  When a micro cantilever with a nano-scale tip is manipulated on a substrate
with atomic-scale roughness, the periodic lateral frictional force and
stochastic fluctuations may induce stick-slip motion of the cantilever tip,
which greatly decreases the precision of the nano manipulation. This unwanted
motion cannot be reduced by open-loop control especially when there exist
parameter uncertainties in the system model, and thus needs to introduce
feedback control. However, real-time feedback cannot be realized by the
existing virtual reality virtual feedback techniques based on the position
sensing capacity of the atomic force microscopy (AFM). To solve this problem,
we propose a new method to design real-time feedback control based on the force
sensing approach to compensate for the disturbances and thus reduce the
stick-slip motion of the cantilever tip. Theoretical analysis and numerical
simulations show that the controlled motion of the cantilever tip tracks the
desired trajectory with much higher precision. Further investigation shows that
our proposal is robust under various parameter uncertainties. Our study opens
up new perspectives of real-time nano manipulation.
