IMC-PID tuning method for stable FOPDT processes with stochastic time delay

On the basis of IMC framework, this paper addresses PID tuning problem for optimal IAE performance of FOPDT process with stochastic time delay. It should be noted that the traditional deterministic tuning methods can not deal with such problem since they require the exact knowledge or effective estimation of process parameters. From probabilistic point of view, the key idea of the proposed tuning method is to seek and minimize the mean value of IAE in the sense of probability. Meanwhile, the PID tuning rule of the proposed method is derived by means of Maclaurin expansion and the firstorder Taylor approximation that is popular in IMC-PID tuning techniques. In the presence of stochastic time delay in FOPDT process, it shows that the IAE performance of the resulting closed-loop system with the proposed PID tuning is improved in comparison with that of the traditional tuning methods for optimal IAE like Murrill et al. (1967), Smith et al. (1997) and Madhuranthakam et al. (2008).