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Distributed Adaptive Synchronization Control with Friction Compensation of Networked Lagrange Systems

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  • Control Theory and Applications
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Abstract

In this paper, the problem of dynamic friction compensation of networked Lagrange system is considered to design the synchronization controller with better performance. LuGre friction model is introduced to obtain accurate description of friction. The tracking control algorithms for certain and uncertain parameters are provided. Control algorithm for certain parameters has lower computation load, while control algorithm for uncertain parameters has the capability of adapting changes by learning from the tracking error. Both control algorithms achieve synchronization rapidly. Simulations are given to show the effectiveness of the proposed tracking algorithm.

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References

  1. Z. Meng, W. Ren, and Z. You, “Distributed finite-time attitude containment control for multiple rigid bodies,” Automatica, vol. 46, no. 12, pp. 2092–2099, December 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  2. S. J. Chung, U. Ahsun, and J. J. E. Slotine, “Application of synchronization to formation flying spacecraft: Lagrangian approach,” Journal of Guidance, Control, and Dynamics, vol. 32, no. 2, pp. 512–526, March 2009. [click]

    Article  Google Scholar 

  3. D. Morgan, S. J. Chung, and F. Y. Hadaegh, “Model predictive control of swarms of spacecraft using sequential convex programming,” Journal of Guidance, Control, and Dynamics, vol. 37, no. 6, pp. 1725–1740, November 2014. [click]

    Article  Google Scholar 

  4. W. Ren, “Distributed cooperative attitude synchronization and tracking for multiple rigid bodies,” IEEE Trans. on Control Systems Technology, vol. 18, no. 2, pp. 383–392, September 2009.

    Article  Google Scholar 

  5. R. Ghabcheloo, A. P. Aguiar, A. Pascoal, C. Solvestre, I. Kaminer, and J. Hespanha, “Coordinated path-following control of multiple underactuated autonomous vehicles in the presence of communication failures,” Proceedings of the 45th IEEE Conference on Decision and Control, pp. 4345–4350, December 2006.

    Chapter  Google Scholar 

  6. J. Mei, W. Ren, and G. Ma, “Distributed coordinated tracking with a dynamic leader for multiple Euler-Lagrange systems,” IEEE Trans. on Automatic Control, vol. 56, no. 6, pp. 1415–1421, January 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Rodriguez-Angeles and H. Nijmeijer, “Mutual synchronization of robots via estimated state feedback: a cooperative approach,” IEEE Trans. on Automatic Control, vol. 12, no. 4, pp. 542–554, June 2004.

    Google Scholar 

  8. J. A. Fax and R. M. Murray, “Information flow and cooperative control of vehicle formations,” IEEE Trans. on Automatic Control, vol. 49, no. 9, pp. 1465–1476, September 2004. [click]

    Article  MathSciNet  MATH  Google Scholar 

  9. S. J. Chung and J. J. E. Slotine, “Cooperative robot control and concurrent synchronization of Lagrangian systems,” IEEE Trans. on Robotics, vol. 25, no. 3, pp. 686–700, June 2009. [click]

    Article  Google Scholar 

  10. Y. Liu and Y. Jia, “Adaptive consensus control for multiple Euler-Lagrange systems with external disturbance,” International Journal of Control, Automation and Systems, vol. 15, no. 1, pp. 205–211, February 2017. [click]

    Article  Google Scholar 

  11. R. Olfati-Saber and R. M. Murray, “Consensus protocols for networks of dynamic agents,” Proc. 2003 Am. Control Conf., pp. 951–956, 2003.

