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In the Ziegler–Nichols ultimate sensitivity method, the gain is raised under proportional control alone until a sustained oscillation appears, and from that gain Ku and the period of oscillation Tu the PID parameters are set to Kp = 0.6Ku, Ti = 0.5Tu and Td = 0.125Tu. Which of the following are the values for Ku = 8 and Tu = 2 s?

  1. AKp = 4, Ti = 1 s, Td = 0.25 s
  2. BKp = 4.8, Ti = 1 s, Td = 0.25 s
  3. CKp = 4.8, Ti = 4 s, Td = 16 s
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Answer: B. Kp = 4.8, Ti = 1 s, Td = 0.25 s

Kp = 0.6 × 8 = 4.8, Ti = 0.5 × 2 = 1 s and Td = 0.125 × 2 = 0.25 s. In parallel form, the integral gain is Ki = Kp/Ti = 4.8 s⁻¹ and the derivative gain is Kd = Kp·Td = 1.2 s. The ultimate sensitivity method is a practical method that works without a model of the plant, but the response it gives is rather oscillatory, with the amplitude shrinking to about a quarter each cycle. It is therefore used as a starting point, followed by adjustments such as lowering the gain while watching the overshoot.

  • A. Kp = 0.5Ku is the value for proportional control alone.
  • B. Correct. Substitute Ku and Tu into the given formulas.
  • C. This divides Tu by the coefficients. Ti and Td are found by multiplying Tu by the coefficients.
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