Kp, Ki, Kd, Ti, Td and proportional band: units and conventions
Dimensions of PID parameters, seconds and minutes, integral time and reset rate (repeats/min), gain and proportional band. A table of typical mistakes when moving settings between systems.
In short. The same controller is described by different numbers in different systems: Ti in seconds or minutes, integral action as a time or as a rate, gain as a gain or as a proportional band. A wrong convention changes the integral action 60 times or makes the controller 4 times "softer". Before moving settings write down the conventions of the source and of the target.
Parameters and units
Section conventions: e = SP − PV, ideal form (forms).
| Parameter | Form | Meaning | Units |
|---|---|---|---|
| Kc | ideal, series | controller gain | output unit / PV unit, or %/% when normalised |
| Ti | ideal | integral time, "time per repeat" | s or min (per repeat) |
| Td | ideal | derivative time | s or min |
| Kp | parallel | proportional gain | as Kc |
| Ki | parallel | integral gain = Kc/Ti | (output unit / PV unit) · 1/s |
| Kd | parallel | derivative gain = Kc·Td | (output unit / PV unit) · s |
| Reset rate | ideal | 1/Ti, "repeats per minute" | repeats/min or repeats/s |
| PB | ideal | proportional band = 100 % / |Kc| | % |
Integral time and reset rate
Ti is the time in which, at constant error, the integral term repeats the proportional term. The reset rate is the number of such repeats per unit of time:
reset rate [repeats/min] = 1 / Ti [min]
Example: Ti = 40 s = 0.667 min → 1.5 repeats/min. The effect is opposite: larger Ti — weaker integral; larger reset rate — stronger integral.
Proportional band
PB is the percentage of the PV range that drives the output over 100 % of its range:
PB [%] = 100 / |Kc| (Kc normalised, %/%)
NI gives the example: a PB of 50 % is a gain of 2. PB has no sign: the direction of action is set separately (direct and reverse action). The formula applies only when input and output are normalised to their ranges; for Kc in °C/% or mA/bar PB is undefined — first convert Kc to %/% (normalisation).
Example: one controller in different conventions
Ideal form Kc = 2.5 %/%, Ti = 40 s, Td = 4 s.
| Convention | Values |
|---|---|
| Kc, Ti, Td in seconds | 2.5; 40 s; 4 s |
| Kc, Ti, Td in minutes | 2.5; 0.6667 min; 0.0667 min |
| Kc, reset rate | 2.5; 1.5 repeats/min |
| PB, Ti, Td | 40 %; 40 s; 4 s |
| Kp, Ki, Kd (seconds) | 2.5; 0.0625 1/s; 10 s |
| Kp, Ki, Kd (minutes) | 2.5; 3.75 1/min; 0.1667 min |
Check in the converter — switch the time unit and the way the integral is entered.
Typical transfer mistakes
| Mistake | Consequence | Factor |
|---|---|---|
| Ti in minutes entered as seconds | integral stronger | ×60 |
| Ti in seconds entered as minutes | integral weaker | ÷60 |
| Reset rate entered into the Ti (min) field | 1.5 repeats/min becomes "Ti = 1.5 min" instead of 0.667 min — integral weaker | ÷2.25 |
| PB entered as Kc | PB 40 % → "Kc = 40" instead of 2.5 | ×16 |
| Ki in 1/min entered as 1/s | integral stronger | ×60 |
| Kc in engineering units entered into a %/% block | depends on the ranges | see normalisation |
| Parallel Kd entered as ideal Td | D stronger | ×Kc |
How to check settings after moving them
- Write down form, time unit, how the integral is entered and the normalisation of the source and of the target.
- Convert in the converter: enter in the source form, compare with the target form.
- Check one value by hand, e.g. Ki = Kc/Ti.
- For new settings on a running plant start with a reduced Kc and watch the trend (manual tuning).
Limits
Parameter names in blocks are not standardised: "Gain", "P", "Kp" can mean Kc or Kp; "Integral" can be Ti, Ki or a reset rate. Find the meaning in the documentation of the particular block and version, not from the field name.
Connections
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Sources
Updated 2026-10-12