| dc.description.abstract |
<p>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. </p><p>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.</p><p>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.</p>
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