Nanopositioning in Atomic Force Microscopes Robust Control Design, Order Reduction and Numerical Implementability

This thesis can be divided into two overall topics. The first concerns control design for nanopositioning devices, and specifically an Atomic Force Microscope (AFM). The second topic concerns the implementability issues involved with running a complex controller in real-time especially for a stiff system with fast modes. A robust H ∞ multiple-input multiple-output (MIMO) controller is designed for the lateral positioning stage of an AFM. This controller is compared to a H ∞ single-input single-output (SISO) controller based on independent axis design and a PID controller. We consider especially how much benefit there is to a more complex MIMO controller compared to independent axis controllers in terms of cross-coupling gains between the lateral axes. This is important to consider in a scanning application where any cross-coupling can be detrimental to the resulting image. Experiments are performed for this purpose. The results show that the differences in terms of cross-coupling reduction is negligible compared to noise and disturbances. This favors the choice of independent axis controllers over MIMO controllers because of their simple