GATE EC 2015 Set 2 — Question 58
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Control Systems → Frequency-Domain Analysis → Bode Plots
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Question
The transfer function of a mass-spring-damper system is given byThe frequency response data for the system are given in the following table.
The unit step response of the system approaches a steady state value of ____________.
| in rad/s | in dB | in deg |
|---|---|---|
| 0.01 | -18.5 | -0.2 |
| 0.1 | -18.5 | -1.3 |
| 0.2 | -18.4 | -2.6 |
| 1 | -16 | -16.9 |
| 2 | -11.4 | -89.4 |
| 3 | -21.5 | -151 |
| 5 | -32.8 | -167 |
| 10 | -45.3 | -174.5 |
Correct answer
0.1 to 0.13
Solution
For a unit step input, the final value theorem givesAt very low frequencies . The table shows the magnitude settling at dB for and rad/s (phase ), soHence the unit step response settles at about .Answer: (accepted range 0.10 to 0.13)
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