Nonlinear Stochastic Feedback Controllers for Vibratory Energy Harvesters With Power Flow Constraints

This study addresses the formulation of feedback controllers for stochastically-excited vibratory energy harvesters. Maximizing power generation from stochastic disturbances can be accomplished using LQG control theory, with the transducer current treated as the control input. For the case where the power flow direction is unconstrained, an electronic drive capable of extracting as well as delivering power to the transducer is required to implement the optimal controller. It is demonstrated that for stochastic disturbances characterized by second-order, bandpass-filtered white noise, energy harvesters can be passively tuned such that optimal stationary power generation only requires half of the system states for feedback in the active circuit. However, there are many applications where the implementation of a bi-directional power electronic drive is infeasible, due to the higher parasitic losses they must sustain. If the electronics are designed to be capable of only single-directional power flow (i.e., where the electronics are incapable of power injection), then these parasitics can be reduced significantly, which makes single-directional converters more appropriate at smaller power scales. The constraint on the directionality of power flow imposes a constraint on the feedback laws that can be implemented with such converters. In this paper, we present a sub-optimal nonlinear control design technique for this class of problems, which exhibits an analytically computable upper bound on average power generation.