Browsing by Subject "Energy harvesting"

In this thesis, a spherical, rolling magnet generator for passive energy harvesting is investigated. It was designed for gathering energy from human motion. This thesis focuses on the analysis of the dynamics of this device and gives its governing equations. Then under two expected applications, this thesis finds the parameters that greatly influence its efficiency and provide optimal parameter combinations.

This thesis proposes an integrated procedure for identifying the nominal models of the deterministic part and the stochastic part of a system, as well as their model error bounds in different uncertainty structures (e.g. $\mathcal{H}_2$-norm and $\mathcal{H}_{\infty}$-norm) based on the measurement data. In particular, the deterministic part of a system is firstly identified by closed-loop instrumental variable method in which a known external signal sequence uncorrelated with the system noises is injected in the control input for the identifiability of the system in closed loop. By exploiting the second-order statistics of the noise-driven output components, the stochastic part of a system is identified by the improved subspace approach in which a new and straightforward linear-matrix-inequality-based optimization is proposed to obtain a valid model even under insufficient measurement data.

To derive an explicit model error bound on the identification model, we investigate a complete asymptotic analysis for identification of the stochastic part of the system. We first derive the asymptotically normal distributions of the empirical sample covariance and block-Hankel matrix of the outputs. Thanks to these asymptotic distributions and the perturbation analysis of singular value decomposition and discrete algebraic Riccati equation, several central limit theorems for the identified controllability matrix, observability matrix, and the state-space matrices in the associated covariance model are derived, as well as the norm bounds of Kalman gain and the innovations covariance matrix in the innovations model. By combining these asymptotic results, the explicit $\mathcal{H}_2$-norm and $\mathcal{H}_{\infty}$-norm bounds of the model error are identified with a given confidence level.

Practical applicability of the proposed combined deterministic-stochastic identification procedure is illustrated by the application to indirect adaptive control of a multi-generator wave energy harvesting system.

Over the past decade, a significant amount of research activity has been devoted to developing electromechanical systems that can convert ambient mechanical vibrations into usable electric power. Such systems, referred to as vibratory energy harvesters, have a number of useful of applications, ranging in scale from self-powered wireless sensors for structural health monitoring in bridges and buildings to energy harvesting from ocean waves. One of the most challenging aspects of this technology concerns the efficient extraction and transmission of power from transducer to storage. Maximizing the rate of power extraction from vibratory energy harvesters is further complicated by the stochastic nature of the disturbance. The primary purpose of this dissertation is to develop feedback control algorithms which optimize the average power generated from stochastically-excited vibratory energy harvesters.

This dissertation will illustrate the performance of various controllers using two vibratory energy harvesting systems: an electromagnetic transducer embedded within a flexible structure, and a piezoelectric bimorph cantilever beam. Compared with piezoelectric systems, large-scale electromagnetic systems have received much less attention in the literature despite their ability to generate power at the watt--kilowatt scale. Motivated by this observation, the first part of this dissertation focuses on developing an experimentally validated predictive model of an actively controlled electromagnetic transducer. Following this experimental analysis, linear-quadratic-Gaussian control theory is used to compute unconstrained state feedback controllers for two ideal vibratory energy harvesting systems. This theory is then augmented to account for competing objectives, nonlinearities in the harvester dynamics, and non-quadratic transmission loss models in the electronics.

In many vibratory energy harvesting applications, employing a bi-directional power electronic drive to actively control the harvester is infeasible due to the high levels of parasitic power required to operate the drive. For the case where a single-directional drive is used, a constraint on the directionality of power-flow is imposed on the system, which necessitates the use of nonlinear feedback. As such, a sub-optimal controller for power-flow-constrained vibratory energy harvesters is presented, which is analytically guaranteed to outperform the optimal static admittance controller. Finally, the last section of this dissertation explores a numerical approach to compute optimal discretized control manifolds for systems with power-flow constraints. Unlike the sub-optimal nonlinear controller, the numerical controller satisfies the necessary conditions for optimality by solving the stochastic Hamilton-Jacobi equation.

