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Research Papers

Observer Design for Singularly Perturbed Systems With Multirate Sampled and Delayed Measurements

[+] Author and Article Information
Chunyu Yang

School of Information and Electrical Engineering,
China University of Mining and Technology,
Xuzhou 221116, China
e-mail: chunyuyang@cumt.edu.cn

Lingli Zhang

School of Information and Electrical Engineering,
China University of Mining and Technology,
Xuzhou 221116, China
e-mail: sylinglizhang@126.com

Linna Zhou

School of Information and Electrical Engineering,
China University of Mining and Technology,
Xuzhou 221116, China
e-mail: linnazhou@cumt.edu.cn

1Corressponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 27, 2015; final manuscript received February 2, 2016; published online March 11, 2016. Assoc. Editor: M. Porfiri.

J. Dyn. Sys., Meas., Control 138(5), 051007 (Mar 11, 2016) (9 pages) Paper No: DS-15-1349; doi: 10.1115/1.4032747 History: Received July 27, 2015; Revised February 02, 2016

This paper considers observer design problem of singularly perturbed systems (SPSs) with multirate sampled and delayed measurements. The outputs are classified into two sets which are measured at different sampling rates and subject to transmission delays. The error system is modeled as a continuous-time SPS with a slow-varying delay and a fast-varying delay. A new Lyapunov functional taking the delay properties into account is constructed. Based on the Lyapunov–Krasovskii functional, sufficient conditions for stability of the error system are proposed by which an observer design method is proposed. A realistic example is used to illustrate the obtained results.

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Fig. 1

One-link flexible robot arm

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Fig. 2

The state responses and their estimates with Ts=0.5,Tf=0.1,ξ=0.1, and η=0.01

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Fig. 3

Comparison of the estimation errors: case 1—Ts=0.5,Tf=0.1,ξ=0.2, and η=0.02; case 2—Ts=0.5,Tf=0.1,ξ=0.2,and η=0.02; and case 3—Ts=0.8,Tf=0.2,ξ=0.1,η=0.01

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