The time constant of a unity gain, first order plus time delay process is 5 min. If the phase lag at a frequency of 0.2 rad/min is 60°, then the dead time (in minutes) is________________?
Correct answer: D. 5π/12
- A. π/3
- B. π/6
- C. π/12
- D. 5π/12
Explanation
The total phase lag is tan⁻¹(ωτ)+ωθ. With ωτ=0.2×5=1, the first-order lag is 45°, leaving 15° or π/12 rad for the delay, so θ=(π/12)/0.2=5π/12 min.
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