Numerical solutions to optimal power-flow-constrained vibratory energy harvesting problems

This study addresses the formulation of optimal numerical controllers for stochastically-excited vibratory energy harvesters in which a single-directional power electronic converter is used to regulate power-flow. Single-directional converters have implementation advantages for small-scale applications, but restrict the domain of feasible controllers. Optimizing the average power generated in such systems can be accomplished by formulating the constrained control problem in terms of stochastic Hamilton-Jacobi theory. However, solving the stochastic Hamilton-Jacobi equation (HJE) is challenging because it is a nonlinear partial differential equation. As such, we investigate the capability of the pseudospectral (PS) method to solve the HJE with mixed state-control constraints. The performance of the PS controller is computed for a single-degree-of-freedom resonant oscillator with electromagnetic coupling. We compare the PS performance to the performance of the optimal static admittance controller as well as the optimal unconstrained linear-quadratic-Gaussian controller.