复合式微型压电悬臂梁俘能系统的随机动力学及最优控制研究

Vibration-based piezoelectric energy harvesting system has received increasing attention due to its wide application in supplying energy to micro-electronic devices. The hybrid micro-piezoelectric cantilever energy harvesting system has remarkable advantages in both efficient bandwidth and output power,its dynamic research is currently one of the most active research fields. Up to now, the existing study about this kind of system mainly focuses on the dynamic analysis of deterministic systems from experimental and numerical analysis, while ignoring the effects of random factors. Thus, this project aims at the stochastic hybrid micro-piezoelectric cantilever energy harvesting system, and is intended to study the stochastic dynamical characteristics and optimal control problem. The main contents are as follows: The stochastic responses and bifurcations are discussed based on the stochastic multi-scale technique. For analyzing the stochastic stability of this system, the expression of the moment Lyapunov exponent is obtained based on stochastic averaging method and L. Arnold perturbation method. Furthermore, the stochastic optimal control strategy for improving the output energy is constructed by means of stochastic dynamic programming principle. Finally, the numerical simulation is employed to verify the effectiveness and accuracy of the proposed methods. The fulfillment of this project will enrich the research achievements of the stochastic hybrid micro-piezoelectric energy harvesting system and provide some theoretical support for the engineering and science problems in the field of piezoelectric energy harvesting.

微电子设备对可持续自供能微电源的需求，使基于环境振动的压电俘能系统受到广泛关注。而复合式微型压电悬臂梁俘能系统，在有效频宽和输出功率两方面都有优势，其动力学研究已成为当前学术界的热点。目前的研究主要集中于从实验和数值角度对确定性系统进行动力学分析，而忽略了随机因素的影响。本项目拟以随机复合式微型压电悬臂梁俘能系统为研究对象，考虑系统的随机动力学特性和最优控制问题。主要内容包括：应用随机多尺度法研究系统的随机响应和分岔现象；基于随机平均法和L. Arnold摄动法等推导系统的矩Lyapunov指数，进而讨论系统的随机稳定性；利用随机动态规划原理，构造以能量输出最优为指标的随机最优控制策略；并借助数值模拟验证上述理论方法的有效性。本项目的进行将丰富随机复合式微型压电悬臂梁俘能系统的研究成果，为压电俘能领域相关工程和科学问题的解决提供一定的理论依据。

对压电能量俘获系统的随机非线性动力学和控制问题的研究是当今非线性科学研究领域最活跃的科学前沿之一。经过3年探索，项目组开展并完成了如下研究工作：完成了窄带噪声激励下具有多稳态特性的能量俘获系统的随机动力学特性的研究；完成了具有高阶非线性刚度的多稳态压电能量俘获系统的响应和能量俘获特性的研究；完成了有界随机参数作用下非线性压电能量俘获系统的正交多项式逼近分析，对其随机分岔进行了研究；克服模型复杂性，完成了具有谐振电路的二自由度的三稳态压电能量俘获系统的动力学问题的研究工作，得到了系统的频率响应方程和稳定性条件；完成了非线性能量俘获系统输出电压和电量的理论分析，得到了其滞后标准；借助首次穿越时间和概率密度，完成了随机三稳态非线性系统的跃迁行为的研究。完成了具有非线性能量汇的基底激励下系统的动力学特性的研究。在本项目的资助下，已出版论文22篇，其中SCI检索论文 21篇，会议论文1篇。第一作者代表性论文发表在Communications in Nonlinear Science and Numerical Simulation、Nonlinear Dynamics 、Journal of Vibration and Control上，其中1篇入选ESI热点论文，2篇入选ESI高被引论文。