
Concept explainers
(a)
The step response of

Answer to Problem 6.41P
The responses are as follows:
Explanation of Solution
Given:
The given parameters for an armature-controlled motor are as:
Concept Used:
For an armature-controlled motor, the output responses armature current
Calculation:
Since,
Keeping the values of all the parameters, we get
Now, since input armature voltage is a unit step response of strength
Therefore,
On using the partial fraction expansion in order to simplify above expression, we have
On comparing the numerator on both sides, we get
Thus,
On taking the inverse Laplace of above obtained expression, the response
Similarly, for the response
Since,
Keeping the parameters in this transfer function,
Now, since input armature voltage is a unit step response of strength
Therefore,
On using the partial fraction expansion in order to simplify the above expression, we have
Compare the denominator of both sides
Thus,
On taking the inverse Laplace of the above obtained expression, the response
Conclusion:
The responses
(b)
The step response of

Answer to Problem 6.41P
The responses are follows:
Explanation of Solution
Given:
The given parameters for an armature-controlled motor are as:
Concept Used:
For an armature-controlled motor, the output responses armature current
Calculation:
Since,
Keeping the values of all the parameters, we get
Now, since input load torque is a unit step response of strength
Therefore,
On using the partial fraction expansion in order to simplify above expression, we have
On comparing the numerator on both sides, we get
Thus,
On taking the inverse Laplace of the above obtained expression, the response
Similarly, for the response
Since,
Keeping the parameters in this transfer function,
Now, since input load torque is a unit step response of strength
Therefore,
On using the partial fraction expansion in order to simplify above expression, we have
Compare the denominator of both sides
Thus,
On taking the inverse Laplace of the above obtained expression, the response
Conclusion:
The responses
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Chapter 6 Solutions
System Dynamics
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