Onset and stabilization of delay-induced instabilities in piezoelectric digital vibration absorbers
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866913190353305600 |
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| author | Raze, Ghislain Dietrich, Jennifer Kerschen, Gaëtan |
| author_facet | Raze, Ghislain Dietrich, Jennifer Kerschen, Gaëtan |
| contents | The stability of a piezoelectric structure controlled by a digital vibration absorber emulating a shunt circuit is investigated in this work. The formalism of feedback control theory is used to demonstrate that systems with a low electromechanical coupling are prone to delay-induced instabilities entailed by the sampling procedure of the digital unit. An explicit relation is derived between the effective electromechanical coupling factor and the maximum sampling period guaranteeing a stable controlled system. Since this sampling period may be impractically small, a simple modification procedure of the emulated admittance of the shunt circuit is proposed in order to counteract the effect of delays by anticipation. The theoretical developments are experimentally validated on a clamped-free piezoelectric beam. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_06715 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Onset and stabilization of delay-induced instabilities in piezoelectric digital vibration absorbers Raze, Ghislain Dietrich, Jennifer Kerschen, Gaëtan Dynamical Systems The stability of a piezoelectric structure controlled by a digital vibration absorber emulating a shunt circuit is investigated in this work. The formalism of feedback control theory is used to demonstrate that systems with a low electromechanical coupling are prone to delay-induced instabilities entailed by the sampling procedure of the digital unit. An explicit relation is derived between the effective electromechanical coupling factor and the maximum sampling period guaranteeing a stable controlled system. Since this sampling period may be impractically small, a simple modification procedure of the emulated admittance of the shunt circuit is proposed in order to counteract the effect of delays by anticipation. The theoretical developments are experimentally validated on a clamped-free piezoelectric beam. |
| title | Onset and stabilization of delay-induced instabilities in piezoelectric digital vibration absorbers |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2106.06715 |