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Controlling chaos in bi-stable energy harvesting systems using delayed feedback control

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Chaotic behavior in Bi-stable Energy Harvesters (BEHs) drastically decreases the harvested energy and makes the interface circuit design complicated and expensive. Control of chaos in BEHs has been proposed in few recent researches. In controlling chaos for BEHs, it is essential to notice that the amplitude of targeted High Energy Orbit (HEO) is unknown due to the variable nature of the amplitude of input excitation. Control of chaos in the BEHs is considered in this study to increase the energy harvester’s efficiency. A control system based on a chaos detection algorithm and delayed feedback control is presented to control chaos in the harvester. Chaos detection algorithm can predict chaotic behavior and distinguish chaotic behavior from measurement noise. The Delayed Feedback Controller can control the chaotic behavior in the bi-stable energy harvester without a need for the amplitude of the HEO to be known. Numerical simulations of the controlled system’s response show that the control system can successfully detect and control the chaos. The calculation of the output power of the controlled BEH indicates that the energy harvester has maximum output power when the control gain is set to be its minimum possible amount, and the time delay is precisely the time period of the input excitation. A study of the harvester’s energy balance is carried out, and the time required to recover the consumed energy in the actuator is achieved. This study shows that the controlled BEH can quickly recover the consumed energy in the controller.

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Acknowledgements

The authors M. Mohammadpour, P. Safarpour, R. Gavagsaz-Ghoachani, and M. Zandi gratefully acknowledge the Tehran Urban Research and Planning Center for their support of this research.

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Authors and Affiliations

  1. Department of Mechanical and Energy Engineering, Abbaspour University of Technology: Technical and Engineering Campus of Shahid Beheshti University, Tehran, Iran

    M. Mohammadpour, P. Safarpour, R. Gavagsaz-Ghoachani & M. Zandi

  2. Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM, 88003, USA

    A. Abdelkefi

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  1. M. Mohammadpour
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Mohammadpour, M., Abdelkefi, A., Safarpour, P. et al. Controlling chaos in bi-stable energy harvesting systems using delayed feedback control. Meccanica 58, 587–606 (2023). https://doi.org/10.1007/s11012-022-01599-1

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