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 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
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	$0.60 K_u$	$T_u/2$	$T_u/8$
Pessen Integral Rule	$0.7 K_u$	$T_u/2.5$	$3 T_u/20$
some overshoot	$0.33 K_u$	$T_u/2$	$T_u/3$
no overshoot	$0.2 K_u$	$T_u/2$	$T_u/3$

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.

Z–N yields an aggressive gain and overshoot – some applications wish to instead minimize or eliminate overshoot, and for these Z–N is inappropriate.

External links

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