J
jeremy
6 minutes
Ziegler-Nichols Open-Loop (Reaction Curve) Rules
The Ziegler-Nichols open-loop rules, also called the reaction curve method, turn your step test into gains. You need three numbers from the test: the process gain K, the dead time L, and the time constant T. K is the change in measured value divided by the change in output, both in percent of range. For a PID controller the table says Kc = 1.2 T / (K L), Ti = 2 L, and Td = 0.5 L. Here Kc is the controller gain, Ti is the integral time and Td is the derivative time, in the same time units as L. For PI, Kc = 0.9 T / (K L) and Ti = 3.3 L. For P only, Kc = T / (K L). These gains are in the standard form, so convert them if your controller uses another form. Notice what the rule says: more dead time means a lower gain. The rule aims for a quarter amplitude decay, so each swing is a quarter of the last. That makes the gains aggressive, with large overshoot. It works best when the dead time is small next to the time constant, and does poorly when the dead time is long. The rules date from 1942 and came from trials on real plants. Treat the answer as a first guess, not a finish. After this Concept you can turn K, L and T from a step test into starting PID gains.