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A comparative study on the use of black box modelling for piezoelectric actuators

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Abstract

In this article, different approaches of the use of black box modelling techniques for piezoelectric actuators are particularly addressed, regardless of the employed technique/algorithm. A modelling approach in this paper refers to two matters: the first, the role of black box techniques in modelling (i.e. if physics-based techniques are also involved in modelling; if so, how and to what extent). From this aspect, the spectrum of approaches ranges from those merged with/inspired by classical phenomenological models to an approach based on purely system identification-based techniques. The second aspect of modelling approaches, in this article, is the input variables to the model. Current and previous values of input voltage, previous values of the output (displacement), derivatives and extremum values of the system's input/output have been used as the inputs to the model so far. Both aforementioned aspects of modelling approaches are addressed appropriately in this article, and various modelling approaches in the literature are categorized and presented in a uniform and comparable manner, so that readers can easily identify research trends in this area and the gaps in the literature. One of the identified unanswered questions in the literature is whether the extremum values of the system's input/output should/should not be used as an input to black box models of piezoelectric actuators. There are works in the literature which have/have not used the aforementioned input variables, but there is no published investigation to evidently answer the proposed question. This article, in the last section, answers this question by reporting and discussing an experimental study.

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References

  1. Kozek M, Benatzky C, Schirrer A, Stribersky A (2011) Vibration damping of a flexible car body structure using piezo-stack actuators. Control Eng Pract 19(3):298–310. doi:10.1016/j.conengprac.2009.08.001

    Article  Google Scholar 

  2. Masoy S-E, Standal O, Deibele JM, Nasholm SP, Angelsen B, Johansen TF, Tangen TA, Hansen R (2010) Nonlinear propagation acoustics of dual-frequency wide-band excitation pulses in a focused ultrasound system. J Acoust Soc Am 128(5):2695–2703. doi:10.1121/1.3488308

    Article  Google Scholar 

  3. Polit S, Dong J (2011) Development of a high-bandwidth XY nanopositioning stage for high-rate micro-/nanomanufacturing. IEEE-ASME Trans Mechatron 16(4):724–733. doi:10.1109/tmech.2010.2052107

    Article  Google Scholar 

  4. Satkoski C, Shaver G (2011) Piezoelectric fuel injection: pulse-to-pulse coupling and flow rate estimation. IEEE-ASME Trans Mechatron 16(4):627–642. doi:10.1109/tmech.2010.2048334

    Article  Google Scholar 

  5. Thompson SJ, Doel P, Brooks D, Strangwood M (2009) A 1-metre Ni coated CFRP demonstrator for large deformable mirrors. Paper presented at the 1st Ao4elt Conference-Adaptive Optics for Extremely Large Telescopes

  6. Zhang XL, Tan YH, Su MY, Xie YQ (2010) Neural networks based identification and compensation of rate-dependent hysteresis in piezoelectric actuators. Physica B 405(12):2687–2693. doi:10.1016/j.physb.2010.03.050

    Article  Google Scholar 

  7. Soderkvist J (1998) Using FEA to treat piezoelectric low-frequency resonators. IEEE Trans Ultrason Ferroelectr Freq Control 45(3):815–823

    Article  Google Scholar 

  8. Han JH, Cho KD, Youn SH, Lee I (1999) Vibration and actuation characteristics of composite structures with a bonded piezo-ceramic actuator. Smart Mater Struct 8(1):136–143

    Article  Google Scholar 

  9. Wang G, Wereley NM (1998) Frequency response of beams with passively constrained damping layers and piezo-actuators. In: Davis LP (ed) Passive damping and isolation–smart structures and materials 1998, vol 3327. Proceedings of the Society of Photo-Optical Instrumentation Engineers (Spie). pp. 44–60

  10. Boukari AF, Carmona JC, Moraru G, Malburet F, Chaaba A, Douimi M (2011) Piezo-actuators modeling for smart applications. Mechatronics 21(1):339–349. doi:10.1016/j.mechatronics.2010.12.005

