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, $K_p$ 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]	$0.2 K_u$	$T_u/2$	$T_u/3$

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.^[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

1. Ziegler, J.G and Nichols, N. B. (1942). "Optimum settings for automatic controllers" (PDF). Transactions of the ASME 64: 759–768.
2. 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.

External links

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