基于极点配置参数优化的压电分流阻尼抑振研究

Vibration Control with Optimized Piezoelectric Shunt Damping System Using Pole Placement

从结构的力平衡方程、压电元件的电荷平衡方程出发,结合压电分流电路的电压平衡关系,建立了包含RL串联压电分流电路的机电耦合系统的数学模型,并进一步推导出系统的传递函数。以系统自由振动响应的衰减系数最大化为优化目标,采用极点配置参数优化方法对传递函数中的参数进行优化分析,求解出压电分流电路中电感元件和电阻元件的优化值。将分析结果应用于一柔性悬臂梁结构的振动响应抑制实验取得了良好的抑振效果,验证了用极点配置参数优化法进行压电分流阻尼振动控制系统设计的有效性。

Since 1990, interest in passive vibration control using piezoelectric shunt circuit has grown, but we have not been able to find detailed technical information about it in the open literature. We now present the results of our efforts on exploring such information. Starting from the electric charge balance of the piezoelectric material and voltage balance of the piezoelectric shunt circuit, we derive the mathematical model of the coupled electromechanical system of a cantilever beam with piezoelectric circuit, whose resistor R and inductor L are connected in series. Then the transfer function of the system, which is selected as the obiective function, is formulated. Taking the maximum of the decay rate in the motion amplitude of free vibration of the damped beam as the object of optimization, we optimize the parameters in transfer function equation through the pole placement technique. Then the optimal values of resistor and inductor for the piezoelectric shunt circuit are obtained. As an example for verifying the parameter optimization techniques, the vibration control experiment on a cantilever beam with piezoelectric shunt circuit was performed. After the piezoelectric shunt circuit was closed and so was in operation, the decay rate of free vibration increased by about 110% and the amplitude of transfer function, which corresponded to optimal frequency tuning by pole placement criterion, decreased by about 70%. These results validate the effectiveness of parameter optimization techniques in controlling both free vibration and harmonic response.