Trajectory tracking control for tri-axial fast tool servo using hybrid electromagnetic-piezoelectric actuation

名称	型号	主要技术指标
电容位移传感器	5503探头、5810电荷放大器	量程500 µm，带宽20 kHz
电磁功率放大器	SMA5005-1	增益0.8 A/V
压电功率放大器	E-617.001	增益10，带宽2 kHz
数据采集卡	PCIe-6363	16 bit AD\\DA

Table 2. Parameters of notch filters

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Table 2. Parameters of notch filters

参数	数值/（rad·s^-1）	参数	数值	参数	数值
$ω_{x, n, 1}$	$2 π \times 681$	$ξ_{x, n, 1}$	$0.035 00$	$g_{x}$	$0.760 81$
$ω_{x, d, 1}$	$2 π \times 594$	$ξ_{x, d, 1}$	$0.137 00$	$g_{x}$	$0.760 81$
$ω_{z, n, 1}$	$2 π \times 1 331$	$ξ_{z, n, 1}$	$0.018 70$	$g_{z}$	$0.834 96$
$ω_{z, n, 2}$	$2 π \times 1 501$	$ξ_{z, n, 2}$	$0.006 90$
$ω_{z, n, 3}$	$2 π \times 2 871$	$ξ_{z, n, 3}$	$0.023 40$
$ω_{z, d, 1}$	$2 π \times 1 299$	$ξ_{z, d, 1}$	$0.016 70$
$ω_{z, d, 2}$	$2 π \times 1 485$	$ξ_{z, d, 2}$	$0.006 88$
$ω_{z, d, 3}$	$2 π \times 2 717$	$ξ_{z, d, 3}$	$0.001 96$

Table 3. Parameters of hysteresis models for XYZ axes

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Table 3. Parameters of hysteresis models for XYZ axes

X轴	Y轴	Z轴
$μ_{1, x} = 0.890$	$μ_{1, y} = 0.854$	$μ_{1, z} = 1.054$
$μ_{2, x} = 0.228$	$μ_{2, y} = 0.271$	$μ_{2, z} = 0.387$
$μ_{3, x} = 0.100$	$μ_{3, y} = 0.010$	$μ_{3, z} = 0.138$
$μ_{4, x} = - 0.041$	$μ_{4, y} = 0.021$	$μ_{4, z} = 0.224$
$μ_{5, x} = 0.170$	$μ_{5, y} = 0.085$	$μ_{5, z} = - 0.326$
$μ_{6, x} = 1.648$	$μ_{6, y} = 0.782$	$μ_{6, z} = 0.341$
$μ_{7, x} = 0.094$	$μ_{7, y} = 1.961$	$μ_{7, z} = 0.189$
$μ_{8, x} = 0.213$	$μ_{8, y} = - 0.390$	$μ_{8, z} = 0.012$
$c_{m, x} = - 0.021$	$c_{m, y} = 0.005$	$c_{m, z} = 0.142$

Table 4. PID parameters for XYZ axes
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Table 4. PID parameters for XYZ axes
方向 $K_{p}$ $K_{i}$ $K_{d}$ 相位裕度/（°）幅值裕度/dB
X轴 $0$ $40.887$ $0$ $76.1$ $6.08$
Y轴 $0$ $70.851$ $0$ $42.0$ $12.2$
Z轴 $0$ $6 687.581$ $0$ $46.3$ $9.5$

Table 5. Tracking errors of different control systems
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Table 5. Tracking errors of different control systems
控制系统 e_m/% e_rms/%
X Y Z X Y Z
PID+FF 16.90 10.25 3.24 6.49 3.27 1.18
PID+H_i^-1 10.10 6.00 1.72 3.01 2.43 0.50
PID+H_i^-1+FD 4.56 3.19 1.69 1.06 1.06 0.49

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Zhiyuan ZHU, Zihui ZHU, Xiaoqin ZHOU, Limin ZHU, Zhiwei ZHU. Trajectory tracking control for tri-axial fast tool servo using hybrid electromagnetic-piezoelectric actuation[J]. Optics and Precision Engineering, 2023, 31(15): 2236

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