Robust Control PID for Time Delays Systems

In this paper we present a robust stability analysis for a time-delay systems, in closed loop with proportional, proportional integral and proportional derivative (P, PI and PD respectively) controllers. The frequency approach is used in order to obtain necessary and sufficient conditions for the robust stability of the characteristic equation in closed loop and to tune the controller. The time domain analysis is used to obtain sufficient stability conditions for the system in closed loop with the PI controller, with nonlinear uncertainties. Also, the results are applied to a binary column distillation and coupled tanks, process commonly used in industry applications.