    Article  Google Scholar 

  11. 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):30–54. doi:10.1002/acs.1042

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhang JJ, Wang EC, Gao RZ (2008) Neural network predictive control for piezoelectric smart structures. In: Proceedings of the 9th Biennial Conference on Engineering Systems Design and Analysis-vol 2, Haifa, Israel, 2008. pp 417–421

  13. Meeker TR (1996) Publication and proposed revision of ANSI/IEEE standard 176-1987 “ANSI/IEEE standard on piezoelectricity”. IEEE Trans Ultrason Ferroelectr Freq Control 43(5):717–718

    Article  Google Scholar 

  14. Song DW, Li CJ (1999) Modeling of piezo actuator's nonlinear and frequency dependent dynamics. Mechatronics 9(4):391–410

    Article  Google Scholar 

  15. Jung SB, Kim SW (1994) Improvement of scanning accuracy of PZT piezoelectric actuators by feedforward model-reference control. Precis Eng J Am Soc Precis Eng 16(1):49–55

    Google Scholar 

  16. Leigh T, Zimmrman D (1991) An implicit method for the nonlinear modelling and simulation of piezoceramic actuators displaying hysteresis. In: 112th ASME Winter Annual Meeting, Atlanta, USA, 1–6 December, 1991. pp. 57–63

  17. Preisach F (1935) Uber die magnetische Nachwirkung. Z Phys 94:277–302

    Article  Google Scholar 

  18. Ge P, Jouaneh M (1995) Modeling hysteresis in piezoceramic actuators. Precis Eng J Am Soc Precis Eng 17(3):211–221

    Google Scholar 

  19. Liaw HC, 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. doi:10.1109/tie.2010.2050413

    Article  Google Scholar 

  20. Zhang YD, Fang YC, Zhou XW, Dong XK (2009) Image-based hysteresis modeling and compensation for an AFM piezo-scanner. Asian J Control 11(2):166–174. doi:10.1002/asjc.092

    Article  Google Scholar 

  21. Li C, Tan Y (2004) A neural networks model for hysteresis nonlinearity. Sens Actuators A Phys 112(1):49–54. doi:10.1016/j.sna.2003.11.016

    Article  Google Scholar 

  22. Dupre L, Van Keer R, Melkebeek J (2001) Generalized scalar Preisach model for grain oriented materials excited along arbitrary directions. J Appl Phys 89(11):7245–7247

    Article  Google Scholar 

  23. Ge P, Jouaneh M (1997) Generalized Preisach model for hysteresis nonlinearity of piezoceramic actuators. Precis Eng J Am Soc Precis Eng 20(2):99–111

    Google Scholar 

  24. Han Y, Zhu J (2009) Implementation procedure for the generalized moving Preisach model based on a first order reversal curve diagram. Rare Metals 28(4):355–360. doi:10.1007/s12598-009-0071-x

    Article  MathSciNet  Google Scholar 

  25. Yu YH, Naganathan N, Dukkipati R (2002) Preisach modeling of hysteresis for piezoceramic actuator system. Mech Mach Theory 37(1):49–59

    Article  MathSciNet  MATH  Google Scholar 

  26. Makaveev D, Dupre L, De Wulf M, Melkebeek J (2001) Modeling of quasistatic magnetic hysteresis with feed-forward neural networks. J Appl Phys 89(11):6737–6739

    Article  Google Scholar 

  27. Sixdenier F, Scorretti R, Marion R, Morel L (2008) Quasistatic hysteresis modeling with feed-forward neural networks: influence of the last but one extreme values. J Magn Magn Mater 320(20):E992–E996. doi:10.1016/j.jmmm.2008.04.076

    Article  Google Scholar 

  28. Ljung L (1999) System identification, theory for the user, 2nd edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  29. Lin FJ, Shieh HJ, Huang PK (2006) Adaptive wavelet neural network control with hysteresis estimation for piezo-positioning mechanism. IEEE Trans Neural Netw 17(2):432–444. doi:10.1109/tnn.2005.863473

