Model development for atomic force microscope stage mechanisms

SIAM Journal on Applied Mathematics

Volumn 66, Issue 6, 2006, Pages 1998-2026

  Smith, Ralph C ^a   Hatch, Andrew G ^a   De, Tathagata ^b   Salapaka, Murti V ^b   Del Rosario, Ricardo C H ^c   Raye, Julie K ^d  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b Iowa State University   (United States)

^c Institute of Mathematics and Natural Sciences Research Institute   (Philippines)

^d VIRGINIA COMMONWEALTH UNIVERSITY   (United States)

Author keywords

Atomic force microscope; Dynamics; Hysteresis model

Indexed keywords

LEAD ZIRCONATE TITANATE (PZT) DEVICES; NANOPOSITIONER DESIGNS; NONLINEAR CONSTITUTIVE RELATIONS;

LEAD COMPOUNDS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; STOCHASTIC PROGRAMMING;

ATOMIC FORCE MICROSCOPY;

EID: 33845533998     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/05063307X     Document Type: Article

References (40)

1. B.L. BALL, R.C. SMITH, S-J. KIM, AND S. SEELECKE, A stress-dependent hysteresis model for ferroelectric materials, J. Intelligent Material Systems Structures, to appear.
2. H.T. BANKS, K. ITO, AND Y. WANG, Well-posedness for damped second order systems with unbounded input operators, Differential Integral Equations, 8 (1995), pp. 587-606.
3. H.T. BANKS, R.C. SMITH, AND Y. WANG, Smart Material Structures: Modeling, Estimation and Control, Masson/John Wiley, Paris/Chichester, 1996.
4. T.R. BRAUN AND R.C. SMITH, Efficient implementation algorithms for homogenized energy models, Continuum Mech. Thermodynamics, 18 (2006), pp. 137-155.
5. W. CHEN AND C.S. LYNCH, A model for simulating polarization switching and AF-F phase changes in ferroelectric ceramics, J. Intelligent Material Systems Structures, 9 (1998), pp. 427-431.
6. W. CHEN AND C.S. LYNCH, A micro-electro-mechanical model for polarization switching of ferroelectric materials, Acta Mater., 46 (1998), pp. 5303-5311.
7. D. CROFT, G. SHED, AND S. DEVASIA, Creep, hysteresis, and vibration compensation for piezoactuators: Atomic force microscopy application, J. Dynamic Systems, Measurement, and Control, 23 (2001), pp. 35-43.
8. A. DANIELE, S. SALAPAKA, M.V. SALAPAKA, AND M. DAHLEH, Piezoelectric scanners for atomic force microscopes: Design of lateral sensors, identification and control, in Proceedings of the America Control Conference, San Diego, CA, 1999, IEEE Press, Piscataway, NJ, pp. 253-257.
9. R.C.H. DEL ROSARIO AND R.C. SMITH, Spline approximation of thin shell dynamics, Internat. J. Numer. Methods Engrg., 40 (1997), pp. 2807-2840.
10. R.C.H. DEL ROSARIO AND R.C. SMITH, LQR control of thin shell dynamics: Formulation and numerical implementation, J. Intelligent Material Systems Structures, 9 (1998), pp. 301-320.
11. R. GARCÍA AND R. PÉREZ, Dynamic atomic force microscopy methods, Surface Sci. Reports, 47 (2002), pp. 197-301.
12. P. GE AND M. JOUANEH, Modeling hysteresis in piezoceramic actuators. Precision Engineering, 17 (1995), pp. 211-221.
13. R.J. GIESSIBL, Advances in atomic force microscopy, Rev. Modern Phys., 75 (2003), pp. 949-983.
14. P.K. HANSMA, V.B. ELINGS, O. MARTI, AND C.E. BRACKER, Scanning tunneling microscopy and atomic force microscopy: Application to biology and technology, Science, 242 (1988), pp. 209-242.
15. A.G. HATCH, Model Development and Control Design for Atomic Force Microscopy, Ph.D. Dissertation, Department of Mathematics, North Carolina State University, Raleigh, NC, 2004.
16. A.G. HATCH, R.C. SMITH, T. DE, AND M.V. SALAPAKA, Construction and experimental implementation of a model-based inverse filter to attenuate hysteresis in ferroelectric transducers, IEEE Trans. Control Systems Technol., to appear.
17. L. HUANG AND H.F. TIERSTEN, An analytic description of slow hysteresis in polarized ferroelectric ceramic actuators, J. Intelligent Material Systems Structures, 9 (1998), pp. 417-426.
