NANODYNAMICS SYSTEMS LAB
 

Publications in nanotechnology and  dynamical systems

 

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  • Tathagata De, Pranav Agarwal, Deepak R. Sahoo, and Murti V. Salapaka, "Real-time detection of probe loss in atomic force microscopy " Appl. Phys. Lett. 89, 133119 (2006) [Abstract] [pdf]
  • 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 Transactions on Control Systems Technology. Accepted 2006. [Abstract][pdf]
  • R.C. Smith, A.G. Hatch, T. De, M.V. Salapaka, R.C.H. del Rosario, and J.K. Raye. "Model development for atomic force microscope stage mechanisms". SIAM Journal on Applied Mathematics Accepted, 2006. [Abstract][pdf]
  • D. R. Sahoo, T. De, and M. V. Salapaka, “Observer based imaging methods for atomic force microscopy,” Proceedings of 44th IEEE Conference on Decision and Control, pp. 1185–1190, December 12- 15,2005.[pdf]
  • Salapaka, Srinivasa,  De, Tathagata, Sebastian, Abu Sample-profile estimate for fast atomic force microscopy  Source: Applied Physics Letters, v 87, n 5, 2005, p 053112.[Abstract][pdf]
  • Salapaka, Srinivasa M. , De, Tathagata; Sebastian, Abu. " A robust control based solution to the sample-profile estimation problem in fast atomic force microscopy" International Journal of Robust and Nonlinear Control, v 15, n 16, Nov 10, 2005, Control at Small Length Scales, Issue 2, p 821-837. [Abstract][pdf]
  • S. Salapaka, A. Sebastian, J. P. Cleveland and M. V. Salapaka, "High Bandwidth Nano-positioner: A Robust Control Approach", Review of Scientific Instruments, (accepted) 2002.
    • This paper presents the design, identification and control of a new nano-positioning device suited to image biological samples as part of an AFM . The device is actuated by a piezoelectric stack and its motion is sensed by a Linear Variable Differential Transformer (LVDT). It is demonstrated that the conventional $PI$ control architecture does not meet the bandwidth requirements for positioning. The design and implementation of an H infinity controller demonstrates substantial improvements in the positioning speed and precision, while eliminating the undesirable nonlinear effects of the actuator. The characterization of the resulting device in terms of bandwidth, resolution, and repeatability provided illustrates the effectiveness of the modern robust control paradigm.
  • A. Sebastian, M. V. Salapaka, D. J. Chen, J. P. Cleveland, "Harmonic and power balance tools for tapping –mode AFM”, Journal of Applied Physics, June 2001, Vol. 89, Nov. 11, pages. 6473-6480.  
    • The atomic force microscope (AFM) is a powerful tool for investigating surfaces at atomic scales. Harmonic balance and power balance techniques are introduced to analyze the tapping-mode dynamics of the atomic force microscope. The harmonic balance perspective explains observations hitherto unexplained in the AFM literature. A non-conservative model for the cantilever sample interaction is developed. The energy dissipation in the sample is studied and the resulting power balance equations combined with the harmonic balance equations are used to estimate the model parameters. Experimental results confirm that the harmonic and power balance tools can be used effectively to predict the behavior of the tapping cantilever.
  • M.V. Salapaka, D. Chen, J. Cleveland, "Linearity of amplitude and phase in tapping-mode atomic force microscopy", Physical Review B., 2000.
    • In this article tapping-mode atomic force microscope dynamics is studied. The existence of a periodic orbit at the forcing frequency is shown under unrestrictive conditions. The dynamics is further analyzed using the impact model for the tip-sample interaction and a spring-mass-damper model of the cantilever. Stability of the periodic orbit is established. Closed form expressions for various variables important in tapping-mode imaging are obtained. Linear relationship of the amplitude and the sine of the phase of the first harmonic of the periodic orbit with respect to cantilever-sample offset is shown. The study reinforces gentleness of the tapping-mode on the sample. Experimental results are in excellent qualitative agreement with the theoretical predictions. The linear relationship of the sine of the phase and the amplitude can be used to infer sample properties. The comparasion between the theory and the experiments indicates essential features that are needed in a more refined model.
