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 Ku is the controller gain and Tu is the period of oscillation.

Fast Performance
Controller Kc Ti Td
P 0.5Ku � �
PI 0.4Ku 0.8Tu �
PID 0.6Ku 0.5Tu 0.12Tu

Normal Performance
Controller Kc Ti Td
P 0.2Ku � �
PI 0.18Ku 0.8Tu �
PID 0.25Ku 0.5Tu 0.12Tu

Slow Performance
Controller Kc Ti Td
P 0.13Ku � �
PI 0.13Ku 0.8Tu �
PID 0.15Ku 0.5Tu 0.12Tu

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 TP 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