Upper Bound of Power Harvested by an On-Off Electrical Damping in a State Space System

This paper presents the theoretical upper bound of the harvested power, which is amplified by a generalized electrical damping switching controller in a linear time invariant system. The upper bound is found by maximizing a single-variable function with respect to the switching time. The upper bound shows the possibility of raising the power–frequency curve over the optimal passive curves reported in literature. The optimal switching time of the upper bound shows the mechanics that determine the optimality. The upper bound solution is not only a good benchmark to evaluate but also a clear guide to design any other practical controllers. To demonstrate these two benefits, four examples in literature were revisited: the single-degree-of-freedom electromagnetic and piezoelectric energy harvesters, the dual-mass vibration energy harvester and the quarter car hybrid electromagnetic suspension. A demonstration controller is proposed in all examples. The upper bound is used to evaluate the demonstration controller. The optimal switching time is used to explain the reason of a good or bad controller.