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Electric load optimization of a nonlinear mono-stable Duffing harvester excited by white noise. (English) Zbl 1343.93099

Summary: This paper investigates the electric load optimization of a nonlinear mono-stable Duffing energy harvester under white noise excitations considering symmetric and asymmetric nonlinear restoring forces. Statistical linearization is utilized to obtain approximate analytical expressions for the statistical averages including the average output power, which is then optimized with respect to the electric load. It is shown that the optimal load is dependent on the nonlinearity unless the ratio between the period of the mechanical system and the time constant of the harvesting circuit is large. Furthermore, it is demonstrated that, under optimal electric loading, a mono-stable Duffing harvester with a symmetric nonlinear restoring force can never produce higher average power levels than an equivalent linear harvester regardless of the magnitude of the nonlinearity. On the other hand, asymmetries in the restoring force are shown to provide performance improvements over an equivalent linear harvester.

MSC:

93E20 Optimal stochastic control
93C10 Nonlinear systems in control theory
49N90 Applications of optimal control and differential games
49J55 Existence of optimal solutions to problems involving randomness
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H40 White noise theory
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