Nonlinear stochastic controllers for power-flow-constrained vibratory energy harvesters

This study addresses the formulation of nonlinear feedback controllers for stochastically excited vibratory energy harvesters. Maximizing the average power generated from such systems requires the transducer current to be regulated using a bi-directional power electronic converter. There are many applications where the implementation of these types of converters is infeasible, due to the higher parasitic losses they must sustain. If instead the transducer current is regulated using a converter capable of single-directional power-flow, then these parasitic losses can be reduced significantly. However, the constraint on the power-flow directionality restricts the domain of feasible feedback laws. The only feasible linear feedback law imposes a static relationship between current and voltage, i.e., a static admittance. In stochastic response, the power generation performance can be enhanced significantly beyond that of the optimal static admittance, using nonlinear feedback. In this paper, a general approach to nonlinear control synthesis for power-flow-constrained energy harvesters is presented, which is analytically guaranteed to outperform the optimal static admittance in stationary stochastic response. Simulation results are presented for a single-degree-of-freedom resonant oscillator with an electromagnetic transducer, as well as for a piezoelectric bimorph cantilever beam.