Reducing stick-slip motion in one-dimensional nano manipulation by real-time feedback control

When a micro cantilever with a nanoscale tip is manipulated on a substrate with atomic roughness, e.g., pushing an atomic-scale sample or etching the surface of the substrate to draw desired patterns, the periodical lateral frictional forces with stochastic fluctuations will induce stick-slip motion of the cantilever tip, which may greatly influence the precision of the nano manipulation. To reduce such a stick-slip motion, we propose a feedback control strategy based on the position estimation of the cantilever tip to compensate the periodical frictional force. Numerical simulations show that the motion of the cantilever tip under feedback control can track the desired trajectory asymptotically. Our proposal can also be extended to the case when the cantilever tip moves over a Gaussian-shape defection on the substrate and when the stochastic fluctuations in the lateral force are with non-zero correlation time.