On robust stability of second order plus interval time delay plants using Fractional-Order Proportional Integral Derivative controllers

Abstract

The robust stability assessment of the second order plus interval time delay (SOPITD) plant controlled by Fractional-Order Proportional Integral Derivative (FOPID) controllers is the focus of this research. A simple graphical procedure for analyzing the robust stability of the interval system is presented based on the zero exclusion condition and the value set concept. The incorporation of an auxiliary function, derived through a judicious application of fundamental geometric principles intrinsic to convex polygons, serves to significantly alleviate the complexity and facilitate the application of the robust stability analysis approach, thereby affording a more streamlined and efficient means of designing robust control systems. Moreover, the computational burden for the robust stability analysis is also reduced by novel bounds. Moreover, a novel robust performance checking function is provided to improve the performance system. Three illustrative examples are then given to support the findings and show their applicability.