压电定位系统建模及滑模逆补偿控制

李智斌; 辛源泽; 张建强; 孙崇尚

doi:10.37188/CO.EN-2024-0012

压电定位系统建模及滑模逆补偿控制

1.
山东科技大学电气与自动化工程学院, 山东青岛 266590
2.
南京大学高端控制与智能运维研发中心, 江苏苏州 215163

详细信息

中图分类号: O482.31
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出版历程
- 收稿日期: 2024-04-08
- 录用日期: 2024-05-15
- 网络出版日期: 2024-05-25

Modeling of piezo-positioning system and sliding mode inverse compensation control

doi: 10.37188/CO.EN-2024-0012

1.
College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
2.
Center for Advanced Control and Smart Operations, Nanjing University, Suzhou 215163, China

Funds: Supported by National Natural Science Foundation of China (No. U23A20336, No. 52227811, No. 61933006); Natural Science Foundation of Shandong Province (No. ZR2021QF117, No. ZR2021QF140)

More Information

Author Bio:
LI Zhi-bin (1965—), male, born in Bazhong, Sichuan Province, Ph.D., professor, doctoral supervisor. He obtained his Ph.D. from Tsinghua University in 2003. He is currently a Professor at College of Electrical Engineering and Automation, Shandong University of Science and Technology. His main research interests include modeling and control of complex system dynamics. E-mail: zhibin.li@sdust.edu.cn

ZHANG Jian-qiang (1992—), male, born in Qingzhou, Shandong Province, Ph.D., assistant professor at Center for Advanced Control and Smart Operations, Nanjing University. He obtained his Ph.D. from Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences in 2020. His main research focuses on laser communication servo systems, robust control, and model identification. E-mail: zhangjq7170@163.com

Corresponding author: zhangjq7170@163.com

摘要

摘要:
为了提高压电定位系统（Piezo-positioning system）的控制性能，对迟滞特性产生的影响及其补偿控制方法进行了研究。利用Hammerstein模型表征压电陶瓷定位器的动态迟滞非线性特性，分别以Prandtl-Ishlinskii（P-I）模型和Hankel矩阵系统辨识法求得的模型表示Hammerstein模型的静态非线性部分和动态线性部分。此模型对于200 Hz以内的典型输入频率具有较好的泛化能力。在此基础上，还提出了基于P-I逆模型与积分增广的滑模逆补偿跟踪控制策略。实验结果表明，相较于PID逆补偿控制和无逆补偿的滑模控制，滑模逆补偿控制具有更加理想的阶跃响应，无超调且调节时间仅为6.2 ms，在频域内系统闭环跟踪带宽达到119.9 Hz，且扰动抑制带宽达到86.2 Hz。所提控制策略实现了迟滞非线性的有效补偿，提高了压电定位系统的跟踪精度与抗扰性能。
- 压电定位系统 /
- 迟滞非线性 /
- Hammerstein模型 /
- P-I模型 /
- 系统辨识 /
- 滑模控制
Abstract:
In order to enhance the control performance of piezo-positioning system, the influence of hysteresis characteristics and its compensation method are studied. Hammerstein model is used to represented the dynamic hysteresis nonlinear characteristics of piezo-positioning actuator. The static nonlinear part and dynamic linear part of the Hammerstein model are represented by models obtained through the Prandtl-Ishlinskii (P-I) model and Hankel matrix system identification method, respectively. This model demonstrates good generalization capability for typical input frequencies below 200 Hz. A sliding mode inverse compensation tracking control strategy based on P-I inverse model and integral augmentation is proposed. Experimental results show that compared with PID inverse compensation control and sliding mode control without inverse compensation, the sliding mode inverse compensation control has a more ideal step response and no overshoot, moreover the settling time is only 6.2 ms. In the frequency domain, the system closed-loop tracking bandwidth reaches 119.9 Hz, and the disturbance rejection bandwidth reaches 86.2 Hz. The proposed control strategy can effectively compensate the hysteresis nonlinearity, and improve the tracking accuracy and anti-disturbance capability of piezo-positioning system.
- piezo-positioning system /
- hysteresis nonlinearity /
- Hammerstein model /
- Prandtl-Ishlinskii (P-I) model /
- system identification /
- sliding mode control

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Figure 1. Hysteresis characteristic curves

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Figure 2. Play operator

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Figure 3. Hammerstein model structure

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Figure 4. Experimental platform of piezo-positioning system

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Figure 5. Modeling and measured hysteresis curves

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Figure 6. Input and output data of piezo-positioning system

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Figure 7. Singular value distribution

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Figure 8. Comparison diagrams of frequency response

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Figure 9. Block diagram of P-I inverse model feed forward control

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Figure 10. Model performance adjustment effect

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Figure 11. Block diagram of sliding mode control of piezo-positioning system with inverse compensation

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Figure 12. Structural block diagram of piezo-positioning actuator control system

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Figure 13. Control effect fitting diagram

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Figure 14. System step response curve

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Figure 15. Closed-loop frequency characteristic curve

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Figure 16. Disturbance rejection magnitude-frequency characteristic curves for three control schemes

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Table 1. Model test errors at different frequencies

Frequency (Hz)	RMSE (μm)	RE
1	0.1835	0.0121
10	0.3141	0.0214
30	0.3538	0.0244
50	0.3106	0.0219
70	0.2557	0.0185
100	0.2289	0.0173
130	0.2572	0.0201
160	0.3717	0.0297
200	0.4345	0.0365

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