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Robust tracking control of a shaking table with dry friction

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Abstract

In this paper, the design, analysis, implementation, and evaluation of two tracking algorithms to control the motion of a shaking table are described. This mechanism is a component of an experimental platform used to study the effect of oscillatory signals on mechanical structures. The table, driven by a linear brushless motor, presents high dry friction. It is intended to attenuate the negative effects due to this phenomena. The first algorithm is a classical PD controller with friction and disturbance compensation. This controller requires a prior modeling of the mechanism and a good tuning of the control parameters. The second algorithm is a sliding-mode controller based on a non-connected switching surface. This controller makes the system produce a combined sliding motion of first order in a first stage and then a second-order sliding motion. It makes the system converge to the desired trajectory in finite time. The platform instrumentation provides only the measurement of the table position; thus, a discontinuous observer has been included to estimate the velocity. It is shown that both controllers display a good tracking, although the discontinuous algorithm exhibits a better performance.

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Acknowledgments

This work was partially funded by the National Council for Science and Technology of Mexico (CONACYT), under the Grant Nb. CB2012-180011-Y.

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  1. Centro de Investigación Científica y de Educación Superior de Ensenada, Carretera Ensenada-Tijuana No. 3918, Zona Playitas, Ensenada, B.C., Mexico

    Gerardo Hirata, Joaquin Alvarez & Ricardo Cuesta

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  1. Gerardo Hirata
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  2. Joaquin Alvarez
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  3. Ricardo Cuesta
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Correspondence to Gerardo Hirata.

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Hirata, G., Alvarez, J. & Cuesta, R. Robust tracking control of a shaking table with dry friction. Nonlinear Dyn 86, 1535–1547 (2016). https://doi.org/10.1007/s11071-016-2975-y

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