The and sliding mode observers are important in integer-order dynamic systems. However, these observers are not well explored in the field of fractional-order dynamic systems. In this paper, the filter and the fractional-order sliding mode unknown input observer are developed to estimate state of the linear time-invariant fractional-order dynamic systems with consideration of proper initial memory effect. As the first result, the fractional-order filter is introduced, and it is shown that the gain from the noise to the estimation error is bounded in the sense of the norm. Based on the extended bounded real lemma, the filter design is formulated in a linear matrix inequality form, and it will be seen that numerical methods to solve convex optimization problems are feasible in fractional-order systems (FOSs). As the second result of this paper, not only state but also unknown input disturbance are estimated by fractional-order sliding-mode unknown input observer, simultaneously. In this paper, it is shown that the design and stability analysis of the two estimation techniques are not related with the initial history. Through two numerical examples, the performance of the fractional-order filter and the fractional-order sliding-mode observer is illustrated with consideration of the initialization functions.
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September 2014
Research-Article
and Sliding Mode Observers for Linear Time-Invariant Fractional-Order Dynamic Systems With Initial Memory Effect
Sang-Chul Lee,
Sang-Chul Lee
School of Mechatronics,
e-mail: sclee@gist.ac.kr
Gwangju Institute of Science
and Technology (GIST)
,123 Cheomdan-gwagiro, Buk-gu
,Gwangju 500-712
, Korea
e-mail: sclee@gist.ac.kr
Search for other works by this author on:
Yan Li,
Yan Li
School of Control Science and Engineering,
e-mail: liyan.sdu@gmail.com
Shandong University
,17923 Jingshi Road
,Jinan Shandong Province 250061
, China
e-mail: liyan.sdu@gmail.com
Search for other works by this author on:
YangQuan Chen,
YangQuan Chen
School of Engineering,
e-mail: ychen53@ucmerced.edu
University of California Merced
,5200 North Lake Road
,Merced, CA 95343
e-mail: ychen53@ucmerced.edu
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Hyo-Sung Ahn
Hyo-Sung Ahn
School of Mechatronics,
e-mail: hyosung@gist.ac.kr
Gwangju Institute of Science
and Technology (GIST)
,123 Cheomdan-gwagiro, Buk-gu
,Gwangju 500-712
, Korea
e-mail: hyosung@gist.ac.kr
Search for other works by this author on:
Sang-Chul Lee
School of Mechatronics,
e-mail: sclee@gist.ac.kr
Gwangju Institute of Science
and Technology (GIST)
,123 Cheomdan-gwagiro, Buk-gu
,Gwangju 500-712
, Korea
e-mail: sclee@gist.ac.kr
Yan Li
School of Control Science and Engineering,
e-mail: liyan.sdu@gmail.com
Shandong University
,17923 Jingshi Road
,Jinan Shandong Province 250061
, China
e-mail: liyan.sdu@gmail.com
YangQuan Chen
School of Engineering,
e-mail: ychen53@ucmerced.edu
University of California Merced
,5200 North Lake Road
,Merced, CA 95343
e-mail: ychen53@ucmerced.edu
Hyo-Sung Ahn
School of Mechatronics,
e-mail: hyosung@gist.ac.kr
Gwangju Institute of Science
and Technology (GIST)
,123 Cheomdan-gwagiro, Buk-gu
,Gwangju 500-712
, Korea
e-mail: hyosung@gist.ac.kr
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 13, 2013; final manuscript received March 21, 2014; published online July 9, 2014. Assoc. Editor: Hashem Ashrafiuon.
J. Dyn. Sys., Meas., Control. Sep 2014, 136(5): 051022 (13 pages)
Published Online: July 9, 2014
Article history
Received:
September 13, 2013
Revision Received:
March 21, 2014
Citation
Lee, S., Li, Y., Chen, Y., and Ahn, H. (July 9, 2014). " and Sliding Mode Observers for Linear Time-Invariant Fractional-Order Dynamic Systems With Initial Memory Effect." ASME. J. Dyn. Sys., Meas., Control. September 2014; 136(5): 051022. https://doi.org/10.1115/1.4027289
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