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Dynamic modeling and vibration suppression for double flexible manipulator with a tip payload

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Abstract

In the manipulator transmission system, there are many nonlinear inducements, such as flexibility and friction torque. It is easy to lead to fluctuations of the output rotation speed of the system, and even cause serious resonance. Therefore, PI control strategy based on fuzzy theory is proposed to solve this trouble. Firstly, the dynamic equations of the transmission system of the double flexible manipulator was established. Then, the effects of friction torque and mode order on the output characteristics of the system are analyzed. Based on the fuzzy rules, the controller parameters change constantly to reduce the oscillation of the servo system output rotation speed. Finally, numerical simulation analysis and control experiment verify the effectiveness of the control strategy described in this paper. The results are that the proposed control method can decrease the average value of the load rotation angle tracking error by 13.8 %.

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Abbreviations

l :

Length of flexible load (m)

m :

Mass of flexible load (kg)

M :

Tip payload mass (kg)

EI :

Flexural rigidity of flexible load (N·m2)

ρA :

Linear density of flexible load (kg/m)

J l :

Rotational inertia of flexible load (kg·m2)

ω l :

Modal frequency of flexible load (rad/s)

α l :

Characteristic root value of mode function

J m :

Motor rotational inertia (kg·m2)

K s :

Torsional stiffness (N·m/rad)

Tm :

Motor electromagnetic torque (N·m)

M f :

Motor friction torque (N·m)

T l :

Flexible load torque (N·m)

T s :

Spring torque (N·m)

θ m :

Rotation angle of motor (rad)

θ l :

Rotation angle of flexible load (rad)

ω m :

Angular velocity of motor (rad/s)

ω l :

Angular velocity of flexible load (rad/s)

X 0 Oy 0 :

Moving reference coordinate system

XOY :

Fixed coordinate system

y(x, t) :

Deformation of flexible load (m)

y(l, t) :

Deformation of flexible load end (m)

K p1, K l1 :

Initial controller parameters

Kp2, K 12:

Termination controller parameters

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Acknowledgments

The project is supported by the Applied Basic Research Program of Liaoning Province (2023JH2/101300159) and the National Natural Science Foundation of China (No. 52275090).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110169, China

    Sainan Zhou, Xiaopeng Li, Dongyang Shang & Zhengding Li

  2. Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China

    Meng Yin

Authors
  1. Sainan Zhou
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  2. Xiaopeng Li
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  3. Meng Yin
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  4. Dongyang Shang
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  5. Zhengding Li
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Corresponding author

Correspondence to Xiaopeng Li.

Additional information

Sainan Zhou received her B.S. degree from Northeastern University in 2021. Currently, she is a master candidate of School of Mechanical Engineering and Automation, Northeastern University. Her research interests include dynamic modeling and control theory research of manipulator, vibration suppression of flexible manipulator.

Xiaopeng Li received his Ph.D. degree from Northeastern University in 2006. Currently, he is a Professor of Mechanical Design and Theory, School of Mechanical Engineering and Automation, Northeastern University. He specializes in machine design theory and methodology.

Meng Yin received the Ph.D. degree from State Key Laboratory of Robotics, Chinese Academy of Sciences, University of Chinese Academy of Sciences in China. He is currently a Post-Doctoral Researcher with the Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China. His research interests include tendon-sheath driven humanoid robots, mechanical design and optimization, and compliant control.

Dongyang Shang received his B.S. degree in mechanical design and automation from Shenyang Aerospace University in 2018, and his M.S. degree in mechanical design and theory from Northeastern University in 2021. Currently, he is a Ph.D. candidate at School of Mechanical Engineering and Automation, Northeastern University. His research interests include control theory and application, manipulator control with flexible joints.

Zhengding Li received his B.S. degree from Northeastern University in 2019. Currently, he is a master candidate of School of Mechanical Engineering and Automation, Northeastern University. His research interests include dynamic modeling and control theory research of manipulator, vibration suppression of flexible manipulator.

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Zhou, S., Li, X., Yin, M. et al. Dynamic modeling and vibration suppression for double flexible manipulator with a tip payload. J Mech Sci Technol 37, 4441–4454 (2023). https://doi.org/10.1007/s12206-023-0803-0

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  • DOI: https://doi.org/10.1007/s12206-023-0803-0

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