压电执行器改进Bouc-Wen模型及其定位补偿控制研究

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (10) : 155-164.

论文

周民瑞1，周振华1,2，刘鑫1,2，曹太山1,2，李战慧1,2

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Improved Bouc-Wen model of piezoelectric actuator and its positioning compensation control study

ZHOU Minrui1,ZHOU Zhenhua1,2,LIU Xin1,2,CAO Taishan1,2,LI Zhanhui1,2

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摘要

针对多数迟滞模型无法描述压电陶瓷执行器(piezoelectric actuator ,PEA)的非对称、率相关迟滞非线性，提出一种改进Bouc-Wen(improved Bouc–Wen ,IBW)模型并基于提出的IBW模型对其补偿控制进行实验研究。首先，基于传统Bouc-Wen (classical Bouc–Wen,CBW)迟滞模型引入两项非对称项并引入二阶IIR滤波器以精确描述压电陶瓷执行器的迟滞非线性，进一步分析了模型参数值与频率变化规律并修正率相关参数。然后，搭建基于NI CompactRIO测控系统压电陶瓷执行器精密定位实验平台，对提出的IBW模型进行了实验验证并基于IBW模型对其补偿控制进行了实验研究。实验结果表明：IBW模型性能显著优于传统Bouc-Wen(CBW)模型和增强型Bouc-Wen(enhanced Bouc–Wen ,EBW)模型，对于激励频率10-100Hz多频正弦信号，IBW模型均方根误差相较于CBW模型和EBW模型分别下降了82.07%和62.10%，实验中压电陶瓷执行器实测最大输出位移6.15μm，基于IBW模型所提出复合补偿控制均方根误差为0.039μm，仅为最大输出位移的0.64%，最大跟踪误差仅为0.153μm。若忽略测量噪声，定位误差接近于零，说明所提出的IBW模型及其补偿控制算法有助于实现压电陶瓷执行器的高速、宽频超精密定位及主动振动控制。

Abstract

To address the asymmetric and frequency-dependent hysteresis nonlinearity of piezoelectric actuator (PEA) that can not be described by most hysteresis models, an improved Bouc-Wen (IBW) model is proposed and its compensation control is experimentally investigated based on the proposed IBW model. Firstly, based on the classical Bouc-Wen (CBW) hysteresis model, two asymmetric terms and a second-order IIR filter are introduced to accurately describe the hysteresis nonlinearity of the PEA, and the model parameters are further analyzed for the frequency variation law and the parameters are corrected to frequency-dependent. Then, based on NI CompactRIO measurement and control system, piezoelectric actuator precision positioning experimental platform is set up, and the proposed IBW model is experimentally verified and its compensation control is further experimentally studied based on the IBW model. The experimental results show that the IBW model performs significantly better than the CBW model and the enhanced Bouc-Wen (EBW) model. Compared with the CBW model and EBW model, the root mean square error of the IBW model decreases by 82.07% and 62.10% for multi-frequency sinusoidal signals with excitation frequencies of 10-100Hz, respectively. The maximum output displacement measured in the experiment is 6.15μm, and the root mean square error of the proposed composite compensation control based on the IBW model is 0.039μm, which is only 0.64% of the maximum output displacement. The maximum tracking error is only 0.153μm, and the positioning error is close to zero if the measurement noise is ignored. It is shown that the proposed IBW model and its compensation control algorithm can help realize high-speed, wide-frequency ultra-precision positioning and active vibration control of PEA.

导出引用

周民瑞1，周振华1,2，刘鑫1,2，曹太山1,2，李战慧1,2. 压电执行器改进Bouc-Wen模型及其定位补偿控制研究[J]. 振动与冲击, 2023, 42(10): 155-164

ZHOU Minrui1,ZHOU Zhenhua1,2,LIU Xin1,2,CAO Taishan1,2,LI Zhanhui1,2. Improved Bouc-Wen model of piezoelectric actuator and its positioning compensation control study[J]. Journal of Vibration and Shock, 2023, 42(10): 155-164

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