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PID tuning

When process identification has been done and control law choosen, PID controller actions are set according to the following tables, given for various PID equations:

  • stable with proportional response,
  • unstable with integral response.
Stable process, proportional response
Process: Gs static gain = ΔS/ΔE (S output, E input), τ pure lag, θ first order time constant.
Controller: GC gain (=100/PB, proportional band), Ti integral constant (s), Td derivative constant (s)
Mode
Action
P
PI
serie
PI
parallel
PID
serie
PID
parallel
PID
mixed
GC (0.8×θ)/(Gs×τ) (0.8×θ)/(Gs×τ) (0.8×θ)/(Gs×τ) (0.85×θ)/(Gs×τ) (0.4+θ/τ)/(1.2×Gs) (0.4+θ/τ)/(1.2×Gs)
Ti maxi θ (Gs×τ)/0.8 θ (Gs×τ)/0.75 θ+0.4×τ
Td 0 0 0 0.4×τ (0.35×θ)/Gs (θ×τ)/(2.5×θ+τ)
Unstable process, integral response
Process: K static gain = (ΔS/Δt)/ΔE (S output, E input), τ pure lag.
Mode
Action
P
PI
serie
PI
parallel
PID
serie
PID
parallel
PID
mixed
GC 0.8/(K×τ) 0.8/(K×τ) 0.8/(K×τ) 0.85/(K×τ) 0.9/(K×τ) 0.9/(K×τ)
Ti maxi 5×τ (K×τ2)/0.15 4.8×τ (K×τ2)/0.15 5.2×τ
Td 0 0 0 0.4×τ 0.35/K 0.4×τ