Chaotic control of a piezomagnetoelastic beam for improved energy harvesting

Linear cantilevered piezoelectric energy harvesters do not typically operate efficiently through a large span of excitation frequencies. Beam theory dictates optimum displacement at resonance excitation; however, typical environments evolve and vary over time with no clear dominant frequency. Nonlinear, non-resonant harvesting techniques have been implemented, but none so far have embraced chaotic behavior as a desirable property of the system. This work aims to benefit from chaotic phenomena by stabilizing high energy periodic orbits located within a chaotic attractor to improve operating bandwidth. Delay coordinate embedding is used to reconstruct the system states from a single time series measurement of displacement. Orbit selection, local linearization, and control perturbation are all computed from the single time series independent of an explicit system model. Although chaos in non-autonomous systems is typically associated with harmonic inputs, chaotic attractor motion can also exist throughout other excitation sources. Accelerometer data from inside a commercial vehicle and a stochastic excitation signal are used to illustrate the existence of chaos in dynamic environments, allowing such environments to be likely candidates for the proposed bandwidth improving energy harvesting technique.