)
a
a
K
L Js²+(R_J+L_b)s+ (R_b+K²)
L s
a
L Js²+(R_J+L_b)s+ (R_b+K²)
b
L Js²+(RJ+L b)s+ (R_b+K²)
Js+b
L_Js²+(R_J+L_b)s+ (R_b+K²)
a
а
Ls + R₂
a
L Js²+(R_J+L_b)s+ (R_b+K²)
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