PID Tuning Calculator (Step Test and Ultimate Gain)
Turn a bump test or an ultimate gain test into controller settings. The workbook compares Ziegler–Nichols, Cohen–Coon, lambda and IMC tuning side by side, with gain, proportional band, integral and derivative time.
Download
- Calculator sheet with a worked example
- How to Use sheet with steps
- 39 built in formulas, no macros
- Yellow input cells, grey results
- Calculation sign off block
- Excel, Google Sheets and LibreOffice
Worked Example
These are the results of the example already filled in the workbook. Replace the yellow cells with your own data.
Controller settings (ideal form, times in minutes)
| Method | Gain Kc | Proportional band (%) | Ti (min) | Reset (repeats/min) | Td (min) |
|---|---|---|---|---|---|
| ZN open loop P | 2.667 | 37.5 | |||
| ZN open loop PI | 2.400 | 41.7 | 3.330 | 0.300 | |
| ZN open loop PID | 3.200 | 31.2 | 2.000 | 0.500 | 0.500 |
| Cohen–Coon PI | 2.456 | 40.7 | 2.196 | 0.455 | |
| Cohen–Coon PID | 3.722 | 26.9 | 2.233 | 0.448 | 0.348 |
| Lambda PI | 0.533 | 187.5 | 4.000 | 0.250 | |
| IMC PID | 0.667 | 150.0 | 4.500 | 0.222 | 0.444 |
| ZN closed loop PI | 1.800 | 55.6 | 1.667 | 0.600 | |
| ZN closed loop PID | 2.400 | 41.7 | 1.000 | 1.000 | 0.250 |
About this Calculator
Tuning by trial and error wastes time and upsets the process. A single bump test gives the model, and established rules turn it into settings. Comparing several methods side by side shows the trade off between speed and robustness before you touch the live loop.
Basis: Published tuning rules (Ziegler–Nichols 1942, Cohen–Coon 1953, lambda and IMC) for a first order plus dead time model, ideal PID form.
How to use
- Make a step change of the controller output in manual and record the PV response.
- Estimate the process gain K, dead time θ and time constant τ from the curve (tangent or 28 % / 63 % method).
- Enter them, choose λ for lambda and IMC tuning, and optionally Ku and Pu from a closed loop test.
- Pick the method that suits the loop, apply the settings and fine tune on the process.
Formulas used
- Gains and times from the standard rules for each method.
- Proportional band = 100 ÷ Kc; reset rate = 1 ÷ Ti.
Related tools
Frequently Asked Questions
Which tuning method should I use?
Lambda or IMC for most process loops, because they are robust and do not overshoot. Ziegler–Nichols for a quick, aggressive starting point.
What if my controller uses the series form?
Convert the ideal settings with the PID form converter: the series form has slightly different gain and integral time when derivative is used.
What is a good lambda?
Equal to τ for a normal loop, 2τ to 3τ for interacting or critical loops.
Learn more on the blog
PID controller tuning explained
A practical guide on instrumentationblog.in that explains the engineering behind this workbook.
Read Full Article