Stabilizing region of fractional‐order proportional integral derivative controllers for interval delayed fractional‐order plants

Abstract

Abstract This paper concentrates on computing the stabilizing region of fractional‐order proportional integral derivative (FOPID) controllers for interval delayed fractional‐order plants. An interval delayed fractional‐order plant is defined as a fractional‐order transfer function with a time delay whose denominator and numerator coefficients are all uncertain and lie in specified intervals. In the present study, first, a theorem is proven to analyze the robust stability of the given closed‐loop. Then, a method is proposed to solve the problem of robustly stabilizing interval delayed fractional‐order plants by using FOPID controllers. Moreover, two auxiliary functions are presented to fulfill the additional specifications of design, ensuring better performance of the controlled system with respect to the disturbance and noise. Finally, two examples are provided to illustrate the design procedure.