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Cross-coupling control method of the two-axis linear motor based on second-order terminal sliding mode

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Abstract

When the dual-axis linear motor is processing components, its accuracy will be affected by the uncertainty and nonlinearity of the system, and the complexity of the processing curve trajectory. The goal is to improve the machining accuracy and response speed of the XY dual-axis permanent magnet synchronous linear motor two-dimensional platform, improve the anti-interference ability, and reduce the contour error. This paper proposes a coupled control method based on dual closed-loop single-axis high-order terminal sliding mode position control (TSMC). First, an improved mathematical model of equivalent contour error is established. Combine the coordinated controller to get the coupling link. Then, to accelerate error convergence and suppress chattering, a high-order terminal sliding mode controller is designed. The single-axis current controller is designed using high-order sliding mode algorithms. Simulations and experiments show the effectiveness and feasibility of the proposed method.

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Abbreviations

F em :

The thrust of the linear motor

p n :

Number of motor pole pairs

T :

Motor pole pitch

ϕ mf :

Flux linkage

i q :

Motor q-axis current

i d :

Motor d-axis current

L q :

Motor q-axis inductance

L d :

Motor d-axis inductance

m :

The mass of the mover

v :

Motor linear speed

ε :

Definition of contour error

ε′ :

Improved equivalent contour error

ε″ :

Traditional equivalent contour error

PMSLM :

Permanent magnet synchronous linear motor

PID :

Proportional integral derivative

SMC :

Sliding mode control

TSMC :

Terminal sliding mode control

CCC :

Cross-coupling Control

STSMC :

Super-twisted sliding-mode controller

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 51877070, U20A20198, 51577048), the Natural Science Foundation of Hebei Province of China (No. E2021208008), the Talent Engineering Training Support Project of Hebei Province (A201905008), the National Engineering Laboratory of Energy-saving Motor & Control Technique, Anhui University (No. KFKT201901).

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Authors and Affiliations

  1. School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang, 050018, China

    Zheng Li, Qingshan Zhang, Jinfeng An, Huixian Liu & Hexu Sun

Authors
  1. Zheng Li
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  2. Qingshan Zhang
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  3. Jinfeng An
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  4. Huixian Liu
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  5. Hexu Sun
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Corresponding authors

Correspondence to Zheng Li or Hexu Sun.

Additional information

Zheng Li was born in Shijiazhuang, China in 1980. He received a Ph.D. degree in power electronics and electrical drive from Hefei University of Technology (China), in 2007.

Currently, he is a Professor at Hebei University of Science and Technology, in Shijiazhuang (China).

His major research interests include design, analysis, and control of novel motors and actuators, intelligent control, smart grid, and power electronics. He is the author of more than 270 published papers.

Qingshan Zhang was born in Baoding, China in 1996. He received his bachelor’s degree in automation from Hebei University of Science and Technology in 2019. He is currently pursuing a master’s degree at Hebei University of Science and Technology.

Currently, he is a graduate student at Hebei University of Science and Technology. His research interest includes special motor control and linear motor drive.

Jinfeng An was born in Hengshui, China in 1996. He obtained a bachelor’s degree in electrical engineering and automation from Hebei Science and Technology Normal University in 2019 and is currently pursuing a master’s degree in Hebei University of Science and Technology. Currently, he is a graduate student at Hebei University of Science and Technology. His research interest includes linear motor control algorithms and motor drive.

Huixian Liu was born in Ningjin, China, in 1984. She received a Ph.D. degree in control theory and control engineering from Southeast University, Nanjing, China, in 2012.

Since 2011, she has been with the School of Electrical Engineering, Hebei University of Science and Technology, where she is currently an Associate Professor.

Her research interests include nonlinear system control, predictive control with applications to AC motors.

Hexu Sun received a Ph.D. degree in automation from Northeastern University, Shenyang, China in 1993. He has been a Professor at the School of Control Science and Engineering, Hebei University of Technology, Tianjin, China, and the School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang, China. He has authored five books and more than 130 journal and conference papers and holds 13 U.S. patents and five computer software copyrights. His current research interests include robotics and complex engineering system. Dr. Sun is a recipient of many prestigious national awards from China. He has been a Director in many societies and committees in China. He is currently the invited Plenary Speaker and a General Co-Chair of many international conferences.

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Li, Z., Zhang, Q., An, J. et al. Cross-coupling control method of the two-axis linear motor based on second-order terminal sliding mode. J Mech Sci Technol 36, 1485–1495 (2022). https://doi.org/10.1007/s12206-022-0235-2

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  • DOI: https://doi.org/10.1007/s12206-022-0235-2

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