Less Conservative Criteria for Analysis and Synthesis of Nonlinear Systems

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The research objective of this award is to build tools for analysis and synthesis of nonlinear systems with particular emphasis on Atomic Force Microscopy. Existing methodologies are conservative and often the desired performance cannot be achieved even if the potential to obtain the performance is present. The main concept on which the research is based is as follows. Often the nonlinear system is desired to have a certain nominal behavior and near the desired nominal behavior the system typically admits a precise characterization. However, there are external agents that cause the system to deviate from the nominal behavior and this might cause the required nonlinearity description to be complex. One of the main concepts utilized in the proposed research is to first manage the system behavior when the system is away from the desired operating condition. Once it is determinable that the system can recover from such excursions from the nominal condition, a less conservative characterization of the nonlinearity with its domain restricted to a smaller region is employed. This two stage approach has large potential to improve the performance of nonlinear systems. A framework to methodically exploit the above strategy for obtaining less conservative tools for absolute stability, domains of attraction and for addressing influence of external inputs will be developed Framework developed will be applied to Atomic Force Microscopy. The research deliverables include new theoretical tools for nonlinear system analysis and synthesis, new ways of AFM based imaging, engineering student education at the undergraduate and graduate levels and transfer of knowhow to the AFM related industry. If successful, a new body of control theoretic work will be produced. The innovative contributions of this research will directly impact most aspects of AFM, as the proposed methods apply to most of the existing setups. The PI has strong collaboration with AFM related industry. The transfer of knowhow from the PIs academic institution and the AFM industry will make the US industry more competitive. The research will lead to graduate and undergraduate students who will obtain better insights into nonlinear systems with the intuition gained from AFM dynamics.