Hybrid MPC-PI Control for Enhancing Imaging Speed of Non-contact Atomic Force Microscopy

Abstract

Atomic Force Microscopy (AFM) has revolutionized the field of nanoscale characterization, offering highest resolution for imaging a wide range of surfaces. The non-contact mode AFM (NC-AFM) is particularly valuable as it minimizes the intrusive forces between the material sample and cantilever tip, preserving the integrity of soft and biological structures. However, conventional NC-AFM is slower and due to this slowness the real time dynamics processes that requires higher data acquisition are not recorded. This limitation arises from several factors but most important cause is the conventional control in non-contact AFM often struggle to achieve high imaging speeds due to limitations in the feedback loop bandwidth. This limitation arises from minimum stability margins in the open-loop system, which prevent increasing the gain of the conventional proportional-integral controller.

To address these limitations, this thesis presents a hybrid model-predictive-control (MPC) and proportional-integral (PI) control to enhance the imaging speed of NC-AFM. In proposed method the MPC controller is added in the feedback path along with the PI controller. The proposed methods reduce the tracking error, cantilever force and allows the piezo-electric actuator to track the surface of the sample accurately up to 10 scan lines/s which is fives time higher than conventional imaging speed. Meanwhile, due to drift of PZT actuator and model uncertainties the amplitude of cantilever may deviate from set-point at each scanline, thus the PI control in feedback is kept to deal with the residual tracking errors at low frequencies.

Through experimental validation, this thesis evaluates the performance of the proposed controller. A 100-nm and 20nm step shape samples are used to investigate the speed of non-contact mode AFM at 10 scan lines/s and 20 scan lines/s with both proposed and conventional control methods and are compared with the conventional non-contact AFM image at 02 scan lines/s. Finally, the thesis discusses the implications of this research for advancing high-speed, high-resolution non-contact AFM imaging.