Cantilever dynamics modelling for the Transverse Dynamic Force Microscope

This paper studies the dynamics of the cantilever in a Transverse Dynamic Force Microscope (TDFM). A series expansion approach for the irrational transfer functions of modelling the cantilever dynamics is presented in terms of an infinite sum of second-order rational transfer functions and a finite dimensional linear time invariant (LTI) system model is developed. An approximate model of the cantilever can then be obtained using a finite number of rational transfer functions. This approach preserves the physical constants from the underlying partial differential equation, and retains them in the approximate model. Future work will use these finite dimensional LTI systems as the basis for the design of observers and controllers for the TDFM at the NSQI centre at the University of Bristol.