Consider a armature controlled DC motor equation given by dw(t) J +bw(t)-Ki(t)=0 dt di(t) +Ri(t)+Kw(t)=Vin(t), dt where J = 1 kg-m2, b = 0 N-m-s, K = 2 N-m/A, L = 1 H, and R = 0.5 N. The input voltage is harmonic with amplitude of 8 Volts at frequency at 11 Hz. After the transient response has decayed, the system will respond at the input voltage frequency. What is the amplitude of the steady-state armature current (in Amps)? The answer must be in scientific notation with 3 significant figures. Hint: You need the transfer function I(s)/Vin(s).
Consider a armature controlled DC motor equation given by dw(t) J +bw(t)-Ki(t)=0 dt di(t) +Ri(t)+Kw(t)=Vin(t), dt where J = 1 kg-m2, b = 0 N-m-s, K = 2 N-m/A, L = 1 H, and R = 0.5 N. The input voltage is harmonic with amplitude of 8 Volts at frequency at 11 Hz. After the transient response has decayed, the system will respond at the input voltage frequency. What is the amplitude of the steady-state armature current (in Amps)? The answer must be in scientific notation with 3 significant figures. Hint: You need the transfer function I(s)/Vin(s).
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![**Armature Controlled DC Motor Analysis**
Consider an armature controlled DC motor equation given by:
\[ J \frac{d\omega(t)}{dt} + b \omega(t) - K i(t) = 0 \]
\[ L \frac{di(t)}{dt} + Ri(t) + K \omega(t) = v_{in}(t), \]
where \( J = 1 \, \text{kg-m}^2 \), \( b = 0 \, \text{N-m-s} \), \( K = 2 \, \text{N-m/A} \), \( L = 1 \, \text{H} \), and \( R = 0.5 \, \Omega \).
The input voltage is harmonic with an amplitude of 8 Volts at a frequency of 11 Hz. After the transient response has decayed, the system will respond at the input voltage frequency.
**Problem:**
What is the amplitude of the steady-state armature current (in Amps)?
The answer must be in scientific notation with 3 significant figures.
**Hint:** You need the transfer function \( I(s)/V_{in}(s) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2032bc4f-d7c2-4a7d-a3a7-5951ded4fcfd%2F2f737a1c-9f7d-4a8b-b2dc-8d3b6aef7b9e%2F5lqpzds_processed.png&w=3840&q=75)
Transcribed Image Text:**Armature Controlled DC Motor Analysis**
Consider an armature controlled DC motor equation given by:
\[ J \frac{d\omega(t)}{dt} + b \omega(t) - K i(t) = 0 \]
\[ L \frac{di(t)}{dt} + Ri(t) + K \omega(t) = v_{in}(t), \]
where \( J = 1 \, \text{kg-m}^2 \), \( b = 0 \, \text{N-m-s} \), \( K = 2 \, \text{N-m/A} \), \( L = 1 \, \text{H} \), and \( R = 0.5 \, \Omega \).
The input voltage is harmonic with an amplitude of 8 Volts at a frequency of 11 Hz. After the transient response has decayed, the system will respond at the input voltage frequency.
**Problem:**
What is the amplitude of the steady-state armature current (in Amps)?
The answer must be in scientific notation with 3 significant figures.
**Hint:** You need the transfer function \( I(s)/V_{in}(s) \).
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