Optimal fractional Luenberger observers for linear fractional-order systems are developed using the fractional Chebyshev collocation (FCC) method. It is shown that the design method has advantages over existing Luenberger design methods for fractional order systems. To accomplish this, the state transition operator for the solution of linear fractional-order systems is defined in a Banach space and discretized using the FCC method. In addition, the discretized state transition operator is obtained by using the FCC method. Next, the optimal observer gains are obtained by minimizing the spectral radius of the state transition operator for the observer,while ensuring that the observer responds faster than the controller. Finally, a numerical example is provided to demonstrate the validity and the efficiency of the proposed method.
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ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 6–9, 2017
Cleveland, Ohio, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-5820-2
PROCEEDINGS PAPER
Design of Optimal Fractional Luenberger Observers for Linear Fractional-Order Systems
Arman Dabiri,
Arman Dabiri
University of Arizona, Tucson, AZ
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Eric A. Butcher
Eric A. Butcher
University of Arizona, Tucson, AZ
Search for other works by this author on:
Arman Dabiri
University of Arizona, Tucson, AZ
Eric A. Butcher
University of Arizona, Tucson, AZ
Paper No:
DETC2017-68328, V006T10A019; 7 pages
Published Online:
November 3, 2017
Citation
Dabiri, A, & Butcher, EA. "Design of Optimal Fractional Luenberger Observers for Linear Fractional-Order Systems." Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 6: 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Cleveland, Ohio, USA. August 6–9, 2017. V006T10A019. ASME. https://doi.org/10.1115/DETC2017-68328
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