Nanotechnology: a systems and control approach

Recent years have seen significant advances in the fields of nanosciences and nanotechnology. A significant part of the research in nanotechnology deals with developing tools and devices to probe and manipulate matter at the atomic, molecular and macro-molecular levels. Surprisingly in spite of the potential for engineers to contribute substantially to this area, most of the contributions till date have come from physicists and biologists. Engineering ideas primarily from systems theory and control significantly complement the physical studies performed in this area of research. This thesis demonstrates this by the application of systems ideas and tools to address two of the most important goals of nanotechnology, interrogation and positioning of materials at the nanoscale. The atomic force microscope (AFM), a micro-cantilever based device is one of the foremost tools in the interrogation and manipulation of matter at the atomic scale. The AFM operating in the most common tapping-mode has a highly complex dynamics due to the nonlinear tip-sample interaction forces. A systems approach is proposed to analyze the tapping-mode dynamics. The systems perspective is further exploited to develop analytical tools for modeling and identifying tip sample interactions. Some of the distinctly nonlinear features of tapping-mode operation are explained using the asymptotic theory of weakly nonlinear oscillators developed by Bogoliubov and Mitropolski. In the nanopositioning front, through the design and implementation of nanopositioning devices, a new paradigm for the systematic design of nanopositioners with specific bandwidth, resolution and robustness requirements is presented. Many tools from modern robust control like nominal and robust Hoo designs and Glover McFarlane designs are exploited for this. The experimental results demonstrate the efficacy of these design schemes.