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Precision motion control of a piezoelectric cantilever positioning system with rate-dependent hysteresis nonlinearities

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Abstract

The study proposed a feedforward– feedback combined architecture to control a piezoelectric motion system with rate-dependent hysteresis nonlinearities. First, the feedforward control that considered the inverse rate-dependent Prandtl–Ishlinskii (RDPI) model was presented. Based on the inverse RDPI model, a formula that characterizes the output of the inverse compensation considering modeling errors and uncertainties was obtained. More precisely, the output of the inverse compensation of RDPI model consists of an invertible linear term and a bounded nonlinear term. Afterward, the feedforward control is extended with a feedback control architecture. In order to satisfy performance criteria in the presence of the uncertainties, the design of the feedback controller was based on the performances inclusion theorem from interval techniques. Experiments were conducted on a piezoelectric actuator to confirm the effectiveness of the combined feedforward–feedback control.

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Funding

Funding: this study was funded by the French ANR agency, with Number ANR-17-CE05-0014-01 (CODE-Track Project), the Natural Sciences and Engineering Research Council of Canada, and Mobility funding for researchers (the French Embassy in Ottawa).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Memorial University, St. John’s, NL, A1B 3X5, Canada

    Mohammad Al Janaideh

  2. Laboratoire Génie de Production, National School of Engineering in Tarbes (ENIT-INPT), University of Toulouse, Tarbes, France

    Micky Rakotondrabe

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  1. Mohammad Al Janaideh
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  2. Micky Rakotondrabe
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Correspondence to Micky Rakotondrabe.

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Al Janaideh, M., Rakotondrabe, M. Precision motion control of a piezoelectric cantilever positioning system with rate-dependent hysteresis nonlinearities. Nonlinear Dyn 104, 3385–3405 (2021). https://doi.org/10.1007/s11071-021-06460-w

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