An optimal stochastic control theory for distributed energy harvesting networks

A new approach, based on H 2 optimal control theory, is presented for the design of feedback controllers for energy harvesting systems for maximal power generation. The theory applies to stochastically excited vibratory systems in broadband stationary response, and allows for harvested power to be explicitly optimized. It is applicable to both single-transducer systems as well as coupled networks of many transducers. The theory accounts for the influence of energy harvesting on the dynamics of the structure to which the transducers are attached. It also accounts for resistive and semiconductor dissipation in the power-electronic network interfacing the transducers with energy storage. Due to its predominance in the literature, a piezoelectric bimorph cantilever beam is used as the context for the theory, and simulation examples are used to illustrate various aspects of the optimal controllers.