Original Ziegler-Nichols gains listed after improved tuning rules are incorrect

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Edition Second
Version number 3.0j
Submission date 31 Aug 2019
Your name Richard Murray
E-mail address murray@cds.caltech.edu
Chapter 11
Page number 13
Line number 22, 23
Current status Closed

The gains listed in parenthesis in equation (11.10) are not quite correct:

  • For the step response method in equation (11.10a) the original Ziegler-Nichols gains should be $k_p = 1.43T/(K \tau)$ and $k_i = 0.43 T / (K \tau^2)$.
  • For the frequency response method in equation (11.10b) the original Ziegler-Nichols gains should be $k_p = 0.45 k_c$ and $k_i = 0.54 k_c/T_c$.