Analytical Design of Enhanced Fractional Filter PID Controller for Improved Disturbance Rejection of Second Order Plus Time Delay Processes

In this article, a modified fractional internal model control (IMC) filter structure is proposed to design a fractional filter Proportional-Integral-Derivative (FFPID) controller for improved disturbance rejection of second order plus time delay (SOPTD) processes. The proposed method aims at improving the disturbance rejection of slow chemical processes as the tuning rules for such processes are limited. The present design also considers the higher order approximation for time delay as it gives improved response for higher order processes. There is an additional tuning parameter in the proposed IMC filter apart from the conventional IMC filter time constant, which is tuned according to the derived formula. The additional adjustable parameter achieves the disturbance rejection and the closed loop stability. The simulation results have been performed for the same degree of robustness (maximum sensitivity, M-s) for a fair comparison. The results show an improved disturbance rejection for lag dominant and delay significant SOPTD processes with the proposed controllers designed using higher order Pade's approximation of time delay than the proposed method using first order approximation and the conventional method. The closed loop robust performance is observed for perturbations in the process parameters and the performance is also observed for noise in the measurement. The robust stability analysis is carried out using sensitivity functions. In addition, the M-s range is also identified over which the system gives robust performance for the controllers designed using higher order pade's approximation of time delay compared to conventional method.