Energy and Phase Space Analysis of Response Stabilization Control for Nonlinear Wideband Vibration Energy Harvesting

Abstract

This paper presents an analytical and experimental study on the transient behavior of the response stabilization control for a nonlinear wideband vibration energy harvester in order to clarify the energy requirement to stabilize the high-energy orbit of the nonlinear oscillator in the harvester subject to sporadic disturbance. In the nonlinear vibration energy harvesters, a well-recognized difficulty of coexisting attractors then arises that the emergence of the response in the high-energy branch is not guaranteed because it depends on the initial conditions to which steady-state solutions the state is attracted. To solve this problem, the response stabilization control by a negative resistance, which injected a part of the energy back to the mechanical oscillator to destabilize the undesirable low-energy solution and make the high-energy solution globally stable. However, the power necessary to operate the resonance stabilization control was supplied by an external power source, so that the power consumption by the control circuit is still a critical problem. In this study, the energy consumed by the NIC was evaluated by examining the transient response of the harvester induced by the disturbance, which was modeled as a phase discontinuity in the sinusoidal excitation. The experimentally observed responses were characterized as the trajectories on the phase plane, and the flow fields derived by averaging method successfully explained the measured trajectory, which affirms that the transient response of the harvester can be described by the slow dynamics derived by the averaging method. It is also suggested the further investigation for the quantitative evaluation of the power consumption based on the slow dynamics.