A combined approach of linear convolution and higher order Volterra series to reduced order modelling of unsteady transonic aerodynamic loads is presented. The new approach offers a simple method to determine the memory depth of the system, significantly reduces the effort required to generate a model for a wide range of reduced frequencies, and clearly separates the linear and the non-linear contributions. The generated models are completely separated from any specific input signal or a particular reduced frequency. The models were verified in an aeroelastic simulation of a 2D NACA 0012 airfoil. The results correlate well with wind tunnel tests and previously calculated LCO levels.

Our experimental study sought to answer the question: how to maximize the piezoelectric power extraction of an aeroelastic system? A simple rectangular cantilever plate, which experiences LCO, was used as a basic vibrating system. The plate was covered entirely with piezoelectric elements on both sides. By adding small discrete masses along the plate, we were able to increase the power generation efficiency by 260% while reducing the airspeed required to produce this power by 150%, and the level of vibrations by 320%.

Ocean-based wireless sensor networks serve many important purposes ranging from tsunami early warning to anti-submarine warfare. Developing energy harvesting devices that make these networks self-sufficient allows for reduced maintenance cost and greater reliability. Many methods exist for powering these devices, including internal batteries, photovoltaic cells and thermoelectric generators, but the most reliable method, if realized, would be to power these devices with an internal kinetic energy harvester capable of reliably converting wave motion into electrical power. Designing such a device is a challenge, as the ocean excitation environment is characterized by shifting frequencies across a relatively wide bandwidth. As such, traditional linear kinetic energy harvesting designs are not capable of reliably generating power. Instead, a nonlinear device is better suited to the job, and the task of this dissertation is to investigate the behaviors of devices that could be employed to this end.

This dissertation is motivated by the design and analysis of an ocean energy harvester based on a horizontal pendulum system. In the course of investigating the dynamics of this system, several discoveries related to other energy harvesting systems were made and are also reported herein. It is found that the most reliable method of characterizing the behaviors of a nonlinear energy harvesting device in the characteristically random forcing environment of the ocean is to utilize statistical methods to inform the design of a functional device. It is discovered that a horizontal pendulum-like device could serve as an energy harvesting mechanism in small self-

sufficient wireless sensor buoys if properly designed and if the proper transduction mechanisms are designed and employed to convert the mechanical energy of the device into electrical power.

The focus of this dissertation is on the dynamics of electromagnetic systems for energy harvesting and filtering applications. The inclusion of magnets into systems generates nonlinearity due to the nature of electromagnetic interactions. In this work, magnetic nonlinearity manifests in tip interactions for cantilever beams, coupling effects for electromagnetic transduction, and bistable potential wells for a two beam system. These electromagnetic interactions are used to add non-contact coupling effects for the creation of bistable oscillators or arrays of coupled beams for energy filtering.

Nonlinearity at the tip of cantilever beams acts to change the dynamic and static behavior of the system. In this dissertation, these interactions are analyzed both with and without the nonlinear tip interactions. A linear analysis of the system without the tip interaction first provides insight into the shifting frequencies of the first four natural oscillation modes when considering a rigid body tip mass with rotational inertia and a center of mass that is offset from the tip of the beam. Then, the characterization of the nonlinearities in the beam stiffness and magnetic interaction provide insight into the static and dynamic behavior of the beam. The analytical and numerical investigations, using Rayleigh-Ritz methods and an assumed static deflection, are shown to be consistent with experimental tests. These methods provide a framework for theoretically establishing nonlinear static modes and small-amplitude linear modes that are consistent with physical behavior.

In electromagnetic coupling, the role of nonlinearity can have a detrimental or beneficial effect on energy harvesting. This work includes an investigation of the response of an energy harvester that uses electromagnetic induction to convert ambient vibration into electrical energy. The system's response behavior with linear coupling or a physically motivated form of nonlinear coupling is compared with single and multi-frequency base excitation. This analysis is performed with combined theoretical and numerical studies.

