This article reports on the design and experimental characterization of an electromagnetic transducer for energy harvesting from large structures (e.g., multistory buildings and bridges), for which the power levels can be above 100 W and disturbance frequencies below 1 Hz. The transducer consists of a back-driven ballscrew coupled to a permanent-magnet synchronous machine with power harvesting regulated via control of a four-quadrant power electronic drive. Design considerations between various subsystems are illustrated and recommendations in terms of minimal values are made for each design metric. 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. As such, the model can be used to assess the viability of the technology and to correctly design controllers to maximize power generation. To demonstrate the device’s energy harvesting capability, impedance matching theory is used to optimize the power generated from a base-excited tuned mass damper. Both theoretical and experimental investigations are compared and the results are shown to match closely.

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In this paper, an extension of linear-quadratic-Gaussian (LQG) control theory is used to determine the optimal state feedback controller for a vibratory energy harvesting system with Coulomb friction. Specifically, the energy harvester is a base-excited single-degree-of-freedom (SDOF) resonant oscillator with an electromagnetic transducer attached between the base and the moving mass. The development of the optimal controller for this system is based on statistical linearization, whereby the Coulomb friction force is replaced by an equivalent linear viscous damping term, which is calculated from the stationary covariance of the closed-loop system. It is shown that the covariance matrix and optimal feedback gain matrix can be computed by implementing an iterative algorithm involving linear matrix inequalities (LMIs). Furthermore, this theory is augmented to account for a non-quadratic dissipation in the electronics used to control the energy conversion. Simulation results are presented for the SDOF energy harvester in which the performance of the optimal state feedback control law is compared to the performance of the optimal static admittance over a range of disturbance bandwidths.

In many applications of vibratory energy harvesting, the external 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 solvable via LQG (linear-quadratic-Gaussian) control theory. Implementing the optimal feedback controller requires a power electronic drive capable of two-way power flow, which can impose dynamic relationships between the voltage and current of the transducer. Determining the optimal energy harvesting current control is accomplished by solving a nonstandard Riccati equation. In this paper we show that appropriate tuning of the 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 such tuning methods are not used and the solution to the Riccati equation does not decouple, it is possible to determine the states in the feedback law that contribute the most to the average power generated by the harvester. As such, partial-state feedback gains can be optimized using a gradient descent method. Two energy harvesting examples are presented, including a single-degree-of-freedom oscillator with an electromagnetic actuator and a piezoelectric bimorph cantilever beam, to demonstrate these concepts.

This article examines the use of actively controlled electronics to maximize the energy harvested from a stationary stochastic disturbance. In prior work by the authors, it has been shown that when the harvester dynamics are linear and the transmission losses in the electronics are resistive, the optimal feedback controller is the solution to a nonstandard linear-quadratic-Gaussian optimal control problem. This article augments the theory in the following three distinct ways: (a) It illustrates how to use linear matrix inequalities to balance the objective of energy harvesting against other response control objectives (such as minimum requirements on closed-loop damping and maximum levels of voltage response), in the synthesis of the optimal feedback law; (b) it establishes a more realistic characterization of the transmission losses in the actively controlled power electronics used to regulate the extraction of power; and (c) it illustrates how the optimal control theory for resistive loss models can be extended to accommodate the more realistic loss models. The theory is illustrated in the context of a piezoelectric energy harvesting model, and an example is used to illustrate that the theory can be used to simultaneously optimize the feedback law, together with the switching frequency and storage bus voltage of the power electronics.

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