Combining Model Predictive and Adaptive Control for an Atomic Force Microscope Piezo-Scanner-Cantilever System

The paper presents a new control algorithm which
consists of a combination of an adaptive control structure and a
model predictive one. An atomic force microscope in the contact
mode (AFM) is considered to validate the proposed algorithm.
The AFM is a powerful tool to measure the topography of the
sample at the scale of a few nanometers, where a small sharp tip
supported in a micro cantilever scans the surface. In the contact
mode the samples topography is obtained while the closed-loop
control holding the tip sample force constant. The dynamics
of the tip-sample system is very complex with different kinds
of forces that act between the tip and the sample. Here the
dominated force depends on the distance tip-sample and in the
present work we use a modified Hertz model to describe the
non-linear force when the distance tip-sample is less than 20
nm. The proposed control technique consists of a two stage
structure algorithm. In the control strategy, the adaptive part
is devoted to the control of the non-linear dynamics, the model
predictive part improves the transient of the overall control
system in order to have a fast control of the complex tip-sample
system. The procedure is totally general and can be applied to
any drive system.
Index Terms—Model Predictive Control; Adaptive Control;
AFM Cantilever Model.