Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-27T22:24:42.878Z Has data issue: false hasContentIssue false
  • English
  • Français

Chaos Control of Atomic Force Microscope System Using Nonlinear Model Predictive Control

Published online by Cambridge University Press:  13 September 2016

J. Keighobadi ,
J. Faraji  and
S. Rafatnia
J. Keighobadi
Affiliation:
Department of Mechanical EngineeringUniversity of TabrizTabriz, Iran
J. Faraji*
Affiliation:
Department of Mechanical EngineeringUniversity of TabrizTabriz, Iran
S. Rafatnia
Affiliation:
Department of Mechanical EngineeringUniversity of TabrizTabriz, Iran
*
*Corresponding author ([email protected])
Get access

Abstract

Owing to robust and optimal specification, model predictive control method has received wide attentions over recent years. Since in certain operational conditions, an Atomic/scanning Force Microscope (AFM) shows chaos behavior, the chaos feedback control of the AFM system is considered. According to the nonlinear model of forces interacting between the tip of micro cantilever and the substrate of AFM; the nonlinear control methods are proposed. In the paper, the chaos control of a micro cantilever AFM based on the nonlinear model predictive control (NMPC) technique is presented. Through software simulation results, the effectiveness of the designed NMPC of the AFM is assessed. The simulation results together with analytical stability proofs indicate that the proposed method is effective in keeping the system in a stable range.

Keywords

ChaosAtomic force microscope (AFM)Nonlinear model predictive control
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 3 , June 2017 , pp. 405 - 415
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Xie, H., Onal, C., Régnier, S. and Sitti, M., Atomic Force Microscope Based Nanorobotics, modelling, simulation, setup building and experiments series, 71, Springer, Berlin (2011).Google Scholar
2. Jalili, N. and Laxminarayana, K., “A review of atomic force microscopy imaging systems: application to molecular metrology and biological sciences,” Mechatronics, 14, pp. 907–945 (2004).CrossRefGoogle Scholar
3. Arjmand, M. T., Sadeghian, H., Salarieh, H. and Alasty, A., “Chaos control in AFM systems using nonlinear delayed feedback via sliding mode control,” Nonlinear Analysis: Hybrid Systems, 2, pp. 993–1001 (2008).Google Scholar
4. Burnham, N. A., Kulik, A. J., Gremaud, G. and Briggs, G. A. D., “Nanosubharmonics: the dynamics of small nonlinear contacts,” Physical Review Letters, 74, pp. 5092–5095 (1995).CrossRefGoogle ScholarPubMed
5. Ashhab, M., Salapaka, M. V., Dahleh, M. and Mezić, I., “Dynamical analysis and control of microcantilevers,” Automatica, 35, pp. 1663–1670 (1999).Google Scholar
6. Ashhab, M., Salapaka, M. V., Dahleh, M. and Mezić, I., “Melnikov-based dynamical analysis of microcantilevers in scanning probe microscopy,” Nonlinear Dynamics, 20, pp. 197–220 (1999).Google Scholar
7. Basso, M., Giarre, L., Dahleh, M. and Mezić, I., “Numerical analysis of complex dynamics in atomic force microscopes. in Control Applications,” International Conference on Control Applications, Trieste, Italy (1998).Google Scholar
8. Basso, M., Giarre, L., Dahleh, M. and Mezic, I., “Complex dynamics in a harmonically excited Lennard- Jones oscillator: Microcantilever-sample interaction in scanning probe microscopes,” Journal of Dynamic Systems, Measurement, and Control, 122, pp. 240–245 (2000).Google Scholar
9. Lee, S. I., Howell, S. W., Raman, A. and Reifenberger, R., “Nonlinear dynamic perspectives on dynamic force microscopy,” Ultramicroscopy, 97, pp. 185–198 (2003).Google Scholar
10. Rützel, S., Lee, S.I. and Raman, A., “Nonlinear dynamics of atomic–force–microscope probes driven in Lennard–Jones potentials,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 459, pp. 1925–1948 (2003).Google Scholar
11. Hu, S. and Raman, A., “Chaos in atomic force microscopy,” Physical Review Letters, 96, pp. 036107–036180 (2006).Google Scholar
12. Yamasue, K. and Hikihara, T., “Control of microcantilevers in dynamic force microscopy using time delayed feedback,” Review of Scientific Instruments, 77, pp. 053703–053708 (2006).Google Scholar
13. Salarieh, H. and Alasty, A., “Control of chaos in atomic force microscopes using delayed feedback based on entropy minimization,” Communications in Nonlinear Science and Numerical Simulation, 14, pp. 637–644 (2009).Google Scholar
14. Wang, C.-C. and Yau, H.-T., “Chaotic analysis and control of micro cantilevers with PD feedback using differential transformation method,” International Journal of Nonlinear Sciences and Numerical Simulation, 10, pp. 425–444 (2009).Google Scholar
15. Yau, H.-T. and Wang, C.-C., “Dynamics analysis and fuzzy logic controller design of atomic force microscope system with uncertainties,” Journal of Optoelectronics and Advanced Materials, 11, pp. 1178–1184 (2009).Google Scholar
16. Wang, C.-C., Pai, N.-S. and Yau, H.-T., “Chaos control in AFM system using sliding mode control by backstepping design,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 741–751 (2010).Google Scholar
17. Nozaki, R. et al., “Nonlinear control system applied to atomic force microscope including parametric errors,” Journal of Control, Automation and Electrical Systems, 24, pp. 223–231 (2013).Google Scholar
18. Morita, S., Wiesendanger, R. and Meyer, E., Noncontact Atomic Force Microscopy, 1, Springer, Berlin (2002).Google Scholar
19. Zhang, W. M., Meng, G., Zhou, J. B. and Chen, J. Y., “Nonlinear dynamics and chaos of micro cantilever- based TM-AFMs with squeeze film damping effects,” Sensors, 9, pp. 3854–3874 (2009).Google Scholar
20. Balthazar, J.M., Tusset, A.M. and Bueno, A.M., “TM-AFM nonlinear motion control with robustness analysis to parametric errors in the control signal determination,” Journal of Theoretical and Applied Mechanics, 52, pp. 93–106 (2014).Google Scholar
21. Hosseini-Pishrobat, M. and Keighobadi, J., “Force-balancing model predictive control of MEMS vibratory gyroscope sensor,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, DOI: 10.1177/0954406215607899 (2015).Google Scholar
22. Chen, H. and Allgower, F., “A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability,” Control Conference (ECC), Brussels, Belgium (1997).Google Scholar
23. Grüne, L. and Pannek, J., Nonlinear Model Predictive Control, Springer, London, (2011).Google Scholar
24. Kim, H.J., Shim, D.H. and Sastry, S., “Nonlinear model predictive tracking control for rotorcraft-based unmanned aerial vehicles,” American Control Conference, Anchorage, Alaska (2002).Google Scholar
25. Slegers, N., Kyle, J. and Costello, M., “Nonlinear Model Predictive Control Technique for Unmanned Air Vehicles,” Journal of Guidance, Control, and Dynamics, 29, pp. 1179–1188 (2006).Google Scholar
26. Allgöwer, F. and Zheng, A., Nonlinear Model Predictive Control, 26, Birkhäuser, Basel (2012).Google Scholar
27. Nozaki, R., et al. “COMPARISONS BETWEEN MODELING AND CONTROL METHOD APPLIED TO AN ATOMIC FORCE MICROSCOPE,” Proceedings of the 22nd International Congress of Mechanical Engineering (COBEM), Ribeirão Preto, Brazil (2013).Google Scholar