Nonlinear robust stage control of atomic force microscope

This paper proposes a robust nonlinear controller for a stage control of a vertical scanner in atomic force micro-scope to improve a settling time compared to a conventional PI controller, which results in a faster scanning on a sample surface. The physical model of the whole measurement system with respect to a vertical stage control is mainly described by two linear subsystems and a nonlinear and nonsmooth subsystem with a unmatched disturbance generated from a change of shape in a sample surface. First, we propose an approximation model in which a nonsmoothness that is generated by repetitive collisions between cantilever and sample surface is virtually converted into an additional nonsmooth disturbance. Then, the control problem is to design a feedback controller to compensate the two unmatched disturbances as fast as possible. With the object of a specification of a general AFM product, we assume that only output signal is available. Then, a controller including both a softened switching action and a PI compensator is introduced. Simulation results show our superiority in fast response compared to a conventional PI controller.