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Optimal Control of Vibration-Based Micro-energy Harvesters

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Abstract

We analyze the maximal output power that can be obtained from a vibration energy harvester. While recent work focused on the use of mechanical nonlinearities and on determining the optimal resistive load at steady-state operation of the transducers to increase extractable power, we propose an optimal control approach. We consider the open-circuit stiffness and the electrical time constant as control functions of linear two-port harvesters. We provide an analysis of optimal controls by means of Pontryagin’s maximum principle. By making use of geometric methods from optimal control theory, we are able to prove the bang–bang property of optimal controls. Numerical results illustrate our theoretical analysis and show potential for more than 200% improvement of harvested power compared to that of fixed controls.

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Acknowledgements

Financial support from the European Research Council via the Consolidator Grant MODEST-647573 is gratefully acknowledged. Thanks to Prof. Giovanni Colombo for his valuable suggestions and to Robert Rantz for proofreading the article.

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Correspondence to Sebastian Sager.

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Communicated by Lars Grüne.

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Le, T.T.T., Jost, F. & Sager, S. Optimal Control of Vibration-Based Micro-energy Harvesters. J Optim Theory Appl 179, 1025–1042 (2018). https://doi.org/10.1007/s10957-018-1250-4

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  • DOI: https://doi.org/10.1007/s10957-018-1250-4

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