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Adaptive feed-forward controller of piezoelectric actuator for micro/nano-positioning

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Abstract

In this paper, design and implementation of an adaptive feed-forward controller for micro/nano-positioning control of piezoelectric actuator (PEA) is described. Discrete-time Dahl hysteresis-based mathematical model of the PEA is developed and the values of the model parameters are estimated through an autoregressive with exogenous terms (ARX) model identification technique using experimental input–output data. A recursive least-square estimator (RLSE)-based adaptive feed-forward (FF) controller is proposed, which takes into account the parameter uncertainty. The FF controller has also been implemented in a DsPIC30F4011 microcontroller. The established PEA model and the controller are validated by simulation and experimental results including parameter variation.

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References

  1. Schitter G and Stemmer A 2004 Identification and open-loop tracking control of a piezoelectric tube scanner for high-speed scanning-probe microscopy. IEEE Trans. Control Syst. Technol. 12(3): 449–454

    Article  Google Scholar 

  2. Gu G Y and Zhu L M 2013 Motion control of piezoceramic actuators with creep, hysteresis and vibration compensation. Sens. Actuators A: Phys. 197: 76–87

    Article  Google Scholar 

  3. Xu Q 2013 Enhanced discrete-time sliding mode strategy with application to piezoelectric actuator control. IET Control Theory Appl. 7(18): 2153–2163

    Article  MathSciNet  Google Scholar 

  4. Gu G Y, Zhu L M and Chun Y S 2014 Modeling and compensation of asymmetric hysteresis nonlinearity for piezoceramic actuators with a modified Prandtl–Ishlinskii model. IEEE Trans. Ind. Electron. 61(3): 1583–1595

    Article  Google Scholar 

  5. Zheng J C and Fu M Y 2013 Saturation control of a piezoelectric actuator for fast settling-time performance. IEEE Trans. Control Syst. Technol. 21(1): 220–8

    Article  Google Scholar 

  6. Zhou M L, Zhang Q and Wang J Y 2014 Feedforward–feedback hybrid control for magnetic shape memory alloy actuators based on the Krasnosel’skii–Pokrovskii model. PloS One 9: e97086

    Article  Google Scholar 

  7. Rosario T and Ivan I A 2014 Robust structured controllers for piezoelectric microactuators. ISA Trans. 53(6): 1857–1864

    Article  Google Scholar 

  8. Zhou M L, He S B, Hu B and Zhang Q 2015 Modified KP model for hysteresis of magnetic shape memory alloy actuator. IETE Tech. Rev. 32(1): 29–36

    Article  Google Scholar 

  9. Wang X, Alici G and Tan X 2014 Modeling and inverse feedforward control for conducting polymer actuators with hysteresis. Smart Mater. Struct. 23(2): 25015–25023

    Article  Google Scholar 

  10. Janaideh M A and Krejci P 2013 Inverse rate-dependent Prandtl–Ishlinskii model for feedforward compensation of hysteresis in a piezomicropositioning actuator. IEEE/ASME Trans. Mechatron. 18(5): 1498–1507

    Article  Google Scholar 

  11. Zhang J, Merced E, Sepulveda N and Tan X 2014 Modeling and inverse compensation of nonmonotonic hysteresis in VO2-coated microactuators. IEEE/ASME Trans. Mechatron. 19(2): 579–588

    Article  Google Scholar 

  12. Chi Z Q, Jia M P and Xu Q S 2014 Fuzzy PID feedback control of piezoelectric actuator with feedforward compensation. Math. Probl. Eng. 2014: 107184

    MathSciNet  Google Scholar 

  13. Xu Q S 2014 Digital sliding-mode control of piezoelectric micro-positioning system based on input–output model. IEEE Trans. Ind. Electron. 61(10): 5517–5526

    Article  Google Scholar 

  14. Al-Wahab M A, Kasper R, Kostadinov K, Chakarov D and Tiankov T 2008 Structured piezo-ceramic mechatronic handling devices for micro and nano manipulations. In: Proceedings of the 5th International Symposium on Mechatronics and Its Applications (ISM08), Amman, 27–29 May, pp. 1–6

  15. Al Mamun A and Yao K 2015 Analysis and modeling of hysteresis of piezoelectric micro-actuator used in high precision dual-stage servo system. Control Theory Technol. 13(2): 184–203

    Article  MathSciNet  Google Scholar 

  16. Viswamurthy S R and Ganguli R 2007 Modeling and compensation of piezoceramic actuator hysteresis for helicopter vibration control. Sens. Actuators A: Phys. 135(2): 801–810

    Article  Google Scholar 

  17. Viswamurthy S R, Rao A K and Ganguli R 2007 Dynamic hysteresis of piezoceramic stack actuators used in helicopter vibration control: experiments and simulations. Smart Mater. Struct. 16(4): 1109

    Article  Google Scholar 

  18. Liaw H C and Shirinzadeh B 2011 Robust adaptive constrained motion tracking control of piezo-actuated flexure-based mechanisms for micro/nano manipulation. IEEE Trans. Ind. Electron. 58(4): 1406–1415

