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

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

These 3 parameters are used to establish the correction ${\displaystyle u(t)}$ from the error ${\displaystyle e(t)}$ via the equation:

${\displaystyle u(t)=K_{p}\left(e(t)+{\frac {1}{T_{i}}}\int _{0}^{t}e(\tau )d\tau +T_{d}{\frac {de(t)}{dt}}\right)}$

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

${\displaystyle u(s)=K_{p}\left(1+{\frac {1}{T_{i}s}}+T_{d}s\right)e(s)=K_{p}\left({\frac {T_{d}T_{i}s^{2}+T_{i}s+1}{T_{i}s}}\right)e(s)}$

Video Ziegler-Nichols method

Evaluation

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.

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

Maps Ziegler-Nichols method

References

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

• Co, Tomas; Michigan Technological University (February 13, 2004). "Ziegler-Nichols Closed Loop Tuning". Retrieved 2007-06-24. 

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External links

• https://web.archive.org/web/20080616062648/http://controls.engin.umich.edu:80/wiki/index.php/PIDTuningClassical#Ziegler-Nichols_Method

Source of the article : Wikipedia