Enhanced backstepping sliding mode controller for motion tracking of a nonlinear 2-DOF piezo-actuated micromanipulation system

  • Amelia Ahmad Khalili
  • Zaharuddin Mohamed
  • Mohd Ariffanan Mohd Basri
Technical Paper


In this paper a robust backstepping sliding mode controller is developed for tracking control of 2-DOF piezo-actuated micromanipulation system. The control approach is established to obtain high precision tracking in the existence of hysteresis nonlinearity, model uncertainties and external disturbances which treated as a lumped uncertainty. The control scheme is developed based on backstepping technique and a sliding surface is introduced in the final stage of the algorithm. To attenuate the chattering problem caused by a discontinuous switching function, a simple fuzzy system is used. The asymptotical stability of the system can be guaranteed since the control law is derived based on Lyapunov theorem. The effectiveness and feasibility of the suggested approach are tested for tracking of a micrometer-level reference trajectories. From the results, it is shown that the developed control system not only achieves satisfactory control performance, but also eliminates the chattering phenomena in the control effort.



This work is supported by the Universiti Teknologi Malaysia Post-Doctoral Fellowship Scheme for the project ‘A Control Design of a Piezoelectric Actuator for Bio-manipulation Systems.’


  1. Acar C, Murakami T (2008). Underactuated two-wheeled mobile manipulator control using nonlinear backstepping method. In: proceedings of 34th annual conference of the IEEE industrial electronics society. pp 1680–1685Google Scholar
  2. Adriaens HJMTA, de Koning WL, Banning R (1999). Feedback-linearization control of a piezo-actuated positioning mechanism. In: proceedings of european control conference (ECC). pp 1982–1987Google Scholar
  3. Ahmad I, Abdurraqeeb AM (2017) H∞ control design with feed-forward compensator for hysteresis compensation in piezoelectric actuators. Automatika 57(3):691–702Google Scholar
  4. Astrom KJ, Wittenmark B (1995) Adaptive Control. Addison-Wesley, New YorkGoogle Scholar
  5. Badr BM, Ali WG (2010) Nano positioning fuzzy control for piezoelectric actuators. Int J Eng Technol 10:70–74Google Scholar
  6. Bai R, Tong S, Karimi HR (2013) Modeling and backstepping control of the electronic throttle system. Math Probl Eng 87:1–6MathSciNetzbMATHGoogle Scholar
  7. Čas J, Škorc G, Šafarič R (2010) Neural network position control of XY piezo actuator stage by visual feedback. Neural Comput Appl 19(7):1043–1055Google Scholar
  8. Chan CY, Nguang SK (2002) Backstepping control for a class of power systems. Syst Anal Model Simul 42(6):825–849MathSciNetzbMATHGoogle Scholar
  9. de Oliveira AS, da Costa Ferreira D, Chavarette FR, Peruzzi NJ, Marques VC (2015) Piezoelectric optimum placement via LQR controller. Adv Mater Res 1077:166–171Google Scholar
  10. Ding B, Li Y, Xiao X, Tang Y (2016) Optimized PID tracking control for piezoelectric actuators based on the Bouc–Wen model. In: proceedings of IEEE international conference on robotics and biomimetics (ROBIO). pp 1576–1581Google Scholar
  11. Elahinia M, Chen Y, Qiu J, Palacios J, Smith EC (2012) Tracking control of piezoelectric stack actuator using modified Prandtl-Ishlinskii model. J Intell Mater Syst Struct 24(6):753–760Google Scholar
  12. Huang YC, Lin DY (2004) Ultra-fine tracking control on piezoelectric actuated motion stage using piezoelectric hysteretic model. Asian J Control 6(2):208–216MathSciNetGoogle Scholar
  13. Ikhouane F, Rodellar J (2005) On the hysteretic Bouc–Wen model. Nonlinear Dyn 42(1):79–95zbMATHGoogle Scholar
  14. Krstic M, Kanellakopoulos I, Kokotovic P (1995) Nonlinear and adaptive control design, vol 222. Wiley, New YorkzbMATHGoogle Scholar
  15. Lee S-H, Royston TJ, Friedman G (2000) Modeling and compensation of hysteresis in piezoceramic transducers for vibration control. J Intell Mater Syst Struct 11(10):781–790Google Scholar
  16. Lee G, You K, Kang T, Yoon KJ, Lee JO, Park JK (2010) Modeling and design of H-Infinity controller for piezoelectric actuator LIPCA. J Bionic Eng 7(2):168–174Google Scholar
  17. Li Y, Xu Q (2010) Adaptive sliding mode control with perturbation estimation and PID sliding surface for motion tracking of a piezo-driven micromanipulator. IEEE Trans Control Syst Technol 18(4):798–810Google Scholar
  18. Li P, Yan F, Ge C, Zhang M (2012) Ultra-precise tracking control of piezoelectric actuators via a fuzzy hysteresis model. Rev Sci Instrum 83(8):085114Google Scholar
