PID Tuning Calculator
Get starting PID settings from a closed-loop oscillation test or an open-loop step test, using classic Ziegler-Nichols rules and more conservative alternatives.
| Method | Mode | Kp | PB % | Ti | Td | Ki = Kp/Ti | Kd = Kp·Td |
|---|---|---|---|---|---|---|---|
| Ziegler-Nichols | P | 2 | 50 | — | — | — | — |
| Ziegler-Nichols | PI | 1.8 | 55.6 | 25 | — | 0.072 | — |
| Ziegler-Nichols | PID | 2.4 | 41.7 | 15 | 3.75 | 0.16 | 9 |
| Tyreus-Luyben | PI | 1.25 | 80 | 66 | — | 0.0189 | — |
| Tyreus-Luyben | PID | 1.818 | 55 | 66 | 4.762 | 0.0275 | 8.658 |
Results are for the ideal (ISA standard) PID form, with Ti and Td in the same time unit you entered. Ziegler-Nichols settings are aggressive (quarter-amplitude decay); Tyreus-Luyben and lambda tuning are more conservative. Check your controller's algorithm (ideal, series or parallel) and whether it uses gain or proportional band, repeats/min or minutes/repeat. Always test new settings carefully on a live process.
Method 1: Closed-loop (ultimate gain) test
- Put the controller in automatic with integral and derivative action turned off (or as small as possible).
- Increase the proportional gain in small steps, making small setpoint changes each time.
- When the loop oscillates with a steady, constant amplitude, record the gain as Ku and the oscillation period as Pu.
- Enter both values in the calculator.
This test deliberately pushes the loop to the edge of stability, so it is not suitable for every process. Do not use it on loops where oscillation could be unsafe or damage equipment or product.
Method 2: Open-loop step test (process reaction curve)
- Put the controller in manual with the process steady.
- Make a step change in the controller output (for example 5 to 10%).
- Record the process variable response and find:
- Process gain K = change in PV % ÷ change in output %
- Dead time L = time before the PV starts to respond
- Time constant T = time from the end of the dead time to 63.2% of the final change
This works for self-regulating processes such as flow, temperature and pressure. Integrating processes such as most level loops need different rules.
Which rule should I use?
| Rule | Behavior | Good for |
|---|---|---|
| Ziegler-Nichols | Fast, aggressive, quarter-amplitude decay | A quick starting point; usually needs detuning |
| Tyreus-Luyben | More damped than Ziegler-Nichols | Process loops where stability matters more than speed |
| Lambda (IMC) | Smooth, no overshoot; speed set by λ | Self-regulating loops, loops that interact with each other |
Converting between controller forms
- Proportional band: PB % = 100 ÷ Kp.
- Integral: some controllers use repeats per minute (1 ÷ Ti) instead of minutes per repeat (Ti).
- Parallel form: Ki = Kp ÷ Ti and Kd = Kp × Td, as shown in the results table.
- Series (interacting) form: used by some older controllers; convert before entering the values.
Always apply new tuning carefully, watch the response, and adjust in small steps.