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Journal of Optimization Theory and Applications

, Volume 179, Issue 3, pp 1025–1042 | Cite as

Optimal Control of Vibration-Based Micro-energy Harvesters

  • Thuy T. T. Le
  • Felix Jost
  • Sebastian SagerEmail author
Article
  • 176 Downloads

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.

Keywords

Optimal control Pontryagin’s maximum principle Switching function Energy harvesting Power optimization 

Mathematics Subject Classification

49K15 49J30 93B40 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Mathematical Optimization, Mathematical Algorithmic OptimizationOtto-von-Guericke UniversityMagdeburgGermany

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