具有时滞反馈控制的双稳态压电-电磁式俘能器的随机动力学

Stochastic Dynamics of the Bistable Piezoelectric and Electromagnetic Hybrid Energy Harvester with Time-Delayed Feedback Control

本文研究了色噪声激励下具有时滞反馈控制的双稳态压电-电磁混合式俘能器的动力学特性.首先,建立了非线性双稳态压电-电磁俘能器的集中参数型机电耦合运动方程,并基于能量包线随机平均法推导得到系统稳态概率密度函数和平均输出功率表达式,通过蒙特卡洛数值方法验证了理论解的正确性.其次,分析了时滞和反馈增益系数对系统输出功率的影响.研究结果表明:在一定参数范围内,随着位移时滞与速度时滞的增加,输出功率出现周期性变化,并在特定的时滞与反馈增益组合下达到最大值;调节反馈增益系数可以改变输出功率的相位和大小.说明通过合理地设置时滞反馈控制可以提高俘能器的采集功率,为随机激励下非线性振动俘能器的设计和优化提供一定的理论依据.

In this paper,the dynamical behaviors of a bistable piezoelectric and electromagnetic hybrid energy harvester under the colored noise are studied,which is considered the effects of time-delayed feedback control.Firstly,the lumped parameter electromechanical coupling motion equation of a bistable piezoelectric and electromagnetic energy harvester is established.The expressions of stationary probability density(SPD)and average output power of the system are derived by adopting the improved stochastics averaging method of energy envelope.The obtained theoretical solution is verified by numerical results through Monte Carlo numerical method.Secondly,the influences of time delay and feedback gains on the system output power is analyzed.The results show that within a certain parameter range,the output power changes periodically with the increase of time delays in the path of displacement and velocity.An optimal combination of time delay and feedback gains exist to make the maximum of output power.The phase and value of output power can be changed by adjusting the feedback gains.That is,the harvesting performance can be greatly improved by choosing the proper design of time-delayed feedback control.Therefore,the dynamical analysis in this paper provides a theoretical basis for the parameter optimalization and design of nonlinear vibration energy harvester under random excitation.