An Operator-based Nonlinear Vibration Control System Using a Flexible Arm with Shape Memory Alloy

  • Hiroki MatsumoriEmail author
  • Ming-Cong Deng
  • Yuichi Noge
Research Article


In the past, arms used in the fields of industry and robotics have been designed not to vibrate by increasing their mass and stiffness. The weight of arms has tended to be reduced to improve speed of operation, and decrease the cost of their production. Since the weight saving makes the arms lose their stiffness and therefore vibrate more easily, the vibration suppression control is needed for realizing the above purpose. Incidentally, the use of various smart materials in actuators has grown. In particular, a shape memory alloy (SMA) is applied widely and has several advantages: light weight, large displacement by temperature change, and large force to mass ratio. However, the SMA actuators possess hysteresis nonlinearity between their own temperature and displacement obtained by the temperature. The hysteretic behavior of the SMA actuators affects their control performance. In previous research, an operator-based control system including a hysteresis compensator has been proposed. The vibration of a flexible arm is dealt with as the controlled object; one end of the arm is clamped and the other end is free. The effectiveness of the hysteresis compensator has been confirmed by simulations and experiments. Nevertheless, the feedback signal of the previous designed system has increased exponentially. It is difficult to use the system in the long-term because of the phenomenon. Additionally, the SMA actuator generates and radiates heat because electric current passing through the SMA actuator provides heat, and strain on the SMA actuator is generated. With long-time use of the SMA actuator, the environmental temperature around the SMA actuator varies through radiation of the heat. There exists a risk that the ambient temperature change dealt with as disturbance affects the temperature and strain of the SMA actuator. In this research, a design method of the operator-based control system is proposed considering the long-term use of the system. In the method, the hysteresis characteristics of the SMA actuator and the temperature change around the actuator are considered. The effectiveness of the proposed method is verified by simulations and experiments.


Operator theory nonlinear control stability right coprime factorization shape memory alloy hysteresis characteristics 