    Article  Google Scholar 

  19. Rakotondrabe M and Ivan I A 2011 Development and force/position control of a new hybrid thermo-piezoelectric micro gripper dedicated to micromanipulation tasks. IEEE Trans. Autom. Sci. Eng. 8(4): 824–834

    Article  Google Scholar 

  20. Leaning K K and Devasia S 2007 Feedback linearized inverse feedforward for creep, hysteresis and vibration compensation in AFM piezoactuators. IEEE Trans. Control Syst. Technol. 15(5): 927–935

    Article  Google Scholar 

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

    Article  Google Scholar 

  22. Li Y and 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): 798–810

    Article  Google Scholar 

  23. Chen X 2011 High precision adaptive control for XY-table driven by piezo-actuator. In: Proceedings of the 2011 International Conference on Advanced Mechatronic Systems, Zhengzhou, China, August 11–13

  24. Liu D and Fujii F 2014 An adaptive internal model control system of a piezo-ceramic actuator with two RBF neural networks. In: Proceedings of the 2014 IEEE International Conference on Mechatronics and Automation, August 3–6, Tianjin, China

  25. Lin F J, Shieh H J, Huang P K and Teng L T 2006 Adaptive control with hysteresis estimation and compensation using RFNN for piezo-actuator. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53(9): 1649–1661

    Article  Google Scholar 

  26. Astrom K J and Wittenmark B 1994 Adaptive control, 2nd ed. Mineola, N.Y.: Dover Publications Inc.

    Google Scholar 

  27. Li J and Yang L 2014 Adaptive PI-based sliding mode control for nanopositioning of piezoelectric actuators. Math. Probl. Eng. vol. 2014, Article ID 357864, pp. 10, DOI: 10.1155/2014/357864

    MathSciNet  Google Scholar 

  28. Shieh H J and Hsu C H 2008 An adaptive approximator-based backstepping control approach for piezoactuator-driven stages. IEEE Trans. Ind. Electron. 55(4): 1729–1738

    Article  Google Scholar 

  29. Zhang L J, Yang L X, Zhang X W and Sun L N 2010 Adaptive output feedback control with feedback feedfoward compensator for piezoactuator-driven stages. In: Proceedings of the 8th World Congress on Intelligent Control and Automation, July 6–9, Jinan, China

  30. Tao G and Kokotovic P 1995 Adaptive control of plants with unknown hysteresis. IEEE Trans. Autom. Control 40(2): 200–212

    Article  Google Scholar 

  31. Zhou M, Yang P, Wang J and Gao W 2016 Adaptive sliding mode control based on Duhem model for piezoelectric actuators. IETE Tech. Rev., DOI: 10.1080/02564602.2015.1126202

    Article  Google Scholar 

  32. Minh T V, Linh N M and Chen X 2016 Tracking control of piezoelectric actuator using adaptive model. Robot. Biomim. 3: 5, DOI: 10.1186/s40638-016-0039-x

  33. Adriaens H J M T A, Koning W L D and Banning R 2000 Modeling of piezoelectric actuators. IEEE/ASME Trans. Mechatron. 5(4): 331–334

    Article  Google Scholar 

  34. Jang M J, Chen C L and Lee J R 2005 Modeling and control of a piezoelectric actuator driven system with asymmetric hysteresis. J. Franklin Inst. 346(1): 17–32

    Article  Google Scholar 

  35. Zhang Y L, Han M L, Yu M Y, Shee C Y and Ang W T 2012 Automatic hysteresis modeling of piezoelectric micromanipulator in vision-guided micromanipulation systems. IEEE/ASME Trans. Mechatron. 17(3): 547–553

    Article  Google Scholar 

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

    Article  Google Scholar 

  37. Rakotondrabe M 2011 Bouc–Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators. IEEE Trans. Autom. Sci. Eng. 8(2): 428–431

    Article  Google Scholar 

  38. Xu Q and Li Y 2010 Dahl model-based hysteresis compensation and precise positioning control of an XY parallel micromanipulator with piezoelectric actuation. J. Dyn. Syst. Meas. Control 132: 041011.

    Article  Google Scholar 

  39. Deng L and Tan Y 2008 Modeling of rate-dependent hysteresis in piezoelectric actuators. In: Proceedings of the IEEE International Conference on Control Applications, CCA 2008, DOI: 10.1109/CCA.2008.4629578

  40. Liu L, Tan K, Chen S, Teo T and Lee T 2012 Identification and compensation of hysteretic dynamics of piezoelectric actuators for accurate and fast scanning. In: Proceedings of the IEEE Conference on Industrial Electronics and Applications (ICIEA), DOI: 10.1109/ICIEA.2012.6360987

  41. Lampaert V and Sweavers J 2001 Online identification of hysteresis functions with non-local memory. In: Proceedings of the 2001 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, DOI: 10.1109/AIM.2001.936774

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Shome, S.K., Mukherjee, A., Karmakar, P. et al. Adaptive feed-forward controller of piezoelectric actuator for micro/nano-positioning. Sādhanā 43, 158 (2018). https://doi.org/10.1007/s12046-018-0925-8

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  • DOI: https://doi.org/10.1007/s12046-018-0925-8

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