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Adaptive nonstationary positioning control of vibration systems by means of solutions of time-varying Riccati equations

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Abstract

The author’s previous study proposed an efficient design method of time-varying gain type controller using the solutions of time-varying Riccati equations (TVREs) and its application to positioning control of time-invariant vibration systems. The responses of this method become similar to the responses of conventional nonstationary optimal regulators (NORs) which are effective controllers for positioning of vibration systems. This method generates the solutions of a TVRE and the responses of a controlled object simultaneously. The time-varying gains are obtained by real-time computations in actual implementations. This feature is convenient for the realization of some adaptive control. However, such a control method has not been fully addressed yet. This study proposes an adaptive nonstationary control (ANSC) method based on the feature of the previous study. We choose a cart with a time-varying vibration system whose natural frequency is time-varying as a controlled object example. The positioning and residual vibration reduction of the object are discussed in this paper. The effectiveness of the ANSC method is verified by simulations and experiments.

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Acknowledgments

The author would like to thank Mr. Michinori Ando from Koriyama Giken Co., Ltd. for his help in conducting the experiments and acknowledges the support of “Academic Frontier” Project for Future Data Storage Materials: matching fund subsidy from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, 2004–2008. A part of this work has close connection with the research project supported by the Grant-in-Aid for Young Scientists by MEXT.

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Authors and Affiliations

  1. Department of Advanced Science and Technology, School of Engineering, Toyota Technological Institute, 2-12-1 Hisakata, Tempaku-ku, Nagoya-shi, Aichi, 468-8511, Japan

    Susumu Hara

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  1. Susumu Hara
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Correspondence to Susumu Hara.

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Hara, S. Adaptive nonstationary positioning control of vibration systems by means of solutions of time-varying Riccati equations. Microsyst Technol 13, 1063–1075 (2007). https://doi.org/10.1007/s00542-006-0316-7

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  • DOI: https://doi.org/10.1007/s00542-006-0316-7

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