PID Units Converter: Gain, PB, Repeats and Ki
Convert PID settings between the units used by different controllers: gain or proportional band, integral time or repeats per minute, and ideal or parallel gains.
All conversions
| Quantity | Value |
|---|---|
| Proportional band | 50 % |
| Integral time | 4 min = 240 s |
| Integral as repeats per minute | 0.25 |
| Integral as repeats per second | 0.004167 |
| Parallel Ki = Kc ÷ Ti | 0.5 per min = 0.008333 per s |
| Parallel Kd = Kc × Td | 1 min = 60 s |
| Derivative time | 0.5 min = 30 s |
Conversions
Repeats per minute = 1 ÷ Ti (min)
Ki = Kc ÷ Ti, Kd = Kc × Td (ideal to parallel)
Ideal (ISA) form: u = Kc [e + (1/Ti) ∫e dt + Td de/dt]. Parallel form: u = Kp e + Ki ∫e dt + Kd de/dt.
Worked example
Kc = 2, Ti = 4 min, Td = 0.5 min: PB = 50 %, 0.25 repeats per minute, Ki = 0.5 per min, Kd = 1 min.
Frequently Asked Questions
Is integral time the same as reset rate?
No. Reset rate (repeats per minute) is the inverse of integral time (minutes per repeat).
What is proportional band?
100 ÷ gain, in %: the error that drives the output through its full range.
Which form does my controller use?
Check the manual; DCS often use ideal or series, PLCs often parallel.
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