The ability of magnets to add nonlinearity to a system allows for the expansion of the phenomenological behavior of said system and potential advantages and disadvantages for energy harvesting. This work studies a two beam system made up of carbon fiber cantilever beams and attached magnetic tip masses with a focus on energy harvesting potential. Numerical and experimental investigations reveal an array of phenomena from static bifurcations, chaotic oscillations, and sub-harmonic orbits. These features are used to highlight the harvesting prospects for a similarly coupled system.

Beyond nonlinearity, the non-contacting coupling effects of magnets allow for the hypothetical creation of energy filtering systems. In this work, the band structure of a two dimensional lattice of oscillating beams with magnetic tip masses is explored. The focus of the wave propagation analysis is primarily on regions in the band structure where propagation does not occur for the infinite construction of the system. These band gaps are created in this system of 2 x 2 repeating unit cells by periodically varying the mass properties and, for certain configurations, the frequency band gaps manifest in different size and band location. Uncertainty in these regions is analyzed using potential variations associated with specific physical parameters in order to elucidate their influence on the band gap regions. Boundary effects and damping are also investigated for a finite-dimensional array, revealing an erosion of band gaps that could limit the expected functionality.

This paper investigates the static and dynamic characteristics of the semi-elliptical rocking disk on which a pendulum pinned. This coupled system’s response is also analyzed analytically and numerically when a vertical harmonic excitation is applied to the bottom of the rocking disk. Lagrange’s Equation is used to derive the motion equations of the disk-pendulum coupled system. The second derivative test for the system’s potential energy shows how the location of the pendulum’s pivotal point affects the number and stability of equilibria, and the change of location presents different bifurcation diagrams for different geometries of the rocking disk. For both vertically excited and unforced cases, the coupled system shows chaos easily, but the proper chosen parameters can still help the system reach and keep the steady state. For the steady state of the vertically excited rocking disk without a pendulum, the variation of the excitation’s amplitude and frequency result in the hysteresis for the amplitude of the response. When a pendulum is pinned on the rocking disk, three major categories of steady states are presently in the numerical way.

The primary focus of this thesis is on the modeling and control of an electromechanical transducer to harvest energy from large structures (e.g. buildings and bridges). The transducer consists of a back-driven ballscrew coupled to a permanent-magnet synchronous machine. Developing control algorithms to take full advantage of the unique features of this type of transducer requires a mechanical model that can

adequately characterize the device's intrinsic nonlinear behavior. A new model is proposed that can effectively capture this behavior. Comparison with experimental results verifies that the model is accurate over a wide range of operating conditions and that it can be used to correctly design controllers to maximize power generation.

In most vibratory energy harvesting systems the disturbance is most appropriately modeled as a broadband stochastic process. Optimization of the average power generated from such disturbances is a feedback control problem, and the controller can be determined by solving a nonstandard Riccati equation. In this thesis we show that appropriate tuning of passive parameters in the harvesting system results in a decoupled solution to the Riccati equation and a corresponding controller that only requires half of the states for feedback. However, even when the optimal controller requires all of the states for feedback, it is possible to determine the states that contribute the most to the power generation and optimize those partial-state feedback gains using a gradient descent method.

To demonstrate the energy harvesting capability of the transducer, impedance matching theory is used to optimize power from a small, base-excited single-degree-of-freedom (SDOF) oscillator. For this system, both theoretical and experimental investigations are compared and results are shown to match closely. Finally, statistical linearization is used to determine the optimal full-state controller and the optimal static admittance for the experimental SDOF oscillator when it is excited by a stochastic disturbance.

Energy harvesting is a process where self-powered electronic devices scavenge ambient energy and convert it to electrical power. Traditional linear energy harvesters which operate based on linear resonance work well only when excitation frequency is close to its natural frequency. While various control methods applied to an energy harvester realize resonant frequency tuning, they are either energy-consuming or exhibit low efficiency when operating under multi-frequency excitations. In order to overcome these limitations in a linear energy harvester, researchers recently suggested using "nonlinearity" for broad-band frequency response.

