Dynamic modeling and control of an atomic force microscope probe measurement system

When measuring with an atomic force microscope (AFM), the probe would move to the prescribed position via the platform and its vibration would occur. To achieve precision positioning for the follow-up scanning and high-speed measurement, in this paper, mathematical modeling and control of the probe is focused to avoid the damage incurred by the collision between the probe and the sample and to obtain the high measurement in the scanning step. The Hamilton's principle is firstly employed to derive the equation of motion and its boundary conditions. Next, the summation method, Lagrangian equation and Laplace transform are applied to obtain natural frequencies, a dynamic model of the AFM probe, and to work out the transfer function of the open-loop system. The proposed model is compared with two conventional AFM probe models: point-mass model and conventional cantilever beam model - where one of the ends of the cantilever and basic platform are assumed to be fixed. Finally, collocated control is exercised to designate the positions for actuator and sensor and the root locus method cooperated with proportional-integral-derivative controllers to simulate the performance of the control system. The result shows that the controller can ensure the stability of this continuous system and perform effective control.