Simulation of Asymptotic Amplitude-Phase Dynamics for AFM Resonant Modes

Asymptotic AFM amplitude-phase dynamics is a powerful modeling tool for the development of AFM control systems and applications. We explain the model and demonstrate simple practical examples that can be easily programmed and analyzed using simulation tools such as Control and Simulation Loop (National Instruments) or Simulink (Mathworks). We first introduce asymptotic AFM models, then formulate their mathematical properties relevant to AFM, and provide examples of simulation for Hertz and Lennard-Jones tip-sample interaction forces. Material of this paper can be used to study and practice AFM dynamics in simulation, as well as for design of AFM model-based control modes and applications.