On the power optimization of the vibration-based energy harvesters under swept input acceleration

This work is the first time demonstration of the mathematical analysis on maximizing the output power harvested from vibration energy harvester under a single sinusoidal input with time-dependent amplitude. While most of recent works have investigated mechanical nonlinearities to increase extractable power, or optimal resistive load and drive frequency at steady-state operation of the transducers, real-time optimization problems have not been explored yet. In this paper, the open-circuit stiffness and the load resistance are regarded as control subjects of linear two-port harvesters. The mathematical model is treated as an optimal control problem. Analysis of optimal controls is provided by means of Pontryagin Maximum Principle. By making use of Geometric Methods of optimal control theory for this model, we are able to point out the bang-bang property of the optimal controls. Numerical optimization results are illustrated to support the theoretical analysis, which show a significant improvement of the harvested power up to 227% in comparison with those of simulation.