压电定位平台动态迟滞不确定性建模及H∞鲁棒控制

Dynamic hysteresis uncertainty modeling and H∞ robust control of piezo-positioning platforms

中文关键词  压电定位平台  伪随机二值信号  频率响应模型  模型不确定性  H∞鲁棒控制

英文关键词  piezo-positioning platforms  pseudo-random binary signal  frequency response model  model uncertainty  H∞ robust control

中文摘要

      本文为提高压电定位平台的跟踪精度及扰动抑制的能力, 首先, 在Prandtl-Ishlinskii模型建模及逆补偿的基 础上, 利用伪随机二值信号及相关函数计算方法辨识出伪线性动态系统的频率响应模型及标称模型. 其次, 在频域 内对简化过程中的不确定性进行建模. 然后, 考虑模型的加性不确定性、外界扰动及测量噪声的影响, 设计H∞鲁棒 控制器保证闭环鲁棒性, 根据标称模型设计前馈控制器保证系统的跟踪精度. 最后, 实验结果表明: 压电定位平台 在H∞鲁棒控制器及前馈控制器作用下, 可以有效地跟踪1～100 Hz频率范围内的多幅值及复合频率位移轨迹. 对于 多幅值位移轨迹, 相对误差低于5.74%, 均方根误差低于0.7174 μm. 对于复合频率位移轨迹, 相对误差低于1.31%, 均方根误差低于0.1375 μm.

英文摘要

      This paper aims to improve the tracking accuracy and disturbance rejection capabilities of piezo-positioning platforms. Firstly, based on the Prandtl-Ishlinskii model and its inverse compensation, the frequency response model and nominal model of the pseudo-linear dynamic system were identified using pseudo-random binary signals and correlation function methods. Secondly, the uncertainties introduced during the simplification process were modeled in the frequency domain. Then, considering the effects of additive model uncertainties, external disturbances, and measurement noise, an H∞ robust controller was designed to ensure the robustness of the closed-loop system. A feedforward controller was designed based on the nominal model to ensure tracking accuracy. Finally, experimental results demonstrated that the piezo-positioning platform, under the combined action of the H∞ robust controller and feedforward controller, effectively tracked multi-amplitude and composite frequency displacement trajectories within the 1～100Hz frequency range. For multi-amplitude displacement trajectories, the relative error (RE) was kept below 5.74%, with a root mean square error (RMSE) of less than 0.7174 μm. For composite frequency displacement trajectories, the RE was under 1.31%, with an RMSE of less than 0.1375 μm.