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

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 Edition Second 3.0j 31 Aug 2019 Richard Murray murray@cds.caltech.edu 11 13 22, 23 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 $k_i = 0.54 k_c/T_c$.