This publication explains two rules related to the Ziegler-Nichols methods.
Matlab examples are presented in order to simplify the reader.
Both Tuning rules result in a closed control loop giving an overshooting response with a quarter wave decay of the oscillating control variable.
The first method described is applicable if the controller Tuning is done in a closed feedback control loop, while the second method can be utilized where an open loop step response is available or can be measured.
This publication explains two rules related to the Ziegler-Nichols methods