A two-step hybrid approach for modeling the nonlinear dynamic response of piezoelectric energy harvesters

An effective hybrid computational framework is described here in order to assess the nonlinear dynamic response of piezoelectric energy harvesting devices. The proposed strategy basically consists of two steps. First, fully coupled multiphysics finite element (FE) analyses are performed to evaluate the nonlinear static response of the device. An enhanced reduced-order model is then derived, where the global dynamic response is formulated in the state-space using lumped coefficients enriched with the information derived from the FE simulations. The electromechanical response of piezoelectric beams under forced vibrations is studied by means of the proposed approach, which is also validated by comparing numerical predictions with some experimental results. Such numerical and experimental investigations have been carried out with the main aim of studying the influence of material and geometrical parameters on the global nonlinear response. The advantage of the presented approach is that the overall computational and experimental efforts are significantly reduced while preserving a satisfactory accuracy in the assessment of the global behavior

Nonlinear Energy Harvesting Under White Noise

While purposeful introduction of stiffness nonlinearities into the dynamics of energy harvesters is aimed at enhancing performance under non-stationary and random excitations, most of the conclusions reported in the current literature are based on the steady-state response which assumes a harmonic fixed-frequency excitation. As a result, we still do not have a clear understanding of how the nature of the excitation influences the output power, or what role stiffness nonlinearities play in the transduction of energy harvesters under random excitations. To fill this gap in the current knowledge, this thesis investigates the response of nonlinear mono- and bi-stable energy harvesters to environmental excitations that can be approximated via a white noise process. For the mono-stable case, statistical linearization is utilized to analytically approximate the statistical averages of the response. The influence of the nonlinearity and the symmetry of the restoring force on the mean power is investigated under optimal electric loading conditions. It is shown that the nonlinearity has no influence on the output power unless the ratio between the time constant of the harvesting circuit and the period of the mechanical oscillator is small. In such case, a mono-stable harvester with a symmetric nonlinear restoring force can never produce higher mean power levels than an equivalent linear harvester regardless of the magnitude or nature of the nonlinearity. On the other hand, asymmetries in the restoring force are shown to provide performance improvements over an equivalent linear harvester. For energy harvesters with a bi-stable potential function, statistical linearization, direct numerical integration of the stochastic differential equations, and finite element solution of the Fokker-Plank-Kolmogorov equation governing the response probability density function are utilized to understand how the shape and symmetry of the potential energy function influence the mean output power of the harvester. It is observed that, both of the finite element solution and the direct numerical integration provide close predictions for the mean power regardless of the shape of the potential energy function. Statistical linearization, on the other hand, yields non-unique and erroneous predictions unless the potential energy function has shallow potential wells. It is shown that the mean power exhibits a maximum value at an optimal potential shape. This optimal shape is not directly related to the shape that maximizes the mean square displacement even when the time constant ratio, i.e., ratio between the time constants of the mechanical and electrical systems is small. Maximizing the mean square displacement yields a potential shape with a global maximum (unstable potential) for any value of the time constant ratio and any noise intensity, whereas maximizing the average power yields a bi-stable potential which possesses deeper potential wells for larger noise intensities and vise versa. Away from the optimal shape, the mean power drops significantly highlighting the importance of characterizing the noise intensity of the vibration source prior to designing a bi-stable harvester for the purpose of harnessing energy from white noise excitations. Furthermore, it is demonstrated that, the optimal time constant ratio is not necessarily small which challenges previous conceptions that a bi-stable harvester provides better output power when the time constant ratio is small. While maximum variation of the mean power with the nonlinearity occurs for smaller values of the time constant ratio, these values do not necessarily correspond to the optimal performance of the harvester. Finally, it is shown that asymmetries in the potential shape of bi-stable harvesters do not improve the mean power unless the symmetric potential function is designed away from its optimal parameters

Study, optimization and silicon implementation of a smart high-voltage conditioning circuit for electrostatic vibration energy harvesting system

