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Adaptive Fuzzy Sliding Mode Control for Nano-positioning of Piezoelectric Actuators

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Abstract

In this paper, an adaptive fuzzy sliding mode control method is presented, which combines a fuzzy component added on the switching control part for use in controlling the piezoelectric actuators’ systems with uncertainties. The fuzzy logic component employed in the controller is used to compensate the effect of nonlinear terms in the system. The resulting control strategy is devised using sliding mode control schemes. Furthermore, the additional fuzzy term accelerates convergence toward the sliding surface and suppresses the chattering phenomenon. By using Lyapunov-based stability analysis, the asymptotic tracking ability of the designed controller is proved. Experimental results confirm that the designed control approach produces faster response and smaller tracking errors in comparison with the conventional sliding mode controller. The effectiveness and feasibility of the proposed control technique are verified through experimental investigations on a PEA stage.

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References

  1. Moheimani, S.: Invited review article: accurate and fast nanopositioning with piezoelectric tube scanners: emerging trends and future challenges. Rev. Sci. Instrum. 79(7), 071101 (2008)

    Article  Google Scholar 

  2. Putra, A.S., Huang, S., Tan, K.K., Panda, S.K., Lee, T.H.: Design, modeling, and control of piezoelectric actuators for intracytoplasmic sperm injection. Control Syst. Technol. IEEE Trans. 15(5), 879–890 (2007)

    Article  Google Scholar 

  3. Clayton, G.M., Tien, S., Leang, K.K., Zou, Q., Devasia, S.: A review of feedforward control approaches in nanopositioning for high-speed spm. J. Dyn. Syst. Meas. Control 131(6), 061101 (2009)

    Article  Google Scholar 

  4. Song, H., Vdovin, G., Fraanje, R., Schitter, G., Verhaegen, M.: Extracting hysteresis from nonlinear measurement of wavefront-sensorless adaptive optics system. Opt. Lett. 34(1), 61–63 (2009)

    Article  Google Scholar 

  5. Eleftheriou, E.: Nanopositioning for storage applications. Annu. Rev. Control 36(2), 244–254 (2012)

    Article  Google Scholar 

  6. Devasia, S., Eleftheriou, E., Moheimani, S.R.: A survey of control issues in nanopositioning. Control Syst. Technol. IEEE Trans. 15(5), 802–823 (2007)

    Article  Google Scholar 

  7. Clayton, G., Tien, S., Fleming, A., Moheimani, S., Devasia, S.: Inverse-feedforward of charge-controlled piezopositioners. Mechatronics 18(5), 273–281 (2008)

    Article  Google Scholar 

  8. Minase, J., Lu, T.-F., Cazzolato, B., Grainger, S.: A review, supported by experimental results, of voltage, charge and capacitor insertion method for driving piezoelectric actuators. Precis. Eng. 34(4), 692–700 (2010)

    Article  Google Scholar 

  9. Ma, Y.T., Huang, L., Liu, Y.B., Feng, Z.H.: Note: creep character of piezoelectric actuator under switched capacitor charge pump control. Rev. Sci. Instrum. 82(4), 046106 (2011)

    Article  Google Scholar 

  10. Juhász, L., Maas, J., Borovac, B.: Parameter identification and hysteresis compensation of embedded piezoelectric stack actuators. Mechatronics 21(1), 329–338 (2011)

    Article  Google Scholar 

  11. Liu, L., Tan, K., Chen, S., Teo, C., Lee, T.: Discrete composite control of piezoelectric actuators for high-speed and precision scanning. Ind. Inform. IEEE Trans. 9(2), 859–868 (2013)

    Article  Google Scholar 

  12. Mokaberi, B., Requicha, A.A.: Compensation of scanner creep and hysteresis for afm nanomanipulation. Autom. Sci. Eng. IEEE Trans. 5(2), 197–206 (2008)

    Article  Google Scholar 

  13. Huang, Y.-C., Lin, D.-Y.: Ultra-fine tracking control on piezoelectric actuated motion stage using piezoelectric hysteretic model. Asian J. Control 6(2), 208–216 (2004)

    Article  Google Scholar 

  14. Song, G., Zhao, J., Zhou, X., De Abreu-García, J.A.: Tracking control of a piezoceramic actuator with hysteresis compensation using inverse preisach model. Mechatron. IEEE/ASME Trans. 10(2), 198–209 (2005)

    Article  Google Scholar 

  15. Lin, C.-J., Yang, S.-R.: Precise positioning of piezo-actuated stages using hysteresis-observer based control. Mechatronics 16(7), 417–426 (2006)

    Article  Google Scholar 

  16. Sebastian, A., Salapaka, S.M.: Design methodologies for robust nano-positioning. Control Syst. Technol. IEEE Trans. 13(6), 868–876 (2005)

    Article  Google Scholar 

  17. Wang, T., Gao, H., Qiu, J.: A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control. IEEE Trans. Neural Netw. Learn. Syst. (2015). doi:10.1109/TNNLS.2015.2411671

  18. Dong, J., Salapaka, S.M.: Robust control of a parallel-kinematic nanopositioner. J. Dyn. Syst. Meas. Control 130(4), 041007 (2008)

    Article  Google Scholar 

  19. Seo, T.W., Kim, H.S., Kang, D.S., Kim, J.: Gain-scheduled robust control of a novel 3-dof micro parallel positioning platform via a dual stage servo system. Mechatronics 18(9), 495–505 (2008)

