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摘要:
双压电叠堆执行器相较于常规压电叠堆执行器具有位移放大功能，但受制于压电材料的迟滞非线性，位移精度难以满足需求。为减小双压电叠堆执行器的迟滞非线性，建立改进型PI (Prandtl-Ishlinskii)动态迟滞模型并进行参数辨识，提出一种双压电叠堆执行器输出位移分配策略与双压电叠堆并联控制方案，基于迟滞逆模型采用前馈-反馈复合控制进行实验研究，并采用不基于迟滞逆模型的线性自抗扰控制(LADRC)进行对比。基于Links-RT实时控制系统验证控制算法，实验结果表明：在1~200 Hz频率范围内，前馈-反馈复合控制效果最优，当跟踪信号频率为200 Hz时，均方根误差和最大绝对误差分别为0.454 4 μm和1.95 μm，远低于开环的4.369 6 μm和6.08 μm。
Abstract:Compared with common piezoelectric stack actuators, the dual-piezoelectric stack actuator exhibits displacement amplification functionality, but suffers from poor positioning accuracy due to the inherent hysteresis nonlinearity of piezoelectric materials. To reduce the hysteresis nonlinearity of dual-piezoelectric stack actuators, an improved Prandtl-Ishlinskii(PI) dynamic hysteresis model is established and the related parameters are identified. Then, an output displacement allocation strategy and parallel control scheme of the dual-piezoelectric stack actuator are proposed. Based on the inverse hysteresis model, the feedforward-feedback compound control is examined by experiments, and compared with the linear active disturbance rejection control (LADRC) scheme which is independent on the inverse hysteresis model. The control algorithm is validated on the Links-RT real-time control system. Experimental results indicate that the feedforward-feedback compound control performs the best within the frequency range of 1~200 Hz. When the tracking signal frequency reaches 200 Hz, the root mean square error and maximum absolute error are 0.454 4 μm and 1.95 μm respectively, much lower than those of open loop control (4.369 6 μm and 6.08 μm).
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图 1 轴向双压电叠堆执行器结构图
Figure 1. Structurale schematic of axiad dual-piezoelectric stack actuator
图 4 执行器输出位移测量实验平台
Figure 4. Experimental platform for actuator displacement measurement
图 5 不同频率上压电叠堆实验与仿真对比
Figure 5. Comparison between experiment and simulation of upper piezoelectric stack at different frequencies
图 6 不同频率下压电叠堆实验与仿真对比
Figure 6. Comparison between experiment and simulation of lower piezoelectric stack at different frequencies
图 9 不同频率下前馈-反馈复合控制滞环曲线
Figure 9. Hysteresis curve of feedforward-feedback compound control at different frequencies
图 10 前馈-反馈复合控制评价参数对比
Figure 10. Comparison of evaluation parameters for feedforward-feedback compound control
表 1 压电叠堆性能参数表
Table 1. Properties of piezoelectric stack
参数 数值 尺寸/mm 10×10×18 质量 ms/kg 0.014 阻尼 cs/(N·s·m−1) 1 200 刚度 ks/(N·μm−1) 180 标称位移y/μm 20 阻断力/N 3 600 静电容量/nF 7 500 谐振频率/kHz 83 
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表 2 参数辨识结果
Table 2. Parameter identification results
参数 数值 v=1 v=2 w1v −0.014 −0.109 w2v 0.057 0.080 w3v 0.040 0.041 w4v 0 0 w5v 0.053 0.066 w6v −0.099 −0.229 w7v 0.117 0.178 w8v −0.027 0.012 w9v 0 0 w10v 0.014 0.031 w11v −0.019 0.099 p1v 0.721 −0.477 p2v 1.576 1.137 p3v 0.500 0.571 p4v −0.067 −0.071 p5v −0.684 −0.616 p6v 0.113 0.087
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表 3 迟滞逆模型参数辨识结果
Table 3. Parameter identification results of hysteresis inverse model
参数 数值 v=1 v=2 w1v_i −0.011 −0.178 w2v_i 0.107 0.148 w3v_i 0.015 0.003 w4v_i 0 0 w5v_i 0.044 0.057 w6v_i −0.123 −0.213 w7v_i 0.143 0.203 w8v_i −0.027 −0.013 w9v_i 0 0 w10v_i 0.013 0.018 w11v_i −0.018 −0.019 p1v_i 0.785 0.153 p2v_i −2.43 −2.043 p3v_i 0.415 0.426 p4v_i −0.064 −0.064 p5v_i 0.133 0.067 p6v_i 0.208 0.201
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