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Control Engineering Basics

Which of the following correctly describes the Bode plot of an integrator G(s) = 1/s?

  1. AThe gain is 0 dB at every frequency, and the phase is −90° at every frequency
  2. BThe gain is a +20 dB/dec line passing through 0 dB at ω = 1 rad/s, and the phase is +90° at every frequency
  3. CThe gain is a −20 dB/dec line passing through 0 dB at ω = 1 rad/s, and the phase is −90° at every frequency
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Answer: C. The gain is a −20 dB/dec line passing through 0 dB at ω = 1 rad/s, and the phase is −90° at every frequency

The magnitude of G(jω) = 1/(jω) is 1/ω, so it is 0 dB at ω = 1 rad/s and falls by 20 dB for every tenfold increase in frequency. Since 1/j = −j, the phase is −90° at every frequency. Because the gain grows without limit at low frequencies, a system containing an integrator can bring the steady-state error to a step setpoint to zero. A +20 dB/dec line with a phase of +90° belongs to a differentiator s.

  • A. The gain is not constant; it changes in inverse proportion to frequency.
  • B. This is the Bode plot of a differentiator G(s) = s.
  • C. Correct. An integrator has a gain slope of −20 dB/dec and a constant phase lag of 90°.
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More Control Engineering Basics questions

  1. For G(s) = 10/((1 + s/100)(1 + s/1000)), which of the following is the gain at the angular frequency ω = 10⁴ rad/s, found with the straight-line approximation of the Bode plot?
  2. Which of the following correctly describes the frequency characteristics of a time-delay element e^(−Ls) with delay time L, and its effect on a control system whose loop transfer function contains it?
  3. Which of the following correctly describes the gain margin and phase margin read from the Bode plot of the loop transfer function?
  4. Which of the following is closest to the gain margin of the loop transfer function L(s) = 2/(s(s + 1)(s + 2))?
  5. Raising the gain of the loop transfer function reduced the phase margin from 60° to 30°. Which of the following correctly describes the change in the closed-loop step response?

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