  • M. Ashhab, M. V. Salapaka, M. Dahleh, and I. Mezic, "Melnikov-based dynamical analysis of microcantilevers in scanning probe microscopy", Nonlinear Dynamics. 
  • M. Ashhab, M. V. Salapaka, M. Dahleh, and I. Mezic, "Dynamical analysis and control of micro-cantilevers", Automatica,Vol. 35, no. 10, 1663-1670 October 1999.
    • In this paper, we study the dynamical behaviour of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the micro-cantilever by a single mode approximation and the interaction between the sample and cantilever by a van der Waals (vdW) potential. The cantilver is vibrated by a sinusoidal input, and its deflection is detected optically. We analyze the forced dynamics using Melnikov method, which reveals the region in the space of physical parameters where chaotic motion is possible. In addition, using a proportional and derivative controller we compute the Melnikov function in terms of the parameters of the controller. Using this relation it is possible to design controllers that will remove the possibility of chaos.
  • M. V. Salapaka, H. S. Bergh, J. Lai, A. Majumdar, and E. McFarland "Multimode noise analysis of cantilevers for scanning probe microscopy Journal of Applied Physics", 81, no. 6:pp. 2480-2487, 1997.
    • A multi-mode analysis of micro-cantilever dynamics is presented. We derive the power spectral density of the cantilever displacement due to a thermal noise source and predict the cantilevers's fundamental resonant frequency and higher harmonics. The first mode in the muti-mode model is equivalent to the traditional single-mode model. Experimental results obtained with a silicon nitride cantilever at 300 degree Kelvin are in excellent qualitative agreement with the multi-mode model. The multi-mode model may be used to obtain accurate values of the cantilever properties such as the elastic modulus, effective mass, thickness and moment of inertia.
  • Abu Sebastian, M. V. Salapaka, “Analysis of Periodic Solutions in Tapping Mode AFM”, IEEE symposium on Mathematical Theory of Networks and Systems, August 12, 2002 (Accepted)
    • The feedback perspective with the cantilever viewed as a linear system and the tip-sample interaction appearing as a nonlinear feedback is useful in analyzing AFM (Atomic Force Microscope) dynamics. Conditions for the existence and stability of periodic solutions for such a system when forced sinusoidally are obtained. These results are applied to the case where the AFM is operated in the tapping-mode. The near sinusoidal nature of periodic solutions is established by obtaining bounds on the higher harmonics. The concept of Integral Quadratic Constraints (IQC) is widely used in the analysis.
  • S. Salapaka, A. Sebastian, J. P. Cleveland and M. V. Salapaka, "Design, Identification and Control of a fast Nanopositioning Device", American Control Conference, Anchorage, Alaska, May 8, 2002.
  • R. Rajaram, M. V. Salapaka, M. Basso, M. Dahleh, “Experimental verification of stochastic resonance”, Proceedings of the 2000 American Control Conference, Phoenix, Arizona, 2000.
  • A. Sebastian, M. V. Salapaka, D. J. Chen, J. P. Cleveland, “Harmonic analysis based modeling of tapping mode AFM,” Proceedings of the 1999 American Control Conference, San Diego California.
  • M. Basso, M. Dahleh, I. Mezic, M. V. Salapaka, “Stochastic resonance in atomic force microscopes,” Proceedings of the 1999 American Control Conference, San Diego California.
  • M. V. Salapaka, D. J. Chen, J. P. Cleveland, “Stability and sensitivity analysis of periodic orbits in tapping mode atomic force microscopy,” Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, December 1998, pp. 2047-2052.
  • S. Salapaka, M. V. Salapaka, M. Dahleh, I.Mezic, “Complex dynamics in repeated impact oscillators,” Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, December 1998, pp. 2053-2058.
  • A. Daniele, S. Salapaka, M.V. Salapaka, M. Dahleh “Piezoelectric Scanners for Atomic Force Microscopes: Design of Lateral Sensors, Identification and Control” Proceedings of the American Control Conference, San Diego, California , June 1999, pp. 253-257.
  • A. Daniele, T. Nakata, L. Giarre, M. V. Salapaka, M. Dahleh , “Robust Identification and Control of Scanning Probe Microscope Scanner”, Proceedings Volume from the IFAC Symposium, Budapest, Hungary, Oxford, UK: Pergamon, 1997. p. 33-8.
  • M. Ashhab, M. V. Salapaka, M. Dahleh and I. Mezic., “Control of chaos in atomic force microscopes”, Proceedings of the American Control Conference, Albuqueque, New Mexico June 1997.