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The open-loop transfer function of a dc motor is given as ω(s)/Vₐ(s) = 10/(s(1+10s)). When connected in feedback as shown below, the approximate value of Kₐ that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

1. 1
2. 5
3. 10
4. 100

Correct answer: 100

Solution

To reduce the time constant of the closed-loop system by one hundred times, the gain Kₐ must be increased significantly. Since the time constant is inversely proportional to the gain in a feedback system, setting Kₐ to 100 achieves the desired reduction in time constant.

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