Journal of Applied Science and Engineering

Published by Tamkang University Press


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Shuang Zhang This email address is being protected from spambots. You need JavaScript enabled to view it.1, Rui Liu2 and Xinyu Qian3

1School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
2Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, University of Science and Technology Beijing, Beijing 100083, China
3Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing 100083, China


Received: December 26, 2019
Accepted: January 14, 2020
Publication Date: June 1, 2020

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This paper mainly studies how to control the flexible manipulator effectively, which can drive the flexible manipulator to reach the angular and restrain the vibration of the manipulator simultaneously. Firstly, two disturbance observers based on partial differential equations (PDEs) model are improved to ensure its convergence in finite time. Then, on the basis of the disturbance observer, two active boundary controllers are proposed to achieve the control objective. Finally, the stability and effectiveness of the designed controller are verified by theoretical analysis and simulation.

Keywords: Flexible manipulator, vibration control, finite-time disturbance observer, distributed parameter system (DPS)



  1. [1]He W, Dong Y. Adaptive fuzzy neural network control for a constrained robot using impedance learning[J]. IEEE transactions on neural networks and learning systems, 2017, 29(4): 1174-1186.
  2. [2]Zhang S, Dong Y, Ouyang Y, et al. Adaptive neural control for robotic manipulators with output constraints and uncertainties[J]. IEEE transactions on neural networks and learning systems, 2018, 29(11): 5554-5564.
  3. [3]Wei C, Gu H, Liu Y, et al. Attitude reactionless and vibration control in space flexible robot grasping operation[J]. International Journal of Advanced Robotic Systems, 2018, 15(6): 1729881418818302.
  4. [4]Liu Z, Liu J, He W. Dynamic modeling and vibration control for a nonlinear 3‐dimensional flexible manipulator[J]. International Journal of Robust and Nonlinear Control, 2018, 28(13): 3927-3945.
  5. [5]Zhang S, Yang P, Kong L, et al. Neural Networks-Based Fault Tolerant Control of a Robot via Fast Terminal Sliding Mode[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019.
  6. [6]Yang H J, Tan M. Sliding mode control for flexible-link manipulators based on adaptive neural networks[J]. International Journal of Automation and Computing, 2018, 15(2): 239-248.
  7. [7]Cao F, Liu J. Partial differential equation modeling and vibration control for a nonlinear 3D rigid‐flexible manipulator system with actuator faults[J]. International Journal of Robust and Nonlinear Control, 2019, 29(11): 3793-3807.
  8. [8]Yang Y, Liu Z, Ma G. Adaptive Distributed Control of a Flexible Manipulator Using an Iterative Learning Scheme[J]. IEEE Access, 2019, 7: 145934-145943.
  9. [9]Zhang S, Liu R, Peng K, et al. Boundary Output Feedback Control for a Flexible Two-Link Manipulator System With High-Gain Observers[J]. IEEE Transactions on Control Systems Technology, 2019.
  10. [10]Du J, Hong B, Cui C, et al. Dynamic analysis of cable-driven parallel manipulators with time-varying cable lengths[J]. Finite Elements in Analysis & Design, 2012, 48(1):1392-1399.
  11. [11]Gao H J ,He W, et al. Neural Network Control of a Two-Link Flexible Robotic Manipulator Using Assumed Mode Method[J]. IEEE Transactions on Industrial Informatics, 2018, 99:1-1.
  12. [12]Griffith B, Luo X. Hybrid finite difference/finite element immersed boundary method[J]. International journal for numerical methods in biomedical engineering, 2017, 33(12): e2888.
  13. [13]Zebin and M. Alam, “Modeling and control of a two-link flexible manipulator using fuzzy logic and genetic optimization techniques,” Journal of Computers, vol. 7, no. 3, pp. 578–585, 2012.
  14. [14]Ghaedi K, Hejazi F, Ibrahim Z, et al. Flexible foundation effect on seismic analysis of Roller Compacted Concrete (RCC) dams using finite element method[J]. KSCE Journal of Civil Engineering, 2018, 22(4): 1275-1287.
  15. [15]Zhang L J, Liu J K. Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model[J]. IET Control Theory & Applications, 2013,7(1): 43-51.
  16. [16]Meng T, He W. Iterative Learning Control of a Robotic Arm Experiment Platform with Input Constraint[J]. IEEE Transactions on Industrial Electronics, 2017:1-1
  17. [17]He X, He W, Qin H, et al. Boundary control design and stability analysis of an Euler-Bernoulli Beam system with input backlash[C]//2015 34th Chinese Control Conference (CCC). IEEE, 2015: 1389-1394.
  18. [18]Zhao Z J , Liu Y , Guo F , et al. Modelling and control for a class of axially moving nonuniform system[J]. International Journal of Systems Science, 2016, 48(4):1-13.
  19. [19]Feng Y , Yu X , Man Z . Non-singular terminal sliding mode control of rigid manipulators[J]. Automatica, 2002, 38(12):2159-2167.
  20. [20]Chen M , Wu Q X , Cui R X . Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems[J]. ISA Transactions, 2013, 52(2):198-206.
  21. [21]Li S, Sun H, Yang J, et al. Continuous finite-time output regulation for disturbed systems under mismatching condition[J]. IEEE Transactions on Automatic Control, 2014, 60(1): 277-282.
  22. [22]Levant A. Higher-order sliding modes, differentiation and output-feedback control[J]. International journal of Control, 2003, 76(9-10): 924-941.