Introduction & Context

Integral control reset time, denoted TR, is the single tuning parameter that determines how aggressively the integral (reset) term of a PI or PID controller eliminates steady-state error. A short TR produces a large integral gain and therefore rapid elimination of offset, but also amplifies measurement noise and can induce oscillatory or even unstable behaviour. A long TR yields smooth output but sluggish recovery from disturbances. The calculation shown here is used in process engineering to obtain a first-pass value of TR from a user-specified required change in controller output, the current control error, the controller gain, and the execution interval of the algorithm.

Methodology & Formulas

  1. Define the control error

    \[ e = \text{SP} - \text{PV} \]

    where SP is the set-point and PV is the measured process variable (both in consistent engineering units).

  2. Determine the minimum incremental change in the integral (reset) component, ΔmI,req, expressed in percent of the controller output range.

  3. Compute the provisional reset time

    \[ T_{R,\text{calc}} = \frac{K_{c}\,|e|\,\Delta t}{\max(\Delta m_{I,\text{req}},\,\varepsilon)} \]

    with

    • Kc = proportional gain (dimensionless),
    • Δt = controller execution interval [s],
    • ε = machine epsilon (≈ 10-9) to avoid division by zero.

  4. Impose operational limits:

    Condition Interpretation
    \(T_{R,\text{calc}} < T_{R,\text{min}}\) Noise amplification likely; clamp to TR,min = 1 s or retune.
    \(T_{R,\text{calc}} > T_{R,\text{max}}\) Sluggish recovery likely; clamp to TR,max = 3600 s or retune.