Tunning of PID controllers for unstable time delay systems using synthesis method

Many processes of Chemical Engineering importance are represented by unstable first/second order plus time delay systems for the design PID controllers. It is proposed to design PID controller with lead lag filter for unstable First Order Plus Time Delay (FOPTD), Second Order Plus Time Delay (SOPTD) systems using synthesis method. The novelty of the proposed work is the selection of desired closed loop transfer function. For FOPTD systems the closed loop transfer function is selected as third order with second order lead term with time delay and for the SOPTD systems the closed loop transfer function is selected as fourth order with second order lead term with time delay. The closed loop time delay is same as process time delay. Simulation results on various transfer function models and on the non-linear model equations of Jacketed CSTR carrying out first order exothermic reaction show that the controllers designed by the proposed method perform better than the recently reported methods. Robustness of the controller is related to maximum magnitude of the sensitivity function. The proposed controllers are robust to parametric uncertainties as they give low Ms value compared to the recently reported methods.