Research Papers

Fractional-Order Nonlinear Disturbance Observer Based Control of Fractional-Order Systems

[+] Author and Article Information
Aldo Jonathan Muñoz-Vázquez

Mechatronic Engineering,
Polytechnic University of Victoria,
Ciudad Victoria 87138,
Tamaulipas, Mexico
e-mail: amunozv@upv.edu.mx

Vicente Parra-Vega

Robotics and Advanced Manufacturing,
Research Center for Advanced Studies,
Saltillo 25900,
Coahuila, Mexico
e-mail: vparra@cinvestav.edu.mx

Anand Sánchez-Orta

Robotics and Advanced Manufacturing,
Research Center for Advanced Studies,
Saltillo 25900,
Coahuila, Mexico
e-mail: anand.sanchez@cinvestav.edu.mx

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 31, 2018; final manuscript received April 30, 2018; published online May 30, 2018. Assoc. Editor: Zaihua Wang.

J. Comput. Nonlinear Dynam 13(7), 071007 (May 30, 2018) (8 pages) Paper No: CND-18-1047; doi: 10.1115/1.4040129 History: Received January 31, 2018; Revised April 30, 2018

The robust control for a class of disturbed fractional-order systems is presented in this paper. The proposed controller considers a dynamic observer to exactly compensate for matched disturbances in finite time, and a procedure to compensate for unmatched disturbances is then derived. The proposed disturbance observer is built upon continuous fractional sliding modes, producing a fractional-order reaching phase, leading to a continuous control signal, yet able to reject for some continuous but not necessarily differentiable disturbances. Numerical simulations and comparisons are presented to highlight the reliability of the proposed scheme.

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Grahic Jump Location
Fig. 1

Nowhere differentiable disturbance

Grahic Jump Location
Fig. 2

Matched disturbance compensation. Fractional-order disturbance observer φ̂(t)=φ̂(tn)+γtnItαsign(σ(t)): (a) t versus φ̂(t), (b) t versus σ(t)=∫(φ−φ̂), and (c) t versus x(t).

Grahic Jump Location
Fig. 3

Matched disturbance compensation. Integer-order disturbance observer φ̂(t)=γ(σ(t)/‖σ(t)‖): (a) t versus φ̂(t), (b) t versus σ(t)=∫(φ−φ̂), and (c) t versus x(t).

Grahic Jump Location
Fig. 4

Matched disturbance compensation. Approximated integer-order disturbance observer φ̂(t)=γ(σ(t)/‖σ(t)‖+δ): (a) t versus φ̂(t), (b) t versus σ(t)=∫(φ−φ̂), and (c) t versus x(t).

Grahic Jump Location
Fig. 5

Unmatched disturbance. Disturbance estimation: (a) t versus φ1(t), (b) t versus φ̂1(t), and (c) t versus σ(t)=∫(φ1−φ̂1).

Grahic Jump Location
Fig. 6

Unmatched disturbance. Pseudostate and control signal. (a) t versus x̃2(t), (b) t versus u(t), and (c) t versus x1(t).



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