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  1. [1]
    J. M. Stevens, G. D. Bucker. Actuation and control strategies for miniature robotic surgical systems. Journal of Dynamic Systems, Measurement, and Control, vol. 127, no. 4, pp. 537–549, 2005. DOI: 10.1115/1.2098892.CrossRefGoogle Scholar
  2. [2]
    L. C. Brinson. One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable. Journal of Intelligent Material Systems and Structures, vol. 4, no. 2, pp. 229–242, 1993. DOI: 10.1177/1045389x9300400213.CrossRefGoogle Scholar
  3. [3]
    H. Asadi, M. Bodaghi, M. Shakeri, M. M. Aghdam. On the free vibration of thermally pre/post-buckled shear deformable SMA hybrid composite beams. Aerospace Science and Technology, vol. 31, no. 1, pp. 73–86, 2013. DOI: 10.1016/j.ast.2013.09.008.CrossRefGoogle Scholar
  4. [4]
    H. Asadi, M. Bodaghi, M. Shakeri, M. M. Aghdam. An analytical approach for nonlinear vibration and thermal stability of shape memory alloy hybrid laminated composite beams. European Journal of Mechanics-A/Solids, vol. 42, pp. 454–468, 2013. DOI: 10.1016/j.euromechsol. 2013.07.011.CrossRefzbMATHGoogle Scholar
  5. [5]
    H. Asadi, M. Bodaghi, M. Shakeri, M. M. Aghdam. Nonlinear dynamics of SMA-fiber-reinforced composite beams subjected to a primary/secondary-resonance excitation. Acta Mechanica, vol. 226, no. 2, pp. 43755, 2015. DOI: 10.1007/s00707-014-1191-4.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    H. Asadia, A. H. Akbarzadehbc, Q. Wang. Nonlinear thermo-inertial instability of functionally graded shape memory alloy sandwich plates. Composite Structures, vol. 120, pp. 496–508, 2015. DOI: 10.1016/j.compstruct. 2014.10.027.CrossRefGoogle Scholar
  7. [7]
    M. Samadpoura, H. Asadia, Q. Wang. Nonlinear aerothermal flutter postponement of supersonic laminated composite beams with shape memory alloys. European Journal of Mechanics A/Solids, vol. 57, pp. 18–28, 2016. DOI: 10.1016/j.euromechsol.2015.11.004.MathSciNetCrossRefGoogle Scholar
  8. [8]
    M. Ho, Y. Kim, S. S. Cheng, R. Gullapalli, J. P. Desai. Design, development, and evaluation of an MRI-guided SMA spring-actuated neurosurgical robot. The International Journal of Robotics Research, vol. 34, no. 8, pp. 1147–1163, 2015. DOI: 10.1177/0278364915579069.CrossRefGoogle Scholar
  9. [9]
    S. S. Ying, S. M. Ji, D. H. Cai, G. J. Bao, Z. Fan. A method to implement biomimetic control for a SMA springs array. In Proceedings of IEEE International Conference on Robotics and Biomimetics, Zhuhai, China, pp. 2419–2424, 2015. DOI: 10.1109/ROBIO.2015.7419701.Google Scholar
  10. [10]
    M. C. Deng. Operator-based Nonlinear Control Systems: Design and Applications. Hoboken, USA: IEEE Press, pp. 5–15, 27–31, 2014.CrossRefGoogle Scholar
  11. [11]
    M. Deng, A. Inoue, K. Ishikawa. Operator-based nonlinear feedback control design using robust right coprime factorization. IEEE Transactions of Automatic Control, vol. 51, no. 4, pp. 645–648, 2006. DOI: 10.1109/TAC.2006. 872758.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    S. Kawahata, M. C. Deng. Operator-based nonlinear temperature control experiment for microreactor group actuated by Peltier devices. International Journal of Automation and Computing, vol. 13, no. 4, pp. 401 08, 2016. DOI: 10.1007/s11633-016-0994-2.CrossRefGoogle Scholar
  13. [13]
    G. R. Chen, Z. Z. Han. Robust right coprime factorization and robust stabilization of nonlinear feedback control systems. IEEE Transactions on Automatic Control, vol. 43, no. 10, pp. 1505–1509, 1998. DOI: 10.1109/9.720519.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    N. Bu, M. C. Deng. System design for nonlinear plants using operator-based robust right coprime factorization and isomorphism. IEEE Transactions on Automatic Control, vol. 56, no. 4, pp. 952–957, 2011. DOI: 10.1109/TAC.2011. 2108370.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    M. C. Deng, A. Inoue, A. Yanou. Stable robust feedback control system design for unstable plants with input constraints using robust right coprime factorization. International Journal of Robust and Nonlinear Control, vol. 17, no. 18, pp. 1716–1733, 2007. Doi: 10.1002/rnc.1189.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    M. C. Deng, A. Inoue. Networked non-linear control for an aluminum plate thermal process with time-delays. International Journal of Systems Science, vol. 39, no. 11, pp. 1075–1080, 2008. DOI: 10.1080/00207720802085294.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    M. C. Deng, A. Inoue. Operator-based framework for fault diagnosis in nonlinear tracking control systems. Measurement and Control, vol. 39, no. 5, pp. 147–150, 2006. DOI: 10.1177/002029400603900501.CrossRefGoogle Scholar
  18. [18]
    M. C. Deng, S. J. Wen, A. Inoue. Sensorless anti-swing robust nonlinear control for travelling crane system using SVR with generalized Gaussian function and robust right coprime factorization. Transactions of the Society of Instrument and Control Engineers, vol. 47, no. 9, pp. 366–373, 2011. DOI: 10.9746/sicetr.47.366.CrossRefGoogle Scholar
  19. [19]
    S. Saito, M. C. Deng, M. Minami, C. A. Jiang, A. Yanou. Operator-based vibration control system design of a flexible arm using an SMA actuator with hysteresis. SICE Journal of Control, Measurement, and System Integration, vol. 5, no. 2, pp. 115–123, 2012. DOI: 10.9746/jcmsi.5.115.CrossRefGoogle Scholar
  20. [20]
    R. C. Smith, Z. Ounaies. A hysteresis model for piezoceramic materials. In Proceedings of ASME International Mechanical Engineering Congress and Exposition, Nashville, USA, pp. 27–32, 1999.Google Scholar
  21. [21]
    M. Brokate, P. Krejci. Wellposedness of kinematic hardening models in elastoplasticity. Mathematical Modelling and Numerical Analysis, vol. 32, no. 2, pp. 177–209, 1998. DOI: 10.1051/m2an/1998320201771.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    S. H. Bi, M. C. Deng, Y. F. Xiao. Robust stability and tracking for operator-based nonlinear uncertain systems. IEEE Transactions on Automation Science and Engineering, vol. 12, no. 3, pp. 1059–1066, 2015. DOI: 10.1109/TASE.2014.2325953.CrossRefGoogle Scholar
  23. [23]
    C. A. Jiang, M. C. Deng, A. Inoue. Robust stability of nonlinear plants with a non-symmetric Prandtl-Ishlinskii hysteresis model. International Journal of Automation and Computing, vol. 7, no. 2, pp. 213–218, 2010. DOI: 10.1007/s11633-010-0213-5.CrossRefGoogle Scholar
  24. [24]
    X. K. Chen, T. Hisayama, C. Y. Su. Robust control for the uncertain systems preceded by hysteresis and disturbances. In Proceedings of the 22nd IEEE International Symposium on Intelligent Control, Singapore, Singapore, pp. 395–400, 2007. DOI: 10.1109/ISIC.2007.4450918.Google Scholar

Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Tokyo University of Agriculture and TechnologyKoganei, TokyoJapan

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