    Article  Google Scholar 

  20. Liaw, H.C., Shirinzadeh, B., Smith, J.: Enhanced sliding mode motion tracking control of piezoelectric actuators. Sens. Actuators A 138(1), 194–202 (2007)

    Article  Google Scholar 

  21. Liaw, H.C., Shirinzadeh, B., Smith, J.: Sliding-mode enhanced adaptive motion tracking control of piezoelectric actuation systems for micro/nano manipulation. Control Syst. Technol. IEEE Trans. 16(4), 826–833 (2008)

    Article  Google Scholar 

  22. Shen, J.-C., Jywe, W.-Y., Liu, C.-H., Jian, Y.-T., Yang, J.: Sliding-mode control of a three-degrees-of-freedom nanopositioner. Asian J. Control 10(3), 267–276 (2008)

    Article  MathSciNet  Google Scholar 

  23. Li, H., Pan, Y., Zhou, Q.: Filter design for interval type-2 fuzzy systems with d stability constraints under a unified frame. IEEE Trans. Fuzzy Syst. 23(3), 719–725 (2014)

    Article  Google Scholar 

  24. Qiu, J., Feng, G., Gao, H.: Fuzzy-model-based piecewise \(H_\infty\) static-output-feedback controller design for networked nonlinear systems. IEEE Trans. Fuzzy Syst. 18(5), 919–934 (2010)

    Article  Google Scholar 

  25. Lin, C.-Y., Chen, P.-Y.: Precision tracking control of a biaxial piezo stage using repetitive control and double-feedforward compensation. Mechatronics 21(1), 239–249 (2011)

    Article  Google Scholar 

  26. Slotine, J.-J.E., Li, W., et al.: Applied Nonlinear Control, vol. 199, 1st edn. Prentice Hall, New Jersey (1991)

    MATH  Google Scholar 

  27. Duan, S., An, G., Xue, J., Wu, J., Wang, M., Lin, T.: Adaptive sliding mode control for electrohydraulic servo force control systems. Jixie Gongcheng Xuebao (Chin. J. Mech. Eng.) (China) 38(5), 109–113 (2002)

    Article  Google Scholar 

  28. Li, H., Sun, X., Wu, L., Lam, H.: State and output feedback control of a class of fuzzy systems with mismatched membership functions. IEEE Trans. Fuzzy Syst. (2014). doi:10.1109/TFUZZ.2014.2387876

  29. Lin, C.-M., Hsu, C.-F., Chen, T.-Y.: Adaptive fuzzy total sliding-mode control of unknown nonlinear systems. IEEE Trans. Fuzzy Syst. 14(3), 434–443 (2012)

    MathSciNet  Google Scholar 

  30. Su, X., Wu, L., Shi, P., Chen, C.P.: Model approximation for fuzzy switched systems with stochastic perturbation. IEEE Trans. Fuzzy Syst. (2014). doi:10.1109/TFUZZ.2014.2362153

  31. Jhi, H.-L., Tseng, C.-S.: Robust static output feedback fuzzy control design for nonlinear discrete-time systems with persistent bounded disturbances. Int. J. Fuzzy Syst. 14(1), 131–140 (2012)

    MathSciNet  Google Scholar 

  32. Qiu, J., Feng, G., Yang, J.: A new design of delay-dependent robust \(H_\infty\) filtering for discrete-time t-s fuzzy systems with time-varying delay. IEEE Trans. Fuzzy Syst. 17(5), 1044–1058 (2009)

    Article  Google Scholar 

  33. Ho, H., Wong, Y.-K., Rad, A.B.: Adaptive fuzzy sliding mode control with chattering elimination for nonlinear siso systems. Simul. Model. Pract. Theory 17(7), 1199–1210 (2009)

    Article  Google Scholar 

  34. Li, H., Wu, C., Shi, P., Gao, Y.: Control of nonlinear networked systems with packet dropouts: interval type-2 fuzzy model-based approach. IEEE Trans. Cybern. (2014). doi:10.1109/TCYB.2014.2371814

  35. Su, X., Wu, L., Shi, P., Song, Y.-D.: A novel approach to output feedback control of fuzzy stochastic systems. Automatica 50(12), 3268–3275 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  36. Cerman, O., Hušek, P.: Adaptive fuzzy sliding mode control for electro-hydraulic servo mechanism. Expert Syst. Appl. 39(11), 10269–10277 (2012)

    Article  Google Scholar 

  37. Xu, Q., Li, Y.: Fuzzy sliding mode control with perturbation estimation for a piezoactuated micromanipulator. In: Zeng, Z., Wang, J. (eds.) Advances in Neural Network Research and Applications, pp. 153–160. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  38. Wang, L.-X.: A Course in Fuzzy Systems. Prentice-Hall Press, Upper Saddle River (1999)

    Google Scholar 

  39. Dawson, D.M., Hu, J., Burg, T.C.: Nonlinear Control of Electric Machinery. Marcel Dekker, New York (1998)

    Google Scholar 

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Acknowledgments

The authors would like to thank Dr. Jinjun Shan of York University for his equipments support used for experiments in this paper.

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Correspondence to Jin Li.

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Yang, L., Li, J. Adaptive Fuzzy Sliding Mode Control for Nano-positioning of Piezoelectric Actuators. Int. J. Fuzzy Syst. 19, 238–246 (2017). https://doi.org/10.1007/s40815-015-0084-6

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  • DOI: https://doi.org/10.1007/s40815-015-0084-6

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