PID Tuning Tools · Free Tool
SIMC PID Tuning Calculator (Skogestad)
SIMC (Skogestad IMC) rules give robust PI settings with one tuning parameter τc. The default τc = θ gives a good balance of speed and robustness.
Skogestad rulesSelf regulatingIntegratingOne tuning knob
min
min
min
PI gain Kc1.333
Integral time Ti4 min
Proportional band75 %
How this result was calculated
- Kc = τ ÷ (K (τc + θ))
- Ti = min(τ, 4 (τc + θ))
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SIMC Rules (Skogestad 2003)
Self regulating: Kc = τ ÷ (K (τc + θ)), Ti = min(τ, 4 (τc + θ))
Integrating: Kc = 1 ÷ (k′ (τc + θ)), Ti = 4 (τc + θ)
Integrating: Kc = 1 ÷ (k′ (τc + θ)), Ti = 4 (τc + θ)
K process gain, τ time constant, θ dead time, k′ integrating slope (rate of PV change per % output per minute), τc the chosen closed loop time constant.
Worked example
K = 1.5, τ = 4 min, θ = 1 min, τc = 1 min: Kc = 1.33, Ti = 4 min.
Key insight: the min() in the integral time stops lag dominant loops from being too slow to reject disturbances, a common weakness of plain IMC rules.
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Frequently Asked Questions
What τc should I choose?
τc = θ is a good default; larger τc gives slower, more robust control.
Is SIMC the same as lambda tuning?
It is closely related; SIMC adds the Ti limit for better disturbance rejection.
Does it give derivative?
This calculator gives PI; SIMC PID uses a second order model.
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