Abstract
This research article deals with the design and real time implementation of a fractional order Proportional-Integral controller (PI?) 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 (KP and KI) in terms of frequency (?) and fractional order (?) 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 ? is constructed. Average values of KP and KI, for each ?, are taken. Among these values, the best fit of KP average and KI average and corresponding ? are identified by means of optimization techniques. The real time implementation of PI? controller with the identified controller settings in LLS is done. The PI? 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? controller outperforms the conventional PI controllers. In addition the load disturbance studies are also carried out and it justifies the supremacy of PI? controller.
Highlights
PID controllers belong to the dominating form of feedback industrial controllers and there is a continuous effort to improve their quality and robustness
From the Global Stability Region, the average values of KP and KI corresponding to the each value of λ is obtained Among these values, the best fit of KP average and KI average and corresponding λ are identified by means of optimization techniques
The global stability region based on KP and KI for different λ are constructed
Summary
PID controllers belong to the dominating form of feedback industrial controllers and there is a continuous effort to improve their quality and robustness. Design and tuning of PID controllers have been a large research horizon ever since Ziegler and Nichols presented their methods in 1942. Specifications, stability, design, applications and performance of the PID controller have been widely treated since . There is an increasing number of studies related to the application of fractional controllers in many areas of science and engineering. Fractional Order PID (FO-PID) controllers could benefit the industry significantly with a wide spread impact when FO-PID parameter tuning techniques have been well developed. This fact is due to a better understanding of the Fractional Calculus (FC) revealed by studies on viscoelasticity, damping, chaos, diffusion, wave propagation, percolation and irreversibility
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