Abstract
A time-delayed feedback control is applied to a nonlinear piezoelectric energy harvesting system excited by additive and multiplicative Gaussian white noises to improve its energy harvesting performance. An equivalent decoupling system can be obtained by using a variable transformation. Based on the standard stochastic averaging method, the Fokker–Plank–Kolmogorov equation and the stationary probability density functions of the amplitude, displacement, and velocity of the harvester are obtained, respectively. In addition, the approximate expressions of mean square electric voltage and the mean extracted output power are derived. Finally, the paper explores the influences of parameters on the mean square electric voltage. The results show that noise intensity, time delay, feedback strength, time constant ratio, and coupling coefficients have great influences on the mean square electric voltage. The accuracy of the theoretical method is verified by the Monte Carlo simulation.
Highlights
Due to the development of wireless sensors towards low energy consumption and miniaturization, conventional power supply devices are no longer adapted to technological innovation [1, 2]
Panyam and Daqaq [24] explored the responses of the tristable energy harvester to harmonic excitation, and the results showed that the tristable energy harvesters have higher output power than the bistable energy harvesters
The time-delayed feedback control is utilized to improve the efficiency of a nonlinear piezoelectric energy harvesting system under the influences of the additive and multiplicative Gaussian white noise excitation. e standard stochastic averaging method has been applied to derive the stationary probability density functions (PDFs) of amplitude, displacement, and velocity. en, the expression of mean square electric voltage (MSEV) is deduced via the approximate relationship between voltage and mechanical states
Summary
Due to the development of wireless sensors towards low energy consumption and miniaturization, conventional power supply devices are no longer adapted to technological innovation [1, 2]. Guo et al [37] proposed a time-delayed feedback control to improve collection performance of the multiple attractors wind-induced vibration energy harvester system. E results show that time-delayed feedback is a powerful tool for achieving a wide range of operating regimes and enhancing amplitude-frequency characteristics and controlling the stochastic or deterministic dynamics of nonlinear systems. Time-delayed feedback control of the nonlinear piezoelectric energy harvesting system [38, 39] may influence the harvesting performance and the power generation under different excitation conditions, but it has not yet been explored. The aimed system is a nonlinear piezoelectric energy harvesting system containing time-delayed feedback control in the presence of additive and multiplicative Gaussian white noise.
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