Fractional-Order Fast Terminal Sliding Mode Control for a Class of Dynamical Systems

This study aims to develop a variable-order fuzzy fractional proportional-integral-differential (VOFFPID) control system for controlling the mover position of a newly designed voice coil motors- (VCMs-) driven dual-axis positioning stage. First, the operation principle and dynamics of the stage are analyzed. After that, the design of a fuzzy fractional proportional-integral-differential (FFPID) control system is introduced on the basis of a fractional calculus and fuzzy logic system. With an additional degree of freedom to the control parameters and fuzzy operation, the FFPID control system can upgrade the contour tracking performance of a conventional proportional-integral-differential (PID) control system with respect to the specified dynamics of the stage. Moreover, the VOFFPID control system is designed to further improve the tracking responses of the FFPID control system. In this system, the five control parameters are optimized with the cuckoo search algorithm via an adaptive strategy. Lastly, nominal and payload conditions attributed to two nonlinear contour demands are provided to evaluate the contouring performance of the PID, FFPID, and VOFFPID control systems. The experimental results subjected to different performance measures demonstrate that the proposed VOFFPID controller outperforms PID and FFPID controllers in terms of the designed VCMs-driven dual-axis positioning stage under both conditions.

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“…where m is an integer such that m > λ. Moreover, the λ thorder RL FO integral of f(t) is defined as follows [30]:…”

Section: Fo Integral and Differentialmentioning

confidence: 99%

Nonlinear Contour Tracking of a Voice Coil Motors-Driven Dual-Axis Positioning Stage Using Fuzzy Fractional PID Control with Variable Orders

Chen

Yang²

2021

Mathematical Problems in Engineering

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“…X.Cai used multiple fractional differential equations to simulate fractional order control systems [28]. G.D. Zhao proposed a new hierarchical fast terminal sliding mode control strategy for a class of uncertain dynamical systems [29]. Y. Li analyzed the Mittag Leffler stability automation of fractional order nonlinear dynamical systems [30].Y.…”

Section: Introductionmentioning

confidence: 99%

Study on resonance and bifurcation of fractional order nonlinear Duffing System

Bai

Xie

Yang

et al. 2022

Preprint

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In this paper, resonance and bifurcation of a nonlinear damped fractional-order Duffing system are studied. The amplitude and phase of the steady-state response of system are obtained by means of average method, and then the amplitude-frequency characteristic curves of the system under different parameters are drawn based on the implicit function equation of amplitude. Grunwald-Letnikov fractional derivative is used to discretize the system numerically, and the response curve and phase trajectory of the system under different parameters are obtained, and the dynamic behavior is analyzed. The forked bifurcation behavior and saddle bifurcation behavior of the system under different parameters are investigated by numerical simulation.

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“…27 Zhao proposed a new hierarchical fast terminal sliding mode control strategy for a class of uncertain dynamical systems. 28 Li analyzed the Mittag-Leffler stability automation of fractional order nonlinear dynamical systems. 29 Qin studied an effective analysis method for solving some fractional order dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

“…Cai used multiple fractional differential equations to simulate fractional order control systems 27 . Zhao proposed a new hierarchical fast terminal sliding mode control strategy for a class of uncertain dynamical systems 28 . Li analyzed the Mittag–Leffler stability automation of fractional order nonlinear dynamical systems 29 .…”

Section: Introductionmentioning

confidence: 99%

Analysis of resonance and bifurcation in a fractional order nonlinear Duffing system

Bai

Yang

Xie

et al. 2022

Math Methods in App Sciences

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In this paper, resonance and bifurcation of a nonlinear damped fractional‐order Duffing system are studied. The amplitude and phase of the steady‐state response of system are obtained by means of the average method, the stability is analyzed, and then the amplitude‐frequency characteristic curves of the system with different parameters are drawn based on the implicit function equation of amplitude. Grunwald–Letnikov fractional derivative is used to discretize the system numerically, the response curve and phase trajectory of the system under different parameters are obtained; meanwhile, the dynamic behavior is analyzed. The bifurcation and saddle bifurcation behavior of the system is studied through numerical simulation with different parameters.

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Fractional-Order Fast Terminal Sliding Mode Control for a Class of Dynamical Systems

Cited by 7 publications

References 30 publications

Nonlinear Contour Tracking of a Voice Coil Motors-Driven Dual-Axis Positioning Stage Using Fuzzy Fractional PID Control with Variable Orders

Nonlinear Contour Tracking of a Voice Coil Motors-Driven Dual-Axis Positioning Stage Using Fuzzy Fractional PID Control with Variable Orders

Study on resonance and bifurcation of fractional order nonlinear Duffing System

Analysis of resonance and bifurcation in a fractional order nonlinear Duffing system

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