Optimal V-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems

Abstract

Robust stability is a major concern for real-world control applications. Realization of optimal robust stability requires a stabilization scheme, which ensures that the control system is stable and presents robust performance for a predefined range of system perturbations. This study presented an optimal robust stabilization approach for closed-loop fractional order proportional integral derivative (FOPID) control systems with interval parametric uncertainty and uncertain time delay. This stabilization approach, which is carried out in a v-plane, relies on the placement of the minimum angle system pole to a predefined target angle within the stability region of the first Riemann sheet. For this purpose, tuning of FOPID controller coefficients was performed to minimize a root angle error that is defined as the squared difference of minimum angle root of interval characteristic polynomials and the desired target angle within the stability region of the v-plane. To solve this optimization problem, a particle swarm optimization (PSO) algorithm was implemented. Findings of the study reveal that tuning of the target angle can also be used to improve the robust control performance of interval uncertain FOPID control systems. Illustrative examples demonstrated the effectiveness of the proposed v-domain, optimal, robust stabilization of FOPID control systems.

Optimal fractional-order PID control design for time-delayed multi-input multi-output seismic-excited structural system

“…The idea of combining the theory of fractional calculus with the PID controller introduced a new member of the PID controller family called FOPID controllers, which have attracted many controller designers’ attention. During the past two decades, some analytical and heuristic methods have been utilized to design FOPID controllers in different areas (Muresan et al, 2016a; Zamani et al, 2016; Gad et al, 2017; Dulf et al, 2017; Dulf, 2019; Birs et al, 2020; Mohanty and Panda, 2021; Sibtain et al, 2021; Yang et al, 2021; Parnianifard et al, 2021; Altbawi et al, 2021; Tufenkci et al, 2021). In heuristic methods, some researchers use frequency-domain approaches to define the cost functions (Dulf et al, 2016, 2017; Dulf and Kovacs, 2018; Székely et al, 2019; Ionescu et al, 2020), and some researchers use time-domain approaches for this issue (Alamdar-Ravari and Yaghoobi 2019; Zhang et al, 2019; Hekimoğlu 2019; Ayas and Sahin 2020; Girgis et al, 2020; Jumani et al, 2020; Micev et al, 2020; Mohapatra et al, 2020; Paiva et al, 2020; Yang et al, 2021; Aseem and Kumar 2021; Sibtain et al, 2021).…”