On the Causal Power Generation Limit for a Vibratory Energy Harvester in Broadband Stochastic Response

Abstract

This article illustrates that certain relatively well-known results from feedback control theory can be used to determine the maximum-attainable power generation for a vibratory energy harvester excited by a stationary broadband stochastic disturbance. For such applications, control techniques based on impedance matching theory cannot be used to optimize power generation, because the dynamic controller they prescribe is always anticausal. However, an optimal causal controller does exist, and can be derived using H 2 /LQG theory. Levels of power generation with this controller are compared to those of the anticausal optimal performance, as well as to traditional 'tuning' techniques which match the anticausal impedance only at the resonant frequency. It is demonstrated that tuning techniques can be significantly sub-optimal in broadband applications, especially when electronic conversion is relatively efficient. In addition to being useful in the design of controllers for energy harvesting applications, these results may also be used to ascertain the insurpassable power generation limits associated with a given combination of transducer and electronic hardware.

Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experimental identification

“…[5][6][7][8] To date, most piezoelectric harvesters presume linear response and thus seek electromechanical resonance to extract maximum energy. 2,[9][10][11] However, considering many environmental excitation sources are instead broadband, strategies ranging from control theoretic [12][13][14] to purposeful inclusion of nonlinearity [15][16][17][18][19][20][21][22] are gaining momentum. For very low excitation levels for all such harvesters, linear behavior of the piezoelectric components is an accurate presumption.…”

Passive network design for stochastic vibratory energy harvesters

“…Theorem 1: Let the system in (1) be WSPR, and let the augmented system x ∈ R n be as in (8). Then for any causal, stabilizing mapping from v to i, we have that…”

“…In [2], [8], Scruggs investigated the substitution of a single-directional DC/DC converter for a fully-active Hbridge converter capable of two-way power flow, as illustrated in Fig. 2c.…”

“…In the theory developed in [2], [8], conductive losses in the semiconductor electronics are taken into account in the design process, resulting in a feedback system which maximizes the power transferral from the base excitation to the power bus. In [9], this theory is extended to also account for the gating losses incurred by the MOSFETs in the electronics, which can be of great relevance at small scale or small excitation levels.…”

Stochastic optimal control of jump diffusion excited energy harvesters

“…Stochastic optimal control techniques have been employed to characterize the limits of generation performance of energy harvesting devices, see e.g., [7]. In much of this literature, the force or acceleration induced by the environment is modeled using Wiener process inputs.…”