An Adaptive Control Technique for Motion Synchronization by On-line Estimation of a Recursive Least Square Method

  • Sang-Deok Lee
  • Seul Jung
Regular Papers Control Theory and Applications


This article presents an adaptive technique to tune controller gains for the motion synchronization of two gimbal systems by using a recursive least square method in the real-time fashion. In the master-slave configuration, the slave gimbal system follows the master’s motion while the master tracks the reference. In order for the slave gimbal system to synchronize with the motion of the master gimbal system, the dynamic difference between two systems is compensated by the controller gains. The controller gains of the slave are adaptively adjusted by the recursive least square method to cope with the deviation. The performances of three control schemes such as an independent PD control, a dependent torque control, and an RLS torque control scheme are evaluated by the experimental studies for the low cost gimbal systems. Experimental studies confirm that the RLS-based adaptive scheme actually outperforms by adjusting controller gains for the motion synchronization of the master and slave configuration.


Adaptive control gains gimbal systems master and slave configuration RLS synchronized motions 


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  1. [1]
    D. Sun, G. Feng, C. M. Lam, and H. Dong, “Orientation control of a differential mobile robot through wheel synchronization,” IEEE/ASME Trans. on Mechatronics, vol. 10, no. 3, pp. 345–351, 2005. [click]CrossRefGoogle Scholar
  2. [2]
    I. Furstner and L. Gogolak, “Synchronizing the motion of multiple electric motors-new possibilities for smart motion control,” IEEE Symposium on Intelligent Systems and Informatics, pp.105–110, 2016.Google Scholar
  3. [3]
    B. K. Kim, W. K. Chung, and I. H. Suh, “Robust synchronizing motion control of twin-servo systems based on network modeling,” IEEE Conference on Decision and Control, pp. 1019–1024, 2000. [click]Google Scholar
  4. [4]
    H. Sun and T. C. Chiu, “Motion synchronization for dual cylinder electrohydraulic lift systems,” IEEE/ASME Trans. on Mechatronics, vol. 7, no. 2, pp. 171–181, 2002. [click]CrossRefGoogle Scholar
  5. [5]
    D. Granados, B. Yamamoto, H. Kamide, J. Kinugawa, and K. Kosuge, “Dance teaching by a robot: combining cognitive and physical human-robot interaction for supporting the skill learning process,” IEEE Robotics and Automation Magazine, vol. 2, no. 3, pp. 1452–1459, 2017. [click]CrossRefGoogle Scholar
  6. [6]
    D. Zhao, S. Li, F. Gao, and Q. Zhu, “Robust adaptive terminal sliding mode-based synchronized position control for multiple motion axes systems,” IET Control Theory and Applications, vol. 3, no. 1, pp. 136–150, 2009.MathSciNetCrossRefGoogle Scholar
  7. [7]
    T. Wang, J. Qiu, S. Fu, and W. Ji, “Distributed fuzzy H filtering for nonlinear multi-rate networked doubled-layer industrial processes,” IEEE Transactions on Industrial Electronics, vol. 64, no. 6, pp. 5203–5211, 2017. [click]CrossRefGoogle Scholar
  8. [8]
    T. Wang, H. Gao, and J. Qiu, “A combined fault-tolerant and predictive control for network-based industrial processes,” IEEE Transactions on Industrial Electronics, vol. 63, no. 4, pp. 2529–2536, 2016. [click]Google Scholar
  9. [9]
    T. Wang, J. Qiu, H. Gao, and C. Wang, “Network-based fuzzy control for nonlinear industrial processes with predictive compensation strategy,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 2137–2147, 2017. [click]CrossRefGoogle Scholar
  10. [10]
    C. Chen, Z. Liu, Y. Zhang, C. L. Philip Chen, and S. Xie, “Saturated Nussbaum function based approach for robotic systems with unknown actuator dynamics,” IEEE Transactions on Cybernetics, vol. 46, no. 10, pp. 2311–2322, 2016. [click]CrossRefGoogle Scholar
  11. [11]
    C. Chen, C. Wen, Z. Liu, K. Xie, Y. Zhang, and C. L. Philip Chen, “Adaptive consensus of nonlinear multiagent systems with non-identical partially unknown control directions and bounded modelling errors,” IEEE Transactions on Automatic Control, to be published, doi: 10.1109/TAC.2016.2628204.Google Scholar
  12. [12]