Based on existing investigations of nonlinear energy harvesting, this dissertation introduced a novel type of energy harvester designs for space efficiency and intentional nonlinearity: translational-to-rotational conversion. Two dynamical systems were presented: 1) vertically forced rocking elliptical disks, and 2) non-contact magnetic transmission. Both systems realize the translational-to-rotational conversion and exhibit nonlinear behaviors which are beneficial to broad-band energy harvesting.

This dissertation also explores novel methods to overcome the limitation of nonlinear energy harvesting -- the presence of coexisting attractors. A control method was proposed to render a nonlinear harvesting system operating on the desired attractor. This method is based on reinforcement learning and proved to work with various control constraints and optimized energy consumption.

Apart from investigations of energy harvesting, several techniques were presented to improve the efficiency for analyzing generic linear/nonlinear dynamical systems: 1) an analytical method for stroboscopically sampling general periodic functions with arbitrary frequency sweep rates, and 2) a model-free sampling method for estimating basins of attraction using hybrid active learning.

In applications of ocean wave energy conversion, it is well known that feedback control can be used to achieve favorable performance. Current techniques include methods such as tuning a device to harvest energy at a narrow band of frequencies, which leads to suboptimal performance, or methods that are anticausal and require the future wave excitation to be known. This thesis demonstrates how to determine the maximum-attainable power generation and corresponding controller for a buoy type wave energy converter with multiple generators in a stochastic sea environment using a causal dynamic controller. This is accomplished by solving a nonstandard H2 optimal control problem. The performance of the causal controller is compared to the noncausal controller for various cases. This work provides a significant improvement over current control techniques because it involves a causal controller that can absorb a large amount of power over a broader bandwidth than other control techniques, including absorbing power across multiple modes of resonance. The importance of an adaptive control algorithm is also demonstrated.

Mechanical oscillators form the primary structure of a wide variety of devices including energy harvesters and vibration absorbers, and also have parallel systems in electrical fields for signal processing. In the area of wave propagation, recent study in periodic chains have focused on active tuning methods to control bandgap regions, bands in the frequency response in which no propagating wave modes exist. In energy harvesting, several coupled systems have been proposed to enhance the peak power or bandwidth of a single harvester through arrays or dynamic magnification. Though there are applications in several fields, the work in this dissertation can all fit into the category of coupled non-linear oscillators. In each sub-field, this study demonstrates means to advance state of the art techniques by adding nonlinearity to a coupled system of linear oscillators, or by adding a coupled device to a nonlinear oscillator.

The first part of this dissertation develops the analytical methods for studying wave propagation in nonlinear systems. A framework for studying rotational systems is presented and used to design an testbed for wave propagation experiments using a chain of axially aligned pendulums. Standard analytical methods are also adapted to allow uncertainty analysis techniques to provide insight into the relative impact of variations in design parameters. Most analytical insight in these systems is derived from a linearlized model and assumes low amplitude oscillations. Additional study on the nonlinear system is performed to analyze the types of deviations from this behavior that would be expected as amplitudes increase and nonlinear effects become more prominent.

The second part of this dissertation describes and demonstrates the first means of passive control of bandgap regions in a periodic structure. By imposing an asymmetrical bistability to an oscillator in each unit cell, it is analytically shown that each potential well has different wave propagation behaviors. Experimental demonstrations are also provided to confirm the simulated results.

The final section performs analytical and numerical analysis of a new system design to improve the performance of a nonlinear energy harvester by adding an excited dynamic magnifier. It is shown that this addition results in higher peak power and wider bandwidth than the uncoupled harvester. Unlike standard dynamic magnifiers, this performance does not come at the expense of power efficiency, and unlike harvester arrays, does not require the added cost of multiple energy harvesters.