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Experiment-based identification of time delays in linear systems

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Abstract

This paper presents an identification approach to time delays in single-degree-of-freedom (SDOF) and multiple-degree-of-freedom (MDOF) systems. In an SDOF system, the impedance function of the delayed system is expressed by the system parameters, the feedback gain, and the time delay. The time delay can be treated as the “frequency” of the difference between the impedance function of the delayed system and that of the corresponding uncontrolled system. Thus, it can be identified from the Fourier transform of the difference between the two impedance functions. In an MDOF system, the pseudo-impedance functions are defined. The relationships between the time delay and the pseudo-impedance functions of the delayed system and uncontrolled system are deduced. Similarly, the time delay can be identified from the Fourier transform of the difference between the two pseudo-impedance functions. The results of numerical examples and experimental tests show that the identification approach to keeps a relatively high accuracy.

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Acknowledgements

This project was supported by the National Natural Science Foundation of China (Grant 11272235).

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Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Meng-Shi Jin, Han-Wen Song & Jian Xu

  2. Shanghai Engineering Center for Microsatellites, Shanghai, 201210, China

    Yi-Qiang Sun

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  1. Meng-Shi Jin
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  2. Yi-Qiang Sun
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  3. Han-Wen Song
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  4. Jian Xu
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Correspondence to Han-Wen Song.

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Jin, MS., Sun, YQ., Song, HW. et al. Experiment-based identification of time delays in linear systems. Acta Mech. Sin. 33, 429–439 (2017). https://doi.org/10.1007/s10409-017-0652-0

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