A system is known to exhibit first-order plus deadtime (FOPDT) system behavior. Several experiments have been performed to determine the characteristics of the system and a static gain of 2.5 was...

A system is known to exhibit first-order plus deadtime (FOPDT) system behavior. Several experiments have been performed to determine the characteristics of the system and a static gain of 2.5 was estimated. It was observed that the closed-loop system under P control exhibits sustained oscillations, with a period of 6.28 min (≈2π min), when the P gain is equal to 0.5. Given this information, derive equations to calculate the parameters of the FOPDT model (k, τ, θ) for the process under study.