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Stochastic Stability of a Piezoelectric Vibration Energy Harvester and Stabilization Using Noise

[+] Author Affiliations
Subramanian Ramakrishnan, Connor Edlund

University of Minnesota Duluth, Duluth, MN

Paper No. DSCC2018-9216, pp. V002T21A006; 8 pages
doi:10.1115/DSCC2018-9216
From:
  • ASME 2018 Dynamic Systems and Control Conference
  • Volume 2: Control and Optimization of Connected and Automated Ground Vehicles; Dynamic Systems and Control Education; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Energy Systems; Estimation and Identification; Intelligent Transportation and Vehicles; Manufacturing; Mechatronics; Modeling and Control of IC Engines and Aftertreatment Systems; Modeling and Control of IC Engines and Powertrain Systems; Modeling and Management of Power Systems
  • Atlanta, Georgia, USA, September 30–October 3, 2018
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5190-6
  • Copyright © 2018 by ASME

abstract

Vibration energy harvesters convert the energy of ambient, random vibration into electrical power often using piezoelectric transduction. The stochastic dynamics of a piezoelectric harvester with parameteric uncertainties is yet to be fully explored in the nonequilibrium regime. Motivated by mathematical results that establish the counterintuitive phenomenon of stabilization of response in certain nonlinear systems using noise, we investigate the stochastic stability of a generic harvester in the linear and the monostable nonlinear regimes excited by multiplicative noise characterized by both Brownian and the Lévy stable distributions. First, a lower bound on the magnitude of noise intensity that guarantees exponential stability almost surely, is obtained analytically as an inequality in terms of system parameters in the linear case. This result is validated numerically using the Euler-Maruyama scheme. Next, noise-induced stabilization in the harvester dynamics is demonstrated numerically for both the linear and nonlinear cases wherein Lévy noise was found to achieve stabilization at lower noise intensities than Brownian noise. Additionally, the inclusion of a nonlinear stiffness does not have an appreciable affect on the stabilization behavior. The results indicate that stabilization may be achieved using noise and are expected to be useful in harvester design.

Copyright © 2018 by ASME

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