Passive network design for stochastic vibratory energy harvesters

This paper considers the use of optimal control theory to design circuits for small-scale, single-transducer vibration energy harvesting applications, in which the external disturbance is a broadband stochastic process. Specifically, we investigate the use of a lossless passive two-port network terminated by a single-directional DC/DC converter, to impose transducer voltage feedback laws on energy harvesting systems. Such an implementation requires external power only to gate one MOSFET in a PWM cycle, and requires no active feedback. The optimization of harvested energy reduces to the optimal design of the input admittance Y (s) of the terminated network, which reduces to a positive-real-constrained, sign-indefinite ℋ2 optimal control problem. This class of optimization is nonconvex, and a numerically-efficient means of finding its global minimum remains an open problem. Here we introduce conservatism into the problem in such a way as to make the optimization practical, albeit still nonconvex, and we illustrate its solution in the context of a base-excited piezoelectric bimorph cantilever.