Optimal Energy Harvesting From Low-Frequency Bistate Force Loadings

Abstract

This paper considers techniques for harvesting energy from vibratory loadings that can be characterized by low-frequency alternations between a minimum and maximum force magnitude. In such cases, it may be impossible to tune the harvester to resonate in the frequency band of the excitation due to constraints on the mass and transducer displacement. Here, we consider the case in which the harvester’s transient dynamics are characterized by a natural period, which is orders of magnitude below the fundamental period of the disturbance and which undergoes significant decay in between load alternations. In this case, the damped vibration of the harvester induced by each load alternation may be viewed as an isolated transient response. For such problems, we consider the optimization of generated power through the use of an active power-electronic drive to explicitly regulate transducer current according to an optimized feedback law. The analysis accounts for both mechanical and electrical losses in the harvester, as well as dissipation in the electronics. It also accounts for the static power necessary to operate the control intelligence and gate the drive transistors. We show that the optimal feedback law is, in general, a time-varying linear controller. Further, we show that following the leading edge of each load alternation, there is an optimal time horizon over which to operate the electronic conversion system beyond which the energy expended on static power exceeds the remaining energy recoverable from the dynamic response of the harvester. The analytical derivation of the controller is done generally and is shown to simplify to easily computable closed-form solutions in a number of simple cases. Analytical and simulation results are related to an experimental energy harvesting system involving a single degree-of-freedom electromagnetic transducer.