On the Causal Power Generation Limit for a Vibratory Energy Harvester in Broadband Stochastic Response

This article illustrates that certain relatively well-known results from feedback control theory can be used to determine the maximum-attainable power generation for a vibratory energy harvester excited by a stationary broadband stochastic disturbance. For such applications, control techniques based on impedance matching theory cannot be used to optimize power generation, because the dynamic controller they prescribe is always anticausal. However, an optimal causal controller does exist, and can be derived using H(2)/LQG theory. Levels of power generation with this controller are compared to those of the anticausal optimal performance, as well as to traditional 'tuning' techniques which match the anticausal impedance only at the resonant frequency. It is demonstrated that tuning techniques can be significantly sub-optimal in broadband applications, especially when electronic conversion is relatively efficient. In addition to being useful in the design of controllers for energy harvesting applications, these results may also be used to ascertain the insurpassable power generation limits associated with a given combination of transducer and electronic hardware.