Optimal control of flexible end effector in AFM based nanomanipulation

Atomic force microscope (AFM) based nanomanipulation has been extensively investigated for many years. However, the efficiency and accuracy of the AFM based nanomanipulation is still a major issue due to the nonlinearities and uncertainties in nanomanipulation operations. The deformation of the cantilever caused by manipulation force, in our experience, is one of the most major nonlinearities and uncertainties. It causes difficulties in precisely controlling the tip position, which will cause the tip to miss the position of the object. In order to solve this problem, the traditional approach is to use a rigid cantilever. However, this will significantly reduce the sensitivity of the force feeling during the manipulation, which is essential for achieving an efficient and reliable nanomanipulation. An active AFM probe is used to solve this problem by directly controlling the cantilever´s flexibility or rigidity during manipulation. An infinite dimensional model of the active probe is developed. Control of the active probe employing an optimal LQR control law is also implemented. The experimental results have verified the theoretical model and demonstrated that the precise position control and high sensitive interaction force measurement can be achieved simultaneously.