    Article  Google Scholar 

  30. Lin FJ, Shieh HJ, Huang PK, Teng LT (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 

  31. Yang XF, Li W, Wang YQ, Ye G (2008) Modeling hysteresis in piezo actuator based on neural networks. In: Kang L, Cai ZH, Liu Y (eds) Advances in computation and intelligence, Proceedings, vol 5370. Lecture Notes in Computer Science. pp 290–296

  32. Deng L, Tan YH (2009) Modeling hysteresis in piezoelectric actuators using NARMAX models. Sens Actuators A Phys 149(1):106–112. doi:10.1016/j.sna.2008.09.022

    Article  MathSciNet  Google Scholar 

  33. Zhang XL, Tan YH, Su MY (2009) Modeling of hysteresis in piezoelectric actuators using neural networks. Mech Syst Signal Process 23(8):2699–2711. doi:10.1016/j.ymssp.2009.05.002

    Article  Google Scholar 

  34. Ghaffari A, Mehrabian AR, Mohammad-Zaheri M (2007) Identification and control of power plant de-superheater using soft computing techniques. Eng Appl Artif Intell 20(2):273–287. doi:10.1016/j.engappai.2006.06.006

    Article  Google Scholar 

  35. Jang JR, Sun C, Mizutani E (2006) Neuro-fuzzy and soft computing. Prentice-Hall of India, New Delhi

    Google Scholar 

  36. MathWorks (2011) Fuzzy Logic Toolbox™ user's guide

  37. Dong RL, Tan YH, Chen H, Xie YQ (2008) A neural networks based model for rate-dependent hysteresis for piezoceramic actuators (vol 143, pg 370, 2008). Sens Actuators A Phys 148(1):350–351. doi:10.1016/j.sna.2008.05.001

    Article  Google Scholar 

  38. Dang XJ, Tan YH (2007) RBF neural networks hysteresis modelling for piezoceramic actuator using hybrid model. Mech Syst Signal Process 21(1):430–440. doi:10.1016/j.ymssp.2005.09.016

    Article  Google Scholar 

  39. Hwang CL, Jan C, Chen YH (2001) Piezomechanics using intelligent variable-structure control. IEEE Trans Ind Electron 48(1):47–59

    Article  Google Scholar 

  40. Ying H (1998) General SISO Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators. IEEE Trans Fuzzy Syst 6(4):582–587

    Article  Google Scholar 

  41. Ying H (1998) General Takagi-Sugeno fuzzy systems are universal approximators. 1998 IEEE International Conference on Fuzzy Systems at the IEEE World Congress on Computational Intelligence-Proceedings, vol 1–2

  42. Chen TP, Chen H (1995) Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks. IEEE Trans Neural Netw 6(4):904–910

    Article  Google Scholar 

  43. Chen TP, Chen H (1995) Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical-systems. IEEE Trans Neural Netw 6(4):911–917

    Article  Google Scholar 

  44. Chen TP, Chen H, Liu RW (1995) Approximation capability in C(R-N) by multilayer feedforward networks and related problems. IEEE Trans Neural Netw 6(1):25–30

    Article  MATH  Google Scholar 

  45. Park J, Sandberg IW (1993) Approximation and radial-basis-function networks. Neural Comput 5(2):305–316

    Article  Google Scholar 

  46. Liang JW, Chen HY, Chiang SY (2008) Precision control of a piezo-actuate system using fuzzy sliding-mode control with feedforward predictor-based compensation. In: Hwang SJ, Lee SY (eds) Advanced manufacture: focusing on new and emerging technologies, vol 594. Materials Science Forum. pp 401–406

  47. Lin FJ, Shieh HJ, Huang PK, Shieh PH (2008) An adaptive recurrent radial basis function network tracking controller for a two-dimensional piezo-positioning stage. IEEE Trans Ultrason Ferroelectr Freq Control 55(1):183–198. doi:10.1109/tuffc.2008.627

