QUESTION 1 Consider the equations of motion of an armature controlled DC motor given by Jw(t)+bw (t) Ki (t) = di (l) L + Ri (t) + Kw (t) = -Tfriction - Tload (t) Vin (t), dt where vin(t) is the input voltage and Tload(t) is the input load torque. The outputs are the armature current i(t) and the motor speed w(t). When the input voltage and torque are constant, the transient response of this system has the form of the homogeneous solution. What is the time constant of the transient response? Find the characteristic roots of this system first. Keep 3 significant figures, and do not include units. Use scientific notation. The constants are given below: Nominal voltage, Vin(t) = 17 V Moment of inertia of the rotor, J = 0.02 kg-m² Motor viscous friction constant, b = 0.009 N-m-s Friction torque, Tfric = 0.003 N-m Armature inductance, L = 0.1 H Armature resistance, R = 0.35 Back emf constant and motor torque constant, K = 0.21 N-m/A. **Recall that the time constant (or relaxation time) is the time it takes for an exponential function to decay to 36.8% (exp(-1)) of the initial value. In two relaxation time, the homogeneous solution is 13.5% of the initial value. In four relaxation time, the homogenous solution is only 1.8% of the original value. **
QUESTION 1 Consider the equations of motion of an armature controlled DC motor given by Jw(t)+bw (t) Ki (t) = di (l) L + Ri (t) + Kw (t) = -Tfriction - Tload (t) Vin (t), dt where vin(t) is the input voltage and Tload(t) is the input load torque. The outputs are the armature current i(t) and the motor speed w(t). When the input voltage and torque are constant, the transient response of this system has the form of the homogeneous solution. What is the time constant of the transient response? Find the characteristic roots of this system first. Keep 3 significant figures, and do not include units. Use scientific notation. The constants are given below: Nominal voltage, Vin(t) = 17 V Moment of inertia of the rotor, J = 0.02 kg-m² Motor viscous friction constant, b = 0.009 N-m-s Friction torque, Tfric = 0.003 N-m Armature inductance, L = 0.1 H Armature resistance, R = 0.35 Back emf constant and motor torque constant, K = 0.21 N-m/A. **Recall that the time constant (or relaxation time) is the time it takes for an exponential function to decay to 36.8% (exp(-1)) of the initial value. In two relaxation time, the homogeneous solution is 13.5% of the initial value. In four relaxation time, the homogenous solution is only 1.8% of the original value. **
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 1
Consider the equations of motion of an armature controlled DC motor given by
Jw(t)+bw (t) Ki (t)
=
di (l)
L + Ri (t) + Kw (t)
=
-Tfriction - Tload (t)
Vin (t),
dt
where vin(t) is the input voltage and Tload(t) is the input load torque. The outputs are the armature current i(t) and the motor speed w(t).
When the input voltage and torque are constant, the transient response of this system has the form of the homogeneous solution.
What is the time constant of the transient response? Find the characteristic roots of this system first. Keep 3 significant figures, and do not include units. Use scientific
notation.
The constants are given below:
Nominal voltage, Vin(t) = 17 V
Moment of inertia of the rotor, J = 0.02 kg-m²
Motor viscous friction constant, b = 0.009 N-m-s
Friction torque, Tfric = 0.003 N-m
Armature inductance, L = 0.1 H
Armature resistance, R = 0.35
Back emf constant and motor torque constant, K = 0.21 N-m/A.
**Recall that the time constant (or relaxation time) is the time it takes for an exponential function to decay to 36.8% (exp(-1)) of the initial value. In two relaxation time, the homogeneous solution is 13.5% of the initial value. In four relaxation time, the
homogenous solution is only 1.8% of the original value. **
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