Optimal and sub-optimal power management in broadband vibratory energy harvesters with one-directional power flow constraints

J. T. Scruggs; I. L. Cassidy

doi:10.1117/12.847900

9 April 2010 Optimal and sub-optimal power management in broadband vibratory energy harvesters with one-directional power flow constraints

J. T. Scruggs, I. L. Cassidy

Author Affiliations +

Proceedings Volume 7643, Active and Passive Smart Structures and Integrated Systems 2010; 76430Y (2010) https://doi.org/10.1117/12.847900
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2010, San Diego, California, United States

Abstract

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 and 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); https://doi.org/10.1117/12.847900

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