Analysis and control of micro-cantilever in dynamic mode AFM

The dynamic behavior of micro-cantilever-sample system in atomic force microscopy (AFM) in tapping operational mode is studied. Micro-cantilever is modeled by single-mode approximation and subjected to sinusoidal force input. The interaction between tip and sample is modeled by Lennard-Jones potential. Using this dynamic model, the phase portrait of the system is obtained for a range of cantilever-sample distance, and the effect of cantilever parameters on predictability of the system is discussed. Then the nonlinear behavior of the cantilever-sample system is controlled by a robust sliding-mode controller. System output is designed to track the sinusoidal stimulation of the cantilever base under sample surface perturbation during scanning process. Results of SMC are simulated in MATLAB and compared to a stability that has been proved by PID controller which shows better controller effort and less cantilever tip position accuracy.