Design and real time implementation of fractional order proportional-integral controller (PI λ) in a liquid level system

Abstract

This research article deals with the design and real time implementation of a fractional order Proportional-Integral controller (PI λ) for a Liquid Level System (LLS). The system is approximated as a First Order Plus Time Delay (FOPTD) model. The equivalent transfer function of this system in polynomial format is considered here for controller design. Expressions for controller parameters (K P and K I) in terms of frequency (ω) and fractional order (λ) are derived from the Fractional Order Characteristic Polynomial (FOCP) of the closed loop system. The global stability region based on K P and K I for each λ is constructed. Average values of K P and K I, for each λ, are taken. Among these values, the best fit of K Paverage and K Iaverage and corresponding λ are identified by means of optimization techniques. The real time implementation of PI λ controller with the identified controller settings in LLS is done. The PI λ controller performances are analyzed in terms of ISE and IAE. A comparison of this control strategy with other conventional based controller techniques is made. PI λ controller outperforms the conventional PI controllers. In addition the load disturbance studies are also carried out and it justifies the supremacy of PI λ controller.