  19. Liang Y, Liu Y (2012) Backstepping control for nonlinear systems of offshore platforms. J Theor Appl Inf Technol 45(2):468–471MathSciNetGoogle Scholar
  20. Lin C-J, Yang S-R (2006) Precise positioning of piezo-actuated stages using hysteresis-observer based control. Mechatronics 16(7):417–426Google Scholar
  21. Lin J, Chiang H, Lin C (2011) Tuning PID control parameters for micro-piezo-stage by using grey relational analysis. Expert Syst Appl 38(11):13924–13932Google Scholar
  22. Liu V-T (2012) Self-tuning Neuro-PID controller for piezoelectric actuator. Adv Sci Lett 14(1):141–145Google Scholar
  23. Liu Y, Shan J, Gabbert U, Qi N (2013) Hysteresis and creep modeling and compensation for a piezoelectric actuator using a fractional-order Maxwell resistive capacitor approach. Smart Mater Struct 22(11):115020Google Scholar
  24. Low T, Guo W (1995) Modeling of a three-layer piezoelectric bimorph beam with hysteresis. J Microelectromech Syst 4(4):230–237Google Scholar
  25. Onawola OO, Sinha S (2011) A feedback linearization approach for panel flutter suppression with piezoelectric actuation. J Comput Nonlinear Dyn 6(3):031006Google Scholar
  26. Payam AF, Fathipour M, Yazdanpanah MJ (2009). A backstepping controller for piezoelectric actuators with hysteresis in nanopositioning. In: proceedings of 4th IEEE international conference on nano/micro engineered and molecular systems (NEMS). pp 711–716Google Scholar
  27. Rakotondrabe M (2011) Bouc–Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators. IEEE Trans Autom Sci Eng 8(2):428–431Google Scholar
  28. Ranaweera KMIU, Senevirathne KAC, Weldeab MK, Karimi HR (2013) Backstepping control design for a semiactive vehicle suspension system equipped with magnetorheological rotary brake. Int J Control Theory Appl 6(1):15–27Google Scholar
  29. Shabaninia F, Mavaddat M (2014) Identification and control for a single-axis PZT nanopositioner stage. Univ J Mech Eng 2(4):132–137Google Scholar
  30. Shen JC, Jywe WY, Liu CH, Jian YT, Yang J (2008) Sliding-mode control of a three-degrees-of-freedom nanopositioner. Asian J Control 10(3):267–276MathSciNetGoogle Scholar
  31. Stakvik JÅ, Ragazzon MR, Eielsen AA, Gravdahl JT (2015) On implementation of the Preisach model: identification and inversion for hysteresis compensation. Model Identif Control 36(3):133–142Google Scholar
  32. Svečko R, Kusić D (2015) Feedforward neural network position control of a piezoelectric actuator based on a BAT search algorithm. Expert Syst Appl 42(13):5416–5423Google Scholar
  33. Thomas ME, Gopinath A (2016) LQR Control of Piezoelectric Actuators. Int Res J Eng Technol 3(7):96–102Google Scholar
  34. Toader A, Ursu I (2007) Backstepping control synthesis for hydrostatic type flight controls electrohydraulic actuators. Ann Univ Craiova Ser Autom Comput Electron Mechatron 4(31):1Google Scholar
  35. Wai R-J (2007) Fuzzy sliding-mode control using adaptive tuning technique. IEEE Trans Ind Electron 54(1):586–594Google Scholar
  36. Witkowska A, Śmierzchalski R (2007) The use of backstepping method to ship course controller. TransNav Int J Mar Navig Saf Sea Transp 1(3):313–317zbMATHGoogle Scholar
  37. Xiao S, Li Y (2014) Dynamic compensation and H∞ control for piezoelectric actuators based on the inverse Bouc–Wen model. Robot Comput Integr Manuf 30(1):47–54MathSciNetGoogle Scholar
  38. Xie WF, Fu J, Yao H, Su CY (2009) Neural network-based adaptive control of piezoelectric actuators with unknown hysteresis. Int J Adapt Control Signal Process 23(1):30–54MathSciNetzbMATHGoogle Scholar
  39. Xu Q (2014) Digital sliding-mode control of piezoelectric micropositioning system based on input–output model. IEEE Trans Ind Electron 61(10):5517–5526Google Scholar
  40. Yang L, Li Z, Sun G (2014) Nano-positioning with sliding mode based control for piezoelectric actuators. In: Proceedings of International Conference on Mechatronics and Control (ICMC). pp 802–807Google Scholar
  41. Youssef AMM (2013) Optimized PID tracking controller for piezoelectric hysteretic actuator model. World J Model Simul 9(3):223–234Google Scholar
  42. Yu Y, Naganathan N, Dukkipati R (2002) Preisach modeling of hysteresis for piezoceramic actuator system. Mech Mach Theory 37(1):49–59MathSciNetzbMATHGoogle Scholar
  43. Zhou M, Wang J (2013) Research on hysteresis of piezoceramic actuator based on the Duhem model. Sci World J 2013:1–6Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electrical Engineering, Faculty of EngineeringUniversiti Teknologi Malaysia, UTM Johor BaharuJohor BaharuMalaysia

Personalised recommendations