Ziegler–Nichols method

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 oscillates with a constant amplitude. $K_u$ 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	$K_p$	$K_i$	$K_d$
P	$K_u/2$	-	-
PI	$K_u/2.2$	$1.2K_p/T_u$	-
classic PID^[2]	$0.60 K_u$	$2K_p/T_u$	$K_pT_u/8$
Pessen Integral Rule^[2]	$0.7 K_u$	$2.5K_p/T_u$	$0.15K_p T_u$
some overshoot^[2]	$0.33 K_u$	$2K_p/T_u$	$K_pT_u/3$
no overshoot^[2]	$0.2 K_u$	$2K_p/T_u$	$K_pT_u/3$

Evaluation

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 performance. This setting typically does not give very good command tracking performance."^[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.

References

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

Co, Tomas; Michigan Technological University (February 13, 2004). "Ziegler-Nichols Closed Loop Tuning". http://www.chem.mtu.edu/~tbco/cm416/zn.html. Retrieved 2007-06-24.

External links

http://controls.engin.umich.edu/wiki/index.php/PIDTuningClassical#Ziegler-Nichols_Method