Ziegler–Nichols method

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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, is then increased (from zero) until it reaches the ultimate gain , at which the output of the control loop has stable and consistent oscillations. and the oscillation period are used to set the P, I, and D gains depending on the type of controller used:

Ziegler–Nichols method[1]
Control Type
P - -
PI -
PD -
classic PID[2]
Pessen Integral Rule[2]
some overshoot[2]
no overshoot[2]

The ultimate gain (Ku) is defined as 1/M, where M = the amplitude ratio

These 3 parameters are used to establish the correction from the error via the equation:

which has the following transfer function relationship between error and controller output:


The Ziegler-Nichols tuning creates a "quarter wave decay". This is an acceptable result for some purposes, but not optimal for all applications.

This tuning rule is meant to give PID loops best disturbance rejection.[2]

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


  1. ^ Ziegler, J.G & 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

Bequette, B. Wayne. Process Control: Modeling, Design, and Simulation. Prentice Hall PTR, 2010. [1]

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