18. C.M. LANDIS, Non-linear constitutive modeling of ferroelectrics, Current Opinion in Solid State and Materials Sci., 8 (2004), pp. 59-69.
19. W. LU, D.-N. FANG, AND K-C. HWANG, Nonlinear electric-mechanical behavior and micromechanics modelling of ferroelectric domain evolution, Acta Mater., 47 (1999), pp. 2913-2926.
20. J.A. MAIN, E. GARCIA, AND D.V. NEWTON, Precision position control of piezoelectric actuators using charge feedback, J. Guidance, Control, and Dynamics, 18 (1995), pp. 1068-73.
21. J.A. MAIN, D. NEWTON. L. MASSENGIL. AND E. GARCIA, Efficient power amplifiers for piezoelectric, applications, Smart Materials and Structures, 5 (1996), pp. 766-775.
22. ∞ control design for a magnetostrictive transducer, in Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, 2003, IEEE Press. Piscataway, NJ, pp. 1801-1806.
23. J.M. NEALIS AND R.C. SMITH, Model-based robust control design for magnetostrictive transducers operating in hysteretic and nonlinear regimes, IEEE Trans. Control Systems Technol., to appear.
24. M.B. OZER AND T.J. ROYSTON, Modeling the effect of piezoceramic hysteresis in structural vibration control, Smart Structures and Materials 2001, Proc. SPIE 4326. SPIE, Bellingham, WA, 2001. pp. 89-100.
25. P.M. PRENTKR, Splines and Variational Methods, Wiley, New York, 1975.
26. J.K. RAYK AND R.C. SMITH, A temperature-dependent hysteresis model for relaxor ferroelectric compounds, Proc. SPIE. Smart Structures and Materials 2004, 5383, SPIE, Bellingham, WA, 2004, pp. 1-10.
27. G. ROBERT, D. DAMJANOVIC, AND N. SETTER, Preisach modeling of piezoelectric nonlinearity in ferroelectric ceramics, J. Appl. Phys., 89 (2001), pp. 5067-5074.
28. D. RUGAR, O. ZÜGER. S.T. HOEN, C.S. YANNONI, H.-M. VIETH AND R.D. KENDRICK, Force detection of nuclear magnetic resonance, Science, 264 (1994), pp. 1560-1563.
29. S. SALAPAKA, A. SEBASTIAN, J.P. CLEVELAND, AND M.V. SALAPAKA, High bandwidth nano-positionar: A robust control approach, Rev. Scientific Instruments, 73 (2002), pp. 3232-3241.
30. R.C. SMITH, Smart Material Systems: Model Development, Frontiers in Appl. Math. 32, SIAM, Philadelphia, PA, 2005.
31. R.C. SMITH AND A. HATCH. Parameter estimation techniques for nonlinear hysteresis models, in Smart Structures and Materials 2004, Proc. SPIE 5383, SPIE, Bellingham, WA, 2004, pp. 155-163.
32. R.C. SMITH, A. HATCH, B. MUKHERJEE, AND S. LIU, A homogenized energy model for hysteresis in ferroelectric materials: General density formulation, J. Intelligent Material Systems Structures, 16 (2005), pp. 713-732.
33. R.C. SMITH AND C.L. HOM, Domain wall theory for ferroelectric hysteresis, J. Intelligent Material Systems Structures. 10 (1999), pp. 195-213.
34. R.C. SMITH AND Z. OUNAIES, A domain wall model for hysteresis in piezoelectric materials, J. Intelligent Material Systems Structures, 11 (2000), pp. 62-79.
35. R.C. SMITH AND M. SALAPAKA, Model Development for the Positioning Mechanisms in an Atomic Force Microscope. Internat. Ser. Numer. Math. 143, Birkhäuser, Basel, Switzerland, 2002, pp. 249-269.
36. R.C. SMITH AND S. SEELECKE, An energy formulation for Preisach models, Proc. SPIE, Smart Structures and Materials 2002, 4693, SPIE, Bellingham, WA, 2002, pp. 173-182.
37. R.C. SMITH, S. SEELECKE, M.J. DAPINO AND Z. OUNAIES, A unified model for hysteresis in ferroic materials, in Smart Structures and Materials 2003, Proc. SPIE, 5049, SPIE, Bellingham, WA, 2003, pp. 88-99.
38. R.C. SMITH. S. SEELECKE, M.J. DAPINO, AND Z. OUNAIES, A unified framework for modeling hysteresis in ferroic materials, J. Mech. Phys. Solids, 54, (2005), pp. 46-85.
39. R.C. SMITH, S. SEELECKE. Z. OUNAIES. AND J. SMITH, A free energy model for hysteresis in ferroelectric, materials. J. Intelligent Material Systems Structures, 14 (2003), pp. 719-739.
40. S.A. WOLF. D.D. AWSCHALOM. R.A. BUHRMAN, J.M. DAUGHTON, S. VON MOLNÁR, M.L. CHTCHELKANOVA, AND D.M. TEGER, Spintronics: A spin-based electronics vision for the future, Science, 294 (2001), pp. 1488-1495.