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
0.11 to 0.13
Solution
The transfer function of a mass-spring-damper system is given by:For a unit step input, the steady-state value of the output response, , can be found using the Final Value Theorem:Substituting into the transfer function:From the frequency response data table, as approaches 0, the magnitude approaches .
For very small values of (e.g., rad/s or rad/s), the magnitude in dB is approximately -18.5 dB.
To convert this dB value to a linear magnitude:
Therefore, the steady-state value of the unit step response is approximately .
Rounding to two decimal places, the value is approximately . A typical acceptable range for NAT questions would be to .The final answer is (or within the range 0.11 to 0.13).
For very small values of (e.g., rad/s or rad/s), the magnitude in dB is approximately -18.5 dB.
To convert this dB value to a linear magnitude:
Therefore, the steady-state value of the unit step response is approximately .
Rounding to two decimal places, the value is approximately . A typical acceptable range for NAT questions would be to .The final answer is (or within the range 0.11 to 0.13).
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