Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System
Joint Authors
Wang, Yan
Liu, Chongxin
Zhu, Ziwei
Sun, Zhenquan
Liu, Ling
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-11-07
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
In this paper, fractional calculus is applied to establish a novel fractional-order ferroresonance model with fractional-order magnetizing inductance and capacitance.
Some basic dynamic behaviors of this fractional-order ferroresonance system are investigated.
And then, considering noncommensurate orders of inductance and capacitance and unknown parameters in an actual ferroresonance system, this paper presents a novel fractional-order adaptive backstepping control strategy for a class of noncommensurate fractional-order systems with multiple unknown parameters.
The virtual control laws and parameter update laws are designed in each step.
Thereafter, a novel fractional-order adaptive controller is designed in terms of the fractional Lyapunov stability theorem.
The proposed control strategy requires only one control input and can force the output of the chaotic system to track the reference signal asymptotically.
Finally, the proposed method is applied to a noncommensurate fractional-order ferroresonance system with multiple unknown parameters.
Numerical simulation confirms the effectiveness of the proposed method.
In addition, the proposed control strategy also applies to commensurate fractional-order systems with unknown parameters.
American Psychological Association (APA)
Wang, Yan& Liu, Ling& Liu, Chongxin& Zhu, Ziwei& Sun, Zhenquan. 2018. Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1209158
Modern Language Association (MLA)
Wang, Yan…[et al.]. Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System. Mathematical Problems in Engineering No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1209158
American Medical Association (AMA)
Wang, Yan& Liu, Ling& Liu, Chongxin& Zhu, Ziwei& Sun, Zhenquan. Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1209158
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1209158