压电定位平台Hammerstein建模与反馈线性化控制

Hammerstein modeling and feedback linearization control for piezoelectric positioning stage

压电定位平台以压电陶瓷、柔性铰链作为驱动及放大机构,具有高定位精度和快响应速度,被广泛应用于各种精密/超精密定位领域。压电定位平台面临的主要挑战是压电陶瓷的固有迟滞非线性特性,这严重影响平台的定位和跟踪精度。针对此问题,提出一种基于Hammerstein结构的迟滞建模方法及基于此模型的输入-输出反馈线性化控制策略。首先,建立Hammerstein结构的迟滞模型,并进行模型参数估计。接着,以基于Hammerstein模型的输入-输出反馈线性化控制策略设计跟踪控制器。最后,在压电定位平台上对建立的模型和设计的跟踪控制器进行实验验证。模型辨识实验结果表明:提出的Hammerstein模型能有效地拟合压电定位平台输入量与输出量之间的迟滞非线性特性,其均方根误差小于0.5μm。轨迹跟踪实验结果表明:设计的跟踪控制器对期望信号(幅值60μm,频率100 Hz)的跟踪均方根误差为0.9266μm,相较于基于改进的速率相关PI(Modified Rate-dependent Prandtl-Ishlinskii,MRPI)模型的前馈补偿跟踪控制、基于MRPI模型的前馈补偿与PID反馈复合跟踪控制,精度分别提高81.22%、46.25%。

A piezoelectric positioning stage is driven and amplified by piezoelectric ceramic and flexible hinges,which can provide high positioning accuracies and response speeds.Thus,it is widely used in various precision/ultra-precision positioning fields.However,the primary challenge presented by the piezoelectric positioning stage is the inherent hysteresis nonlinear characteristics of piezoelectric ceramics,which significantly affects the positioning and tracking accuracy of the piezoelectric positioning stage.Hence,a hysteresis modeling method based on the Hammerstein structure and an input-output feedback linearization control strategy is proposed herein.First,hysteresis modeling based on the Hammerstein structure is proposed,and the parameters are estimated.Subsequently,based on the Hammerstein model,a tracking controller is designed via an input-output feedback linearization control strategy.Finally,the proposed Hammerstein model and the designed tracking controller are experimentally verified on a piezoelectric positioning stage.The experimental results of model identification reveal that the proposed Hammerstein model can effectively fit the hysteresis nonlinearity between the input and output of the piezoelectric positioning stage and that its root mean square error is less than 0.5μm.Meanwhile,the experimental results of trajectory tracking indicate that the designed tracking controller can track the desired signal(amplitude 60μm;frequency 100 Hz)with a root mean square error of 0.9266μm.Compared with the feedforward compensation tracking control based on the modified rate-dependent Prandtl-Ishlinskii(MRPI)model and the compound tracking control of feedforward compensation based on the MRPI model and proportional-integral-derivative feedback,the proposed model offers an accuracy improvement of 81.22%and 46.25%,respectively.