High-Dimensional Chaos Control Algorithms for Improved Piezoelectric Energy Harvesting Using a Bistable Structure

Linear cantilevered piezoelectric energy harvesters typically rely on excitation around a resonance frequency for peak operation. Compounding the problem, typical ambient environments either vary dynamically in time or possess energy distributed across a wide spectrum of frequencies. Nonlinear broadband techniques have been implemented with success, but rely on chance that steady-state high energy orbits result as opposed to the low energy or chaotic trajectories that coexist in the basin of attraction. This work aims to implement two high dimensional chaotic controllers for large period orbits located within the chaotic attractor. The first control law is defined using traditional OGY, while the second uses the principles of invariant manifolds and is therefore independent of the system Jacobian. Comparison of the two control methods aims to show that invariant principles are less computationally intensive and result in equivalent stabilized orbits. Furthermore, the only necessary measurement for control design is a single time series representing a state of the system. This article compares two methods of chaos control and their ability to stabilize a large period orbit within the chaotic attractor for improved broadband piezoelectric energy harvesting.