U OF M COLLEGE OF ENGINEERING
CONTROL SEMINAR SERIES
WINTER TERM 1998

Electrical and Computer Engineering
Iowa State University

djchen@iastate.edu

Friday, March 20, 1998
4:00 - 5:00 pm
1200 EECS

Title: Stability and Sensitivity Analysis of Periodic Orbits in Atomic Force Microscope Imaging

• Abstract
  
  Atomic Force Microscope's (AFM's) have revolutionized microscopy in the past decade. The main element of an AFM is a cantilever with dimensions in the order of microns, which is sensitive enough to register atomic forces and causes minimal damage to the sample being imaged. This tool has enabled physicists, biologists and engineers to accomplish remarkable feats such as monitoring RNA and DNA activity, thermal imaging with sub-Kelvin resolutions and sub-angstrom scale topography imaging.

  In this paper, the most widely used mode of imaging where the cantilever is oscillated at its resonant frequency is studied. A nonlinear dynamic model for the cantilever-sample system is developed. Utilizing this model it is shown that the system exhibits periodic motion with period equal to that of the forcing. Using the Poincare map technique asymptotic orbital stability of the periodic motion is established. Furthermore, the sensitivity of the Poincare map's fixed point with respect to the cantilever-sample distance is obtained. The fixed point consists of the amplitude and the "phase" of the periodic orbit, which can be measured from the cantilever vibration. The sensitivity study of the fixed point has shown that the amplitude and the sine of the phase of the orbit vary linearly with respect to the cantilever-sample distance. Experiments conducted on a silicon cantilever have shown that the cantilever motion is indeed periodic with period equal to that of the forcing. Furthermore, the variation of the amplitude and sine of the phase were recorded as the sample was moved towards the cantilever. The experimental data confirms the theoretically predicted linear behavior of the quantities with respect to the cantilever-sample distance. This linear behavior provides an attractive and simple method for imaging with very high resolutions. Also, these results can be used to improve the performance of commercially available microscopes.

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  Biosketch

  
  Dr. Chen specializes in the area of control systems and robotics. His research interests include nonlinear control, adaptive control, fuzzy logic control, and their applications. His recent work includes control of ultraprecision motion drives, electric machines, flexible manipulators, space robotics, and smart materials. He is the recipient of the NSF Research Initiation Award, ASME Best Transactions Paper Award (Journal of Dynamic Systems, Measurement and Control), and IEEE Conference on Decision and Control Best Student Paper Award. Before he joined Iowa State University, he was the John R. Pierce Instructor at the California Institute of Technology. Dr. Chen received the B.S. (1984) from Tsinghua University, and the M.S. (1988) and Ph.D. (1992) from the University of California, Santa Barbara.

© UofM College of Engineering Control Research Group - December 1997
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