In applications of vibration energy harvesting to embedded wireless sensing, the available power and energy can be very low. This poses interesting challenges for technological feasibility if the parasitic losses in the electronics used to harvest this energy are prohibitive. In this study, we present a theory for the active control of power generation in energy harvesters in a manner which addresses and compensates for parasitic loss. We conduct the analysis in the context of a single-transducer piezoelectric bimorph cantilever beam subjected to a low-frequency impulse train. The power generation of the vibration energy harvester is maximized while considering mechanical losses, electrical losses, and the static power required to activate control intelligence and facilitate power-electronic conversion. It is shown that the optimal harvesting current can be determined through the use of linear quadratic optimal control techniques. The optimal harvesting time over which energy should be generated, following an impulse, is determined concurrently with the optimal feedback law. We show that this optimal harvesting time exhibits bifurcations as a function of the parameters characterizing the losses in the system.

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