Robust PI/PID controller for interval first order system with time delay

In this paper, a new approach to determine the entire set of stabilisng PI/PID parameters for time delay process with bounded uncertainties has been developed. Our method exploited a combination of the generalised Kharitonov theorem and the Hermit Biehler theorem extended for quasipolynomials to synthesise a robustly stabilising controller. By using a constructive procedure, we obtain all PI and PID gains that stabilise an interval first order delay system. Finally, numerical simulations are given to support our theoretical results.