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: A. 5π/12

  • A. 5π/12
  • B. π/6
  • C. π/12
  • D. π/3

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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