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.