Ziegler–Nichols method

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Main article: PID controller

The Ziegler–Nichols tuning method is a heuristic method of tuning a PID controller. It was developed by John G. Ziegler and Nathaniel B. Nichols. It is performed by setting the I (integral) and D (derivative) gains to zero. The "P" (proportional) gain, K_p is then increased (from zero) until it reaches the ultimate gain K_u, at which the output of the control loop has stable and consistent oscillations. K_u and the oscillation period T_u are used to set the P, I, and D gains depending on the type of controller used:

Ziegler–Nichols method[1]
Control Type K_p T_i T_d
P 0.5 K_u - -
PI 0.45 K_u T_u/1.2 -
PD 0.8 K_u - T_u/8
classic PID[2] 0.60 K_u T_u/2 T_u/8
Pessen Integral Rule[2] 0.7 K_u T_u/2.5 3 T_u/20
some overshoot[2] 0.33 K_u T_u/2 T_u/3
no overshoot[2] 0.2 K_u T_u/2 T_u/3


Z–N tuning creates a "quarter wave decay". This is an acceptable result for some purposes, but not optimal for all applications.

The Ziegler-Nichols tuning rule is meant to give PID loops best disturbance rejection.[2]

Z–N yields an aggressive gain and overshoot[2] – some applications wish to instead minimize or eliminate overshoot, and for these Z–N is inappropriate.


  1. ^ Ziegler, J.G and Nichols, N. B. (1942). "Optimum settings for automatic controllers" (PDF). Transactions of the ASME 64: 759–768. 
  2. ^ a b c d e f Ziegler-Nichols Tuning Rules for PID, Microstar Laboratories

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