Tuning PID for first order plus time delay system under stochastic perturbation

This article presents a method for PID controller design when dealing with stochastic perturbation in first order plus time delay (FOPDT) system. Based on polynomial chaos approach, a computational effective method for analysis stochastic system, one can easily adjust the performance/robustness of system under both stochastic parameter perturbation and additive stochastic input. For validation, the result by polynomial chaos also compare with the result by Monte Carlo Method.