Use reaction-curve and ultimate-cycle tuning responsibly, with assumptions and limitations made explicit.
Kp=0.6Ku,Ti=0.5Pu,Td=0.125Pu
Ziegler–Nichols rules turn a few measured plant features into controller settings. They are historically important and useful as starting points, but often produce aggressive quarter-amplitude damping rather than a finished production tuning.
01
Two different methods
The reaction-curve method uses an open-loop FOPDT approximation. The ultimate-cycle method uses the gain and period of sustained closed-loop oscillation. Their inputs and risks are not interchangeable.
IDENTIFICATION VIEW 01
Read gain, delay and slope from a reaction curve
An open-loop step reveals the process gain and the delayed S-shaped rise used by the reaction-curve method.
Measured responseTangent estimate
READ THE PLOTIdentification quality sets the ceiling for tuning quality
02
Controller form matters
Published coefficients may assume an ideal or standard PID form. PID Loop Lab converts results into its documented parallel PIDF form instead of silently copying gains between incompatible equations.
ULTIMATE VIEW 02
Ku is the edge of sustained oscillation
At the ultimate gain, proportional-only control produces an approximately constant-amplitude cycle with period Pu.
SetpointAt KuBelow Ku
READ THE PLOTThis test deliberately approaches instability
03
Treat the result as a starting point
After applying a rule, test output limits, delay uncertainty, noise and disturbances. A robust operating point usually needs less aggression than the textbook rule.
TUNING VIEW 03
Classic Z–N is intentionally aggressive
Quarter-amplitude damping settles through repeated oscillations. Reducing the gains usually gives a calmer production starting point.
SetpointClassic Z–NSoftened gainsConservative
READ THE PLOTA rule returns a starting point, not a finished design