Fractional-order iterative learning control for singular fractional- order system: (P) - PDa type

Abstract

Iterative learning control (ILC) is one of the recent topics in control theories and it is suitable for controlling a wider class of mechatronic systems -it is especially suitable for the motion control of robotic systems. This paper addresses the problem of application of fractional order ILC for fractional order singular system. Particularly, we study fractional order singular systems in the pseudo-state space. An closed-loop fractional order PDalpha type ILC of the fractional-order singular system is investigated. Also, open-closed loop of the fractional order P-PDa type ILC is considered. Sufficient conditions for the convergence in the time domain of the proposed ILC schemes are given by the corresponding theorems and proved. Finally, numerical simulations show the feasibility and effectiveness of the proposed approach.

Convergence on iterative learning control of Hilfer fractional impulsive evolution equations

“…The results in their paper expose the fact that the learning convergence for fractional‐order derivative gets progressively monotonic when compared to integer order. Also, an example was given by Chen and Moore [10] to elaborate on the advantage of fractional‐order, whereas an algorithm for $$$ P{D}^{\alpha } $$$ was proposed by Lazarevic [11]. Li et al [12] discussed the convergence of the iterative control of fractional‐order system in the time domain.…”

Closed-loop iterative learning control for fractional-order linear singular time-delay system: PDα-type

“…Besides, the fractional order iterative learning control is the latest trend in ILC research, it not only retains the advantages of the classical ILC, but also offers potential for better performances in a variety of complex physical processes. Even since the above literature suggested this good learning performance, there have been made some efforts to synthesize a better FOILC updating law for various types of fractional order systems, and we have witnessed some progress in the previous years, [36][37][38][39][40][41][42][43][44][45][46][47]. For example, a fractional-order D-type ILC algorithm was proposed in the frequency domain [36], and the convergence was investigated by means of the recursively direct discretization technique.…”

“…The most of the existing fractional-order ILC methods for fractional-order systems only focus on the non-singular systems. Moreover, an increasing attention has been paid to fractional calculus (FC) and its application in control and modeling of fractional order singular system [48][49][50][51]. Motivated by the mentioned investigations of ILC algorithms for classical singular systems, as well as ILC fractional order control in the tracking problems of these systems and taking into account that fractional-order models of these systems can be presented as singular systems of fractional order, for the first time, ILC for fractional order singular systems is suggested in paper [48].…”

“…Moreover, an increasing attention has been paid to fractional calculus (FC) and its application in control and modeling of fractional order singular system [48][49][50][51]. Motivated by the mentioned investigations of ILC algorithms for classical singular systems, as well as ILC fractional order control in the tracking problems of these systems and taking into account that fractional-order models of these systems can be presented as singular systems of fractional order, for the first time, ILC for fractional order singular systems is suggested in paper [48]. Namely, we presented and considered in [49], robust iterative learning feedback control second-order for fractional order singular systems, and recently in [50] (P)-PD α type ILC control as well as openclosed-loop fractional-order iterative learning control for singular fractional order system [51].…”