Ziegler-Nichols Autotuning Method

Ziegler and Nichols developed heuristic methods for determining the parameters of a PID controller. The Autotuning Wizard and PID VIs that use the PID Relay autotuning technique use this method.

When using the Ziegler-Nichols autotuning method, select one of the following three types of desired loop response performance: fast (1/4 damping ratio), normal (some overshoot), and slow (little overshoot). The following tables show the tuning formulas for each type of loop performance.

Note  During tuning, the process remains under closed-loop PID control. You do not need to switch off the existing controller and perform the experiment under open-loop conditions. In the setpoint relay experiment, the setpoint signal mirrors the setpoint for the PID controller.

Ziegler-Nichols Closed Loop/Frequency Response Method

The following tables show the tuning formulas for different types of loop performance under proportional-only control, where K_u is the controller gain and T_u is the period of oscillation.

Ziegler-Nichols Open Loop/Step Response Method

The following tables shows the tuning formulas for different types of loop performance under PI or PID control, where T_P is the time constant and is the dead time.

Fast Performance
Controller	Kc	Ti	Td
P	TP/	—	—
PI	0.9TP/	3.33	—
PID	1.1TP/	2.0	0.5

Normal Performance
Controller	Kc	Ti	Td
P	0.44TP/	—	—
PI	0.4TP/	5.33	—
PID	0.53TP/	4.0	0.8

Slow Performance
Controller	Kc	Ti	Td
P	0.26TP/	—	—
PI	0.24TP/	5.33	—
PID	0.32TP/	4.0	0.8

Note  The previous tables provides proportional gain (Kc) values. The following equation describes the relationship between proportional gain and proportional band (PB): Kc = 100/PB