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Energy harvesting represents one of the recent challenging subjects related to vibration and control. The scale of energy harvesters and storage can involve a wide power range, and the scale of some milliwatt is the elective field of piezoelectric applications. This paper investigates the power frontiers of the piezoelectric-based harvesters applied to automotive units. The analysis, supported by experimental data, aims at estimating the upper bound of the specific power of this technology for powering small devices on board cars. Passive optimally tuned piezoelectric harvester and semi-active controlled ones are compared, based on a new control strategy named VFC-Variational Feedback Control, recently developed by the authors. This new technique makes it possible to increase the total energy storage drained from car vibrations. However, the real advantage for their use relies on a sharp balance between the harvested power and the costs for the additional hardware mass transport. Numerical simulations of circuitry and experimental vibration data provides references to assess the energy convenience in installing this type of devices on board.

Energy harvesting from the environment is an important aspect of many technologies. The scale of energy capturing and storage can involve the power range from mWatt up to MWatt, depending on the used devices and the considered environments (from ambient acoustic and vibration to ocean wave motion, or wind). In this paper, the wind turbine energy harvesting problem is approached as an optimal control problem, where the objective function is the absorption of an amount of energy in a given time interval by a fluid-flow environment, that should be maximized. The interest relies on outlining general control models of fluid-flow-based extraction plants and identifying an optimum strategy for the regulation of an electrical machine to obtain a maximum-efficiency process for the related energy storage. The mathematical tools are found in the light of optimal control theory, where solutions to the fundamental equations are in the frame of Variational Control (the basis of the Pontryagin optimal control theory). A special problem, named Optimally Controlled Betz’s Machine OCBM-optimal control steady wind turbine, is solved in closed form, and it is shown that, in the simpler steady case, it reproduces the maximum efficiency machine developed in Betz’s theory.

In this paper the energy harvesting problem involving typical MEMS technology is reduced to an optimal control problem, where the objective function is the absorption of the maximum amount of energy in a given time interval from a vibrating environment. The interest here is to identify a physical upper bound for this energy storage. The mathematical tool is a new optimal control called Krotov’s method, that has not yet been applied to engineering problems, except in quantum dynamics. This approach leads to identify new maximum bounds to the energy harvesting performance. Novel MEMS-based device control configurations for vibration energy harvesting are proposed with particular emphasis to piezoelectric, electromagnetic and capacitive circuits.