In this study, an extension of linear-quadratic-Gaussian (LQG) control theory is used to determine the optimal state feedback controller for a nonlinear energy harvesting system that is driven by a stochastic disturbance. Specifically, the energy harvester is a base-excited single-degree-of-freedom (SDOF) resonant oscillator with an electromagnetic transducer embedded between the ground and moving mass. The electromagnetic transducer used to harvest energy from the SDOF oscillator introduces a nonlinear Coulomb friction force into the system, which must be accounted for in the design of the controller. As such, 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). 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.

Date Published: 27 March 2012
PDF: 12 pages
Proc. SPIE 8341, Active and Passive Smart Structures and Integrated Systems 2012, 834105 (27 March 2012); doi: 10.1117/12.914975

Published in SPIE Proceedings Vol. 8341:
Active and Passive Smart Structures and Integrated Systems 2012
Henry A. Sodano, Editor(s)