9 April 2010 Optimal and sub-optimal power management in broadband vibratory energy harvesters with one-directional power flow constraints
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In many applications of vibratory energy harvesting, the external disturbance are most appropriately modeled as broadband stochastic processes. Optimization of power generation from such disturbances is a feedback control problem, and solvable via a LQG control theory. However, attainment of this performance requires the power conversion system which interfaces the transducers with energy storage to be capable of bi-directional power flow, and there are many applications where this is infeasible. One of the most common approaches to power extraction with one-directional power flow constraints is to control the power conversion system to create a purely resistive input impedance, and then to optimize this effective resistance for maximal absorption. This paper examines the optimization of broadband energy harvesting controllers, subject to the constraint of one-directional power flow. We show that as with the unconstrained control problem, it can be framed as a "Quadratic-Gaussian" stochastic optimal control problem, although its solution is nonlinear and does not have a closed-form. This paper discusses the mathematics for obtaining the optimal power extraction controller for this problem, which involves the stationary solution to an associated Bellman-type partial differential equation. Because the numerical solution to this PDE is computationally prohibitive for harvester dynamics of even moderate complexity, a sub-optimal control design technique is presented, which is comparatively simple to compute and which exhibits analyticallycomputable lower bounds on generated power Examples focus a nondimensionalized, ideal, base-excited SDOF resonator with electromagnetic transduction.
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J. T. Scruggs, J. T. Scruggs, I. L. Cassidy, I. L. Cassidy, } "Optimal and sub-optimal power management in broadband vibratory energy harvesters with one-directional power flow constraints", Proc. SPIE 7643, Active and Passive Smart Structures and Integrated Systems 2010, 76430Y (9 April 2010); doi: 10.1117/12.847900; https://doi.org/10.1117/12.847900

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