Smart structure vibration reduction based on adaptive active vibration control has become a hot research spot in recent years. A filtered-U least mean square algorithm based on an infinite impulse response filter structure is used to solve the interference of controller output to reference signal. The filtered-U least mean square algorithm is very suitable for the nonlinear vibration control of the flexible structure. This study focuses on the analysis and implementation of an adaptive active vibration control system for smart structure with a surface-bonded piezoelectric actuator. The piezoelectric actuator contained in the secondary path has nonlinear hysteresis property. The nonlinear hysteresis property will cause a nonlinear relationship between the structural vibration response and the control voltage, which deteriorates the robustness and control effect of the adaptive control. This study designs an improved version of the filtered-U least mean square algorithm with online hysteresis identification and compensation (filtered-U least mean square–online hysteresis identification and compensation) based on a discrete Prandtl–Ishlinskii model. The Prandtl–Ishlinskii model parameters of the nonlinear hysteresis property are identified online based on the least mean square algorithm. Based on the identified Prandtl–Ishlinskii model parameters, an inverse hysteresis compensator is established for feedforward compensation in the secondary path. Simulation results show that the proposed method can dynamically compensate the hysteresis nonlinearity of the secondary path, linearizing the nonlinear hysteresis. The vibration reduction effect of the proposed method is obviously better than that of other competing methods. A piezoelectric smart cantilever plate with PZT (or lead zirconate titanate, Pb (Zr, Ti)) actuators and sensors is designed to demonstrate the validity and efficiency of the proposed method by experiments. Experiment results demonstrate that the adverse effect of nonlinear hysteresis is eliminated well after feedforward hysteresis compensation is introduced; the unexpected frequency vibration caused by the hysteresis property is suppressed. The proposed methodology possesses an important advantage in application of the adaptive active vibration control of the piezoelectric smart structure.

基于自适应主动振动控制的智能结构减振已成为近年来的研究热点。基于无限冲激响应滤波器结构的滤波-U最小均方算法用于解决控制器输出对参考信号的干扰。滤波-U最小均方算法非常适合于柔性结构的非线性振动控制。这项研究的重点是具有表面键合压电致动器的智能结构的自适应主动振动控制系统的分析和实现。包含在次级路径中的压电致动器具有非线性磁滞特性。非线性磁滞特性将导致结构振动响应与控制电压之间呈非线性关系，这会降低自适应控制的鲁棒性和控制效果。本研究基于离散Prandtl–Ishlinskii模型设计了具有在线滞后识别和补偿（滤波U最小均方在线滞后识别和补偿）的滤波U最小均方算法的改进版本。非线性滞后特性的Prandtl–Ishlinskii模型参数是基于最小均方算法在线确定的。基于已识别的Prandtl–Ishlinskii模型参数，建立了反向磁滞补偿器，用于次级路径中的前馈补偿。仿真结果表明，该方法可以动态补偿二次路径的磁滞非线性，线性化非线性磁滞。所提方法的减振效果明显优于其他竞争方法。设计了带有PZT（或钛酸锆铅，Pb（Zr，Ti）铅）执行器和传感器的压电智能悬臂板，以通过实验证明该方法的有效性和效率。实验结果表明，引入前馈磁滞补偿后，非线性磁滞的不利影响得以消除。抑制了由磁滞特性引起的意外频率振动。所提出的方法在压电智能结构的自适应主动振动控制中具有重要的优势。Ti））执行器和传感器的设计旨在通过实验证明该方法的有效性和效率。实验结果表明，引入前馈磁滞补偿后，非线性磁滞的不利影响得以消除。抑制了由磁滞特性引起的意外频率振动。所提出的方法在压电智能结构的自适应主动振动控制中具有重要的优势。Ti））执行器和传感器的设计旨在通过实验证明该方法的有效性和效率。实验结果表明，引入前馈磁滞补偿后，非线性磁滞的不利影响得以消除。抑制了由磁滞特性引起的意外频率振动。所提出的方法在压电智能结构的自适应主动振动控制中具有重要的优势。抑制了由磁滞特性引起的意外频率振动。所提出的方法在压电智能结构的自适应主动振动控制的应用中具有重要的优势。抑制了由磁滞特性引起的意外频率振动。所提出的方法在压电智能结构的自适应主动振动控制中具有重要的优势。