Modeling and Control of an Electromagentic Transducer for Vibratory Energy Harvesting Applications

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.