    C. Chen, Z. Liu, K. Xie, Y. Liu, Y. Zhang, and C. L. Philip Chen, “Adaptive fuzzy asymptotic control of MIMO systems with unknown input coefficients via a robust Nussbaum gain based approach,” IEEE Transactions on Fuzzy Systems, vol. 25, no. 5, pp. 1252–1263, 2017.CrossRefGoogle Scholar
  13. [13]
    J. Shan, “Six-degrees-of-freedom synchronized adaptive learning control for spacecraft formation flying,” IET Control Theory and Applications, vol. 2, no. 10, pp. 930–949, 2008. [click]MathSciNetCrossRefGoogle Scholar
  14. [14]
    S. P. Viswanathan and A. Sanyal, “Design of an adaptive singularity-free control moment gyroscope actuator for agile and precise attitude control of cubeset,” Proc. of Indian Control Conference, pp. 284–291, 2016. [click]Google Scholar
  15. [15]
    A. Berry, D. Lemus, R. Babuska, and H. Vallery, “Directional singularity-robust torque control for gyroscopic actuators,” IEEE/ASME Trans. on Mechatronics, vol. 21, no. 6, pp. 2755–2763, 2016.CrossRefGoogle Scholar
  16. [16]
    J. Fan and D. Zhou, “Nonlinear attitude control of flexible spacecraft with scissored pairs of control moment gyros,” International Conference on Pervasive Computing, Signal Processing and Applications, pp. 719–722, 2010.Google Scholar
  17. [17]
    H. M. Oliveira and L. V. Melo, “Huygens synchronization of two clocks,” Scientific Reports, vol. 5, pp. 11548, 2015.CrossRefGoogle Scholar
  18. [18]
    X. Zhao, H. Yang, H. Karimi, and Y. Zhu, “Adaptive neural control of MIMO nonstrict-feedback nonlinear systems with time delay,” IEEE Trans. on Cybernetics, vol. 46, no. 6, pp. 1337–1349, 2016. [click]CrossRefGoogle Scholar
  19. [19]
    X. Zhao, P. Shi, X. Zheng, and J. Zhang, “Intelligent tracking control for a class of uncertain high-order nonlinear systems,” IEEE Trans. on Neural Networks and Learning, vol. 27, no. 9, pp. 1976–1982, 2016. [click]MathSciNetCrossRefGoogle Scholar
  20. [20]
    H. Wang, P. Liu, and P. Shi, “Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems,” IEEE Trans. on Cybernetics, vol. 47, no. 9, pp. 2568–2578, 2017. [click]CrossRefGoogle Scholar
  21. [21]
    H. Wang, W. Sun, and P. Liu, “Adaptive intelligent control for a class of nonaffine nonlinear time-delay systems with dynamic uncertainties,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, vol. 47, no. 7, pp. 1474–1485, 2017. [click]CrossRefGoogle Scholar
  22. [22]
    N. Reichbach and A. Kuperman, “Recursive-squares-based real-time estimation of super capacitor parameters,” IEEE Transactions on Energy Conversion, vol. 31, no. 2, pp. 810–812, 2016. [click]CrossRefGoogle Scholar
  23. [23]
    A. Ashrafian and J. Mirsalim, “On-line recursive method of phasor and frequency estimation for power system monitoring and relaying,” IET Generation, Transmission & Distribution, vol. 10, no. 8, pp. 2002–2011, 2016.CrossRefGoogle Scholar
  24. [24]
    A. Wiesel, O. Bibi, and A. Globerson, “Time varying autoregressive moving average models for covariance estimation,” IEEE Transactions on Signal Processing, vol. 61, no. 11, pp. 2791–2801, 2013. [click]MathSciNetCrossRefGoogle Scholar
  25. [25]
    M. Z. A. Bhotto and A. Antoniou, “New improved recursive least-squares adaptive-filtering algorithm,” IEEE Transactions on Circuits and Systems, vol. 60, no. 6, pp. 1548–1558, 2012.MathSciNetCrossRefGoogle Scholar
  26. [26]
    M. Badoni, A. Singh, and B. Singh, “Variable forgetting factor recursive least square control algorithm for DSTATCOM,” IEEE Transactions on Power Delivery, vol. 30, no. 5, pp. 2353–2361, 2015.CrossRefGoogle Scholar
  27. [27]
    A. G. Wu, Y. Y. Qian, and W. J. Wu, “Bias compensationbased recursive least-squares estimation with forgetting factors for output error moving average systems,” IET Signal Processing, vol. 8, no. 5, pp. 483–494, 2014. [click]CrossRefGoogle Scholar
  28. [28]
    M. Beza and M. Bongiorno, “Application of recursive least squares algorithm with variable forgetting factor for frequency component estimation in a generic input signal,” IEEE Transactions on Industry Applications, vol. 50, no. 2, pp. 1168–1176, 2014. [click]CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Intelligent Systems and Emotional Engineering(ISEE) Laboratory, Department of Mechatronics EngineeringChungnam National UniversityDaejeonKorea

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