Energy Harvesting and Energy Efficiency pp 107-142 | Cite as

# Nonlinear Problems in Piezoelectric Harvesters Under Magnetic Field

## Abstract

This chapter focuses on the nonlinear problems in the piezoelectric harvester systems under the magnetic field. In this manner, the chapter initially mentions an introductory section on the studies of piezoelectric harvester dynamics. After the introductory section, the basic properties of the piezoelectric systems and their energy harvester applications will be presented. Since the harvesters have a complicated structure under the magnetic field, the electromagnetic design, modeling and algebraic studies of a novel harvester study will be pointed out. After the presentation of a theoretical outline on the harvester systems, the experimental setups will be explained in detail. Thus, a complete picture of the problem will be produced in order to sustain a comparable study on the theory and experiment. The main dynamic quantities such as displacement and velocity of the vibrating piezoelectric layer as function of the system parameters will be explored. According to results, the effect of periodic magnetic flux can give varieties of responses from regular dynamics to chaotic one. Phase space constructions, Poincare sections and FFTs are evaluated depending on the parameter sets including the excitation frequency *f*, amplitude *Uc* of electromagnet and the distance *d*. It is proven that the periodic magnetic flux can exert high frequency velocity fluctuations nearby the minimal and maximal values of the velocity, whereas the situation differs for the position. Therefore it will be pointed out that the magnetic field mostly governs the velocity by yielding complicated vibrations. According to the detailed analyses, the FFTs prove the high frequency responses in addition to the main frequency. When *f* differs from the natural frequency of the system *f* _{0}, the responses become chaotic. It is proven that lower and higher frequency fluctuations in displacement and velocity, which are different from *f* _{0} decrease the electrical power harvested by the piezoelectric pendulum. Indeed, it is remarkable to get a relation between the rms values of displacement/velocity and the harvested power according to the measurements. Thus this relation can be used to estimate the power output in harvester systems. The piezoelectric harvester generates much energy when *f* is closed to *f* _{0} and the distance to the magnetic device should be closer in order to decrease the nonlinearities in displacement and velocity. The pendulum-like harvesters as the most preferable ones can be applied to many devices or units as a power source. The maximal power for these magnetically-excited structures can be estimated by the system parameters. At the end of the chapter, the recent techniques of maximal power point tracking (MPPT) and proposed controller units are explained for the piezoelectric harvester systems in order to optimize the harvested power.

## Keywords

Piezoelectric harvester Magnetic field Nonlinearity Attractor Maximal power point tracking## Abbreviations and Acronyms

- MEMS
Micro-electro-mechanical system

- CDRG
Coulomb-damped resonant generator

- DAQ
Data acquisition

- FEM
Finite element method

- FFT
Fast Fourier transform

- MPPT
Maximal power point tracking

- RMS
Root mean square

- SIDO
Single inductor dual output

- SSPB
Single-supply pre-biasing

- THD
Total harmonic distortion

- VDRG
Velocity-damped resonant generator

## Notes

### Acknowledgements

The supports from Gazi University Research Development Unit under Grant Nos. BAP 07/2010-01, BAP 07/2012-12, Turkey Ministry for EU Affairs—National Agency under Grant No. 2015-1-TR01-KA203-021342 and The Scientific and Technological Research Council of Turkey (TUBITAK) under grant EEEAG-114E017 are acknowledged.

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