    Article  Google Scholar 

  48. Yang CH, Chang KM (2006) Adaptive neural network control for piezoelectric hysteresis compensation in a positioning system. 2006 IEEE International Symposium on Industrial Electronics, vols 1–7

  49. Mayergoyz ID (1988) Dynamic Preisach models of hysteresis. IEEE Trans Magn 24(6):2925–2927

    Article  Google Scholar 

  50. Serpico C, Visone C (1998) Magnetic hysteresis modeling via feed-forward neural networks. IEEE Trans Magn 34(3):623–628

    Article  Google Scholar 

  51. Makaveev D, Dupre L, De Wulf M, Melkebeek J (2002) Isotropic vector hysteresis modeling with feed-forward neural networks. J Appl Phys 91(10):8322–8324. doi:10.1063/1.1456400

    Article  Google Scholar 

  52. Zhang MM, Xu JZ (2011) Active control of fluctuating pressure induced by blade-vortex interaction. SCIENCE CHINA Technol Sci 54(4):862–868. doi:10.1007/s11431-010-4232-9

    Article  Google Scholar 

  53. Zhang XL, Tan YH (2010) A hybrid model for rate-dependent hysteresis in piezoelectric actuators. Sens Actuators A Phys 157(1):54–60. doi:10.1016/j.sna.2009.10.009

    Article  Google Scholar 

  54. Kosmatopoulos EB, Smyth AW, Masri SF, Chassiakos AG (2001) Robust adaptive neural estimation of restoring forces in nonlinear structures. J Appl Mech Trans Asme 68(6):880–893

    Article  MATH  Google Scholar 

  55. Pei JS, Smyth AW, Kosmatopoulos EB (2004) Analysis and modification of Volterra/Wiener neural networks for the adaptive identification of non-linear hysteretic dynamic systems. J Sound Vib 275(3–5):693–718. doi:10.1016/j.jsv.2003.06.005

    Article  Google Scholar 

  56. Nelles O (2001) Nonlinear system identfication. Springer, Berlin

    Google Scholar 

  57. Mohammadzaheri M, Chen L (2010) Intelliegnt predictive control of model helicopters' yaw angle. Asian J Control 12(6):1–13

    Article  MathSciNet  Google Scholar 

  58. Mohammadzaheri M, Chen L, Mirsepahi A, Ghanbari M, Prime Z (2010) Hybrid intelligent control of an infrared dryer. Paper presented at the 38th Austrlaian Conference of Chemical Engineering, Adelaide, Australia

  59. Mohammadzaheri M, Chen L, Ghaffari A, Willison J (2009) A combination of linear and nonlinear activation functions in neural networks for modeling a de-superheater. Simulat Model Pract Theor 17(2):398–407. doi:10.1016/j.simpat.2008.09.015

    Article  Google Scholar 

  60. Deng H, Li HX, Wu YH (2008) Feedback-linearization-based neural adaptive control for unknown nonaffine nonlinear discrete-time systems. IEEE Trans Neural Netw 19(9):1615–1625. doi:10.1109/tnn.2008.2000804

    Article  Google Scholar 

  61. Mohammadzaheri M, Chen L, Grainger S (2014) A critical review of the most popular types of neuro control. Asian J Control 16(1):1–11

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering, University of Adelaide, Adelaide, Australia

    Morteza Mohammadzaheri, Steven Grainger & Mohsen Bazghaleh

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  1. Morteza Mohammadzaheri
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  2. Steven Grainger
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Correspondence to Morteza Mohammadzaheri.

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Mohammadzaheri, M., Grainger, S. & Bazghaleh, M. A comparative study on the use of black box modelling for piezoelectric actuators. Int J Adv Manuf Technol 63, 1247–1255 (2012). https://doi.org/10.1007/s00170-012-3987-5

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