What is the Ziegler–Nichols method?

A heuristic PID tuning procedure that uses measurements from the onset of sustained, consistent oscillations to choose controller settings.

How is the ultimate gain identified?

Set integral and derivative gains to zero, then increase proportional gain until stable, consistent oscillations occur; that proportional gain is $K_u$.

What is the ultimate period?

The period, $T_u$, of the sustained oscillations observed at the ultimate gain.

How do $K_i$ and $K_d$ relate to $K_p$, $T_i$, and $T_d$?

The integral gain is $K_i=K_p/T_i$, and the derivative gain is $K_d=K_pT_d$.

What is a limitation of classic Ziegler–Nichols tuning?

It tends to produce aggressive gains and overshoot, which can be unsuitable when overshoot must be minimized.

Control systemsLesson 3 of 5 in the course PID control

Ziegler–Nichols Ultimate-Gain PID Tuning

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Summary

The Ziegler–Nichols method is a heuristic procedure for choosing proportional, integral, and derivative settings for a PID controller. It uses the onset of sustained oscillation in a control loop to estimate settings, then applies those settings according to the controller type and desired response.

Begin with the integral and derivative gains set to zero, so the controller acts as a proportional-only controller. Increase the proportional gain, $K_p$ , gradually from zero. The gain at which the control-loop output first reaches stable, consistent oscillations is called the ultimate gain, $K_u$ . Measure the period of those oscillations; this is the ultimate period, $T_u$ .

All flashcards

What is the Ziegler–Nichols method?: A heuristic PID tuning procedure that uses measurements from the onset of sustained, consistent oscillations to choose controller settings.
How is the ultimate gain identified?: Set integral and derivative gains to zero, then increase proportional gain until stable, consistent oscillations occur; that proportional gain is $K_u$ .
What is the ultimate period?: The period, $T_u$ , of the sustained oscillations observed at the ultimate gain.
How do $K_i$ and $K_d$ relate to $K_p$ , $T_i$ , and $T_d$ ?: The integral gain is $K_i=K_p/T_i$ , and the derivative gain is $K_d=K_pT_d$ .
What is a limitation of classic Ziegler–Nichols tuning?: It tends to produce aggressive gains and overshoot, which can be unsuitable when overshoot must be minimized.

Quiz questions

In the frequency-response description of Ziegler–Nichols tuning, how is ultimate gain $K_u$ related to amplitude ratio $M$ ?Answer: $K_u=1/M$ .
In a PID controller, what does proportional action respond to?Answer: The current error.
What is a main objective of classic Ziegler–Nichols PID tuning?Answer: Strong disturbance rejection.
What does quarter-wave decay describe in a response tuned by the classic Ziegler–Nichols rule?Answer: Each successive oscillation is about one quarter the amplitude of the previous one.
When might a less aggressive tuning choice be preferable to classic Ziegler–Nichols tuning?Answer: When avoiding overshoot or exceeding a process limit is important.

Based on the Wikipedia article Ziegler–Nichols method, licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.

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