La récupération de l'énergie des vibrations est un concept relativement nouveau qui peut être utilisé dans l'alimentation des dispositifs embarqués de puissance à micro-échelle avec l'énergie des vibrations omniprésentes dans l environnement. Cette thèse contribue à une étude générale des récupérateurs de l'énergie des vibrations (REV) employant des transducteurs électrostatiques. Un REV électrostatique typique se compose d'un transducteur capacitif, de l'électronique de conditionnement et d un élément de stockage. Ce travail se concentre sur l'examen du circuit de conditionnement auto-synchrone proposé en 2006 par le MIT, qui combine la pompe de charge à base de diodes et le convertisseur DC-DC inductif de type de flyback qui est entraîné par le commutateur. Cette architecture est très prometteuse car elle élimine la commande de grille précise des transistors utilisés dans les architectures synchrones, tandis qu'un commutateur unique se met en marche rarement. Cette thèse propose une analyse théorique du circuit de conditionnement. Nous avons développé un algorithme qui par commutation appropriée de flyback implémente la stratégie de conversion d'énergie optimale en tenant compte des pertes liées à la commutation. En ajoutant une fonction de calibration, le système devient adaptatif pour les fluctuations de l'environnement. Cette étude a été validée par la modélisation comportementale.Une autre contribution consiste en la réalisation de l'algorithme proposé au niveau du circuit CMOS. Les difficultés majeures de conception étaient liées à l'exigence de haute tension et à la priorité de la conception faible puissance. Nous avons conçu un contrôleur du commutateur haute tension de faible puissance en utilisant la technologie AMS035HV. Sa consommation varie entre quelques centaines de nanowatts et quelques microwatts, en fonction de nombreux facteurs - paramètres de vibrations externes, niveaux de tension de la pompe de charge, la fréquence de la commutation de commutateur, la fréquence de la fonction de calibration, etc.Nous avons également réalisé en silicium, fabriqué et testé un commutateur à haute tension avec une nouvelle architecture de l'élévateur de tension de faible puissance. En montant sur des composants discrets de la pompe de charge et du circuit de retour et en utilisant l'interrupteur conçu, nous avons caractérisé le fonctionnement large bande haute-tension du prototype de transducteur MEMS fabriqué à côté de cette thèse à l'ESIEE Paris. Lorsque le capteur est excité par des vibrations stochastiques ayant un niveau d'accélération de 0,8 g rms distribué dans la bande 110-170 Hz, jusqu'à 0,75 W de la puissance nette a été récupérée.Vibration energy harvesting is a relatively new concept that can be used in powering micro-scale power embedded devices with the energy of vibrations omnipresent in the surrounding. This thesis contributes to a general study of vibration energy harvesters (VEHs) employing electrostatic transducers. A typical electrostatic VEH consists of a capacitive transducer, conditioning electronics and a storage element. This work is focused on investigations of the reported by MIT in 2006 auto-synchronous conditioning circuit, which combines the diode-based charge pump and the inductive flyback energy return driven by the switch. This architecture is very promising since it eliminates precise gate control of transistors employed in synchronous architectures, while a unique switch turns on rarely. This thesis addresses the theoretical analysis of the conditioning circuit. We developed an algorithm that by proper switching of the flyback allows the optimal energy conversion strategy taking into account the losses associated with the switching. By adding the calibration function, the system became adaptive to the fluctuations in the environment. This study was validated by the behavioral modeling. Another contribution consists in realization of the proposed algorithm on the circuit level. The major design difficulties were related to the high-voltage requirement and the low-power design priority. We designed a high-voltage analog controller of the switch using AMS035HV technology. Its power consumption varies between several hundred nanowatts and a few microwatts, depending on numerous factors - parameters of external vibrations, voltage levels of the charge pump, frequency of the flyback switching, frequency of calibration function, etc. We also implemented on silicon, fabricated and tested a high-voltage switch with a novel low power level-shifting driver. By mounting on discrete components the charge pump and flyback circuit and employing the proposed switch, we characterized the wideband high-voltage operation of the MEMS transducer prototype fabricated alongside this thesis in ESIEE Paris. When excited with stochastic vibrations having an acceleration level of 0.8 g rms distributed in the band 110-170 Hz, up to 0.75 $\mu$W of net electrical power has been harvested.PARIS-JUSSIEU-Bib.électronique (751059901) / SudocSudocFranceF