    Chapter  Google Scholar 

  12. R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and timedelays,” IEEE Trans. on Automatic Control, vol. 49, no. 9, pp. 1520–1533, September 2004. [click]

    Article  MathSciNet  MATH  Google Scholar 

  13. H. Shen, J. H. Park, Z. G. Wu, and Z. Zhang, “Finitetime H ∞ sychronization for complex networks with semi-Markov jump topology,” Commun. Nonlinear SCI, vol. 24, no. 1, pp. 40–51, July 2015. [click]

    Article  MathSciNet  Google Scholar 

  14. Z. Tang, J. H. Park, and T. H. Lee, “Topology and parameters recognition of uncertain complex networks via nonidentical adaptive synchronization,” Nonlinear Dynamics, vol. 85, no. 4, pp. 2171–2181, May 2016. [click]

    Article  MathSciNet  MATH  Google Scholar 

  15. Z. Tang, J. H. Park, and J. Feng, “Impulsive effects on quasi-synchronization of neural networks with parameter mismatches and time-varying delay,” IEEE T. Neur. Net. Lear., pp. 1–12, 2017.

    Google Scholar 

  16. X. J. Wu, L. Xiang, and J. Zhou, “Distributed adaptive tracking backstepping control in networked nonidentical lagrange systems,” Nonlinear Dynamics, vol. 78, no. 2, pp. 1137–1148, October 2014.

    Article  MathSciNet  MATH  Google Scholar 

  17. R. Cui and W. Yan, “Mutual synchronization of multiple robot manipulators with unknown dynamics,” Journal of Intelligent and Robotic Systems, vol. 68, no. 2, pp. 105–119, November 2012. [click]

    Article  MATH  Google Scholar 

  18. R. Machuca, C. I. Aldana, R. Munguía, and E. Nuño, “Cartesian space consensus of heterogeneous and uncertain Euler-Lagrange systems using artificial neural networks,” International Journal of Control Automation and Systems, vol. 15, no. 3, pp. 1447–1455, June 2017.

    Article  Google Scholar 

  19. X. J. Wu, J. Zhou, L. Xiang, C. N. Lin, and H. Zhang, “Impulsive synchronization motion in networked open-loop multibody systems,” Multibody System Dynamics, vol. 30, no. 1, pp. 37–52, June 2013. [click]

    Article  MathSciNet  MATH  Google Scholar 

  20. S. Yang and J. X. Xu, “Leader follower synchronisation for networked Lagrangian systems with uncertainties: a learning approach,” International Journal of Systems Science, vol. 47, no. 4, pp. 956–965, 2016. [click]

    Article  MathSciNet  MATH  Google Scholar 

  21. S. Cheng, L. Yu, D. Zhang, and J. Ji, “Consensus of multiple Euler-Lagrange systems using one Euler-Lagrange System’s velocity measurements,” International Journal of Control, Automation and Systems, vol. 15, no. 1, pp. 450–456, February 2017. [click]

    Article  Google Scholar 

  22. A. Das and F. L. Lewis, “Distributed adaptive control for synchronization of unknown nonlinear networked systems,” Automatica, vol. 46, no. 12, pp. 2014–2021, December 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  23. J. Zhou, X. J. Wu, and Z. R. Liu, “Distributed coordinated adaptive tracking in networked redundant robotic systems with a dynamic leader,” Science China Technological Sciences, vol. 57, no. 5, pp. 905–913, May 2014. [click]

    Article  Google Scholar 

  24. C. C. De Wit, H. Olsson, K. J. Åström, and P. Lischinsky, “A new model for control of systems with friction,”

  25. H. Olsson, K. J. Åström, C. C. De Wit, M. Gäfvert, and P. Lischinsky, “Friction models and friction compensation,” European Journal of Control, vol. 4, no. 3, pp. 176–195, 1998. [click]

    Article  MATH  Google Scholar 

  26. P. R. Dahl, “A solid friction model,” Aerospace Corp El Segundo Ca, May 1968.

    Google Scholar 

  27. D. A. Haessig and B. Friedland, “On the modeling and simulation of friction,” American Control Conference, pp. 1256–1261, May 1990.

    Google Scholar 

  28. L. C. Bo and D. Pavelescu, “The friction-speed relation and its influence on the critical velocity of stick-slip motion,” Wear, vol. 82, no. 3, pp. 277–289, November 1982. [click]

    Article  Google Scholar 

  29. R. Jimnez and L. Alvarez-lcaza, “LuGre friction model for a magnetorheological damper,” Structural Control and Health Monitoring, vol. 12, no. 1, pp. 91–116, February 2005.

