Ziegler–Nichols method
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] |
These 3 parameters are used to establish the correction from the error via the equation:
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.[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.
References
- ↑ Ziegler, J.G & Nichols, N. B. (1942). "Optimum settings for automatic controllers" (PDF). Transactions of the ASME. 64: 759–768.
- 1 2 3 4 5 6 Ziegler-Nichols Tuning Rules for PID, Microstar Laboratories
- Co, Tomas; Michigan Technological University (February 13, 2004). "Ziegler-Nichols Closed Loop Tuning". Retrieved 2007-06-24.