Implementable robust stability regions for fractional‐order PD controllers with an application to servo system control

ABSTRACT This paper presents a methodology aimed at computing the implementable robust stability regions for Fractional‐Order Proportional‐Derivative (FOPD) controllers in the context of interval fractional‐order plants. The implementable robust stability region of an FOPD controller refers to determining the robust stability region of its integer‐order approximations for interval systems. It is demonstrated that the robust stability region of an FOPD controller differs from that of its integer‐order approximation. Consequently, values conducive to practical controller design are situated within the implementable robust stability region. Initially, robust stability analysis of the fractional‐order system is conducted using integer‐order approximations of FOPD controllers. Subsequently, an algorithm is proposed for computing the implementable robust stability regions of FOPD controllers. Additionally, an auxiliary function is introduced to enhance the performance of the closed‐loop control system. Finally, the proposed approach is applied to the position control of a laboratory modular servo system.