    Article  Google Scholar 

  30. S. J. Huang and C. M. Chiu, “Optimal LuGre friction model identification based on genetic algorithm and sliding mode control of a piezoelectric-actuating table,” Transactions of the Institute of Measurement and Control, vol. 31, no. 2, pp. 183–203, April 2009.

    Article  Google Scholar 

  31. X. Wang and S. Wang, “High performance adaptive control of mechanical servo system with LuGre friction model: Identification and compensation,” Journal of Dynamic Systems, Measurement, and Control, vol. 134, no. 1, pp. 011–021, December 2011.

    Google Scholar 

  32. Y. Tan and I. Kanellakopoulos, “Adaptive nonlinear friction compensation with parametric uncertainties,” Proceedings of the American control conference, pp. 2511–2515, June 1999.

    Google Scholar 

  33. W. F. Xie, “Sliding-mode-observer-based adaptive control for servo actuator with friction,” IEEE Trans. on Industrial Electronics, vol. 54, no. 3, pp. 1517–1527, April 2007. [click]

    Article  MathSciNet  Google Scholar 

  34. M. W. Spong and M. Vidyasagar, Robot Dynamics and Control, John Wiley & Sons, 2008.

    Google Scholar 

  35. G. Anastasi, M. Conti, M. D. Francesco, and A. Passarella, “Energy conservation in wireless sensor networks: A survey,” Ad Hoc Networks, vol. 7, no. 3, pp. 537–568, May 2009. [click]

    Article  Google Scholar 

  36. Y. Mei, Y. H. Lu, Y. C. Hu, and C. S. G. Lee, “Deployment of mobile robots with energy and timing constraints,” IEEE Trans. on Robotics, vol. 22, no. 3, pp. 507–522, June 2006. [click]

    Article  Google Scholar 

  37. M. Brossog, M. Bornschlegl, and J. Franke, “Reducing the energy consumption of industrial robots in manufacturing systems,” The International Journal of Advanced Manufacturing Technology, vol. 78, no. 5, pp. 1315–1328, May 2015. [click]

    Google Scholar 

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Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, P. R. China

    Naijing Jiang, Jian Xu & Shu Zhang

Authors
  1. Naijing Jiang
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  2. Jian Xu
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  3. Shu Zhang
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Corresponding author

Correspondence to Shu Zhang.

Additional information

Recommended by Editor Jessie (Ju H.) Park. This work was supported by the National Natural Science Foundation of China (Nos. 91748205, 11772229, 11502168), the Fundamental Research Funds for the Central Universities and the Program for Young Excellent Talents at Tongji University (No. 2015KJ018).

Naijing Jiang received the B.Sc. degree Mechanics from Tongji University, Shanghai, China, in 2011. He is currently a member of Prof. Jian Xu’s research team. His research interests include nonlinear control, tracking control, and neural network.

Jian Xu received the Ph.D. degree in dynamics and control from Tianjin University, Tianjin, China, in 1994. Since 2000, he has been a Professor with Tongji University, Shanghai, China. He is the winner of National Science Foundation for Distinguished Young Scholars and chairman of the Professional committee of dynamics and control of Chinese Society of Theoretical and Applied Mechanics. His current research interests include nonlinear dynamics and control.

Shu Zhang received the B.Sc. and Ph.D. degrees in Mechanics from Tongji University, Shanghai, China, in 2006 and 2012, respectively. In 2013 and 2014, he held a position of post-doctoral research fellow at Memorial University and York University, Canada, respectively. Since 2015, he has been with the School of Aerospace Engineering and Applied Mechanics at Tongji University where he is currently an Assistant Professor. His research interest includes control theory, nonlinear dynamics and data mining.

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Jiang, N., Xu, J. & Zhang, S. Distributed Adaptive Synchronization Control with Friction Compensation of Networked Lagrange Systems. Int. J. Control Autom. Syst. 16, 1038–1048 (2018). https://doi.org/10.1007/s12555-017-0429-z

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  • DOI: https://doi.org/10.1007/s12555-017-0429-z

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