Browsing by Author "Scruggs, Jeffrey T"

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.

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.

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.