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sci.IMC-tuning-lambda-method Calculator
Calculates IMC-based PID tuning parameters (Kc, Ti, Td) from first-order-plus-dead-time (FOPDT) model and desired closed-loop time constant λ. Increasing λ gives more conservative (slower, more robust) control — rule of thumb: λ = 1–3 × process time constant for good disturbance rejection.
Inputs
K Process
Reference formula or conversion factor shown for context.
Tau S
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Theta S
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Lambda S
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Results
PI gain Kc (IMC-lambda)
The improvement or increase over the baseline.
integral time Ti = τ (s)
Area under the curve between the specified limits. In physics: integral of velocity = displacement; integral of force over time = impulse.
PID derivative Td ≈ θ/2 (s)
The instantaneous rate of change — the slope of the tangent line at a point. In physics: derivative of position = velocity; derivative of velocity = acceleration.
IMC: Kc = τ/[K(λ+θ)]; Ti = τ
Reference formula or conversion factor shown for context.
λ/θ ratio
The proportional relationship between two quantities.