FOPDT

FOPDT stands for First-Order Plus Dead Time, a simple dynamic model used to approximate the response of many process systems. It represents a process as a first-order lag with a pure time delay. The Laplace transfer function is G(s) = K * e^{-L s} / (T s + 1), where K is the steady-state gain, T is the time constant, and L is the dead time (time delay) before the output begins to respond.

The corresponding time-domain response to a step input of magnitude Δu is y(t) = K Δu [1 - exp(-(t - L)/T)] for t > L, and y(t) = 0 for t ≤ L. The final change in output is K Δu, and the response starts after the delay L; the 63.2% point relative to the final value is reached after time constant T following the delay.

Identification and use: FOPDT parameters are typically estimated from open- or closed-loop step-response tests or process reaction curves and are commonly used for initial controller tuning in PID control, as well as in model-based methods like internal model control. Tuning rules such as Ziegler-Nichols and Cohen-Coon often rely on a FOPDT approximation.

Limitations: As a simplified model, FOPDT cannot capture nonlinearity, multiple time constants, non-minimum phase behavior, or significant variation in dynamics with operating point. It is often augmented with more complex models when higher fidelity is required. In practice, dead time is sometimes approximated by a Pade expansion or addressed with a Smith predictor to maintain control performance in the presence of substantial delay.