PID Form Converter (Ideal, Series, Parallel)
PLCs and DCSs use different PID algorithms. Convert tuning parameters between the ideal (ISA), series (interacting) and parallel (independent gain) forms so a loop behaves the same after migration.
- Ti′ = (Ti/2)(1 + √(1 − 4Td/Ti)), Td′ = (Ti/2)(1 − √(1 − 4Td/Ti)), Kc′ = Kc Ti′/Ti
PID Algorithm Forms
Series: u = Kc′ (1 + 1/(Ti′ s))(1 + Td′ s) e
Parallel: u = Kp e + Ki ∫e dt + Kd de/dt
Without derivative (Td = 0) the ideal and series forms are identical. Parallel gains Ki and Kd use time units, so check whether your controller uses seconds or minutes.
Worked example
Ideal Kc = 2, Ti = 4 min, Td = 0.5 min converts to series Kc = 1.71, Ti = 3.41 min, Td = 0.59 min, or parallel Kp = 2, Ki = 0.5 per min, Kd = 1 min.
Frequently Asked Questions
What is the difference between ideal and series PID?
In the series (interacting) form the integral and derivative terms multiply each other, so changing Td also changes the effective gain and integral action.
Why can some ideal settings not be converted to series?
The series form cannot represent an ideal PID with Ti < 4Td, because its zeros would become complex.
What is the parallel PID form?
Each term has an independent gain: Kp, Ki and Kd. It is common in PLC function blocks but less intuitive to tune.
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