Ziegler–Nichols method
Method of tuning a PID controller / From Wikipedia, the free encyclopedia
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, is then increased (from zero) until it reaches the ultimate gain , at which the output of the control loop has stable and consistent oscillations. and the oscillation period are then used to set the P, I, and D gains depending on the type of controller used and behaviour desired:
Control Type | |||||
---|---|---|---|---|---|
P | – | – | – | – | |
PI | – | – | |||
PD | – | – | |||
classic PID[2] | |||||
Pessen Integral Rule[2] | |||||
some overshoot[2] | |||||
no overshoot[2] |
The ultimate gain is defined as 1/M, where M = the amplitude ratio, and .
These 3 parameters are used to establish the correction from the error via the equation:
which has the following transfer function relationship between error and controller output: