Control System Design for High-Speed Atomic Force Microscopy

Video-rate atomic force microscopy is in high demand to visualize dynamic processes in realtime, whereas the functionality of a commercial atomic force microscope (AFM) is restricted to low-speed scans. In the past decades, extensive research efforts have aimed to reinforce the AFM structure toward high-speed atomic force microscopy. However, video-rate imaging of a relatively large scan area is still challenging due to the highly resonant nature of AFM and its conventional method of scanning. The AFM control system also needs to be significantly improved to harness the full potential of AFM mechanical structure at video rate and provide adequate robustness during scan. Therefore, besides the AFM configuration, scanning methods and control techniques contribute significantly to achieving the ultimate goal of sequential AFM imaging at video rate. This dissertation focuses on novel scanning methods and control design methodologies that facilitate sequential atomic force microscopy and improve positioning accuracy at high speed. First, we leverage a technique to smoothen the sequential cycloid trajectory and mitigate the sudden back and forth motions of a positioner in capturing successive frames of a scan. The resulting trajectory reduces the residual tracking error and enhances the AFM image quality. We also propose a systematic design methodology for a novel repetitive non-raster scan trajectory based on the rosette pattern. This pattern, generated by pure harmonic waveforms, can address the conventional issues with sequential non-raster imaging by enabling a smooth and continuous scan. We provide a thorvii ough mathematical analysis of the rosette pattern and a step-by-step design procedure for rosette scanning. We proceed by proposing high-precision model-based control design approaches for sequential AFM imaging using a microelectromechanical system (MEMS) nanopositioner. To precisely follow the reference setpoints in sequential cycloid and rosette scans, we design a tracking controller based on the internal model principle. The internal-model-based controller (IMBC) is intuitive and well-suited for tracking non-raster scan patterns. The controller incorporates the fundamental reference frequencies and their corresponding higher harmonics to reduce the deterministic error originated from uncompensated nonlinearities in the system. However, the resulting controller is of high order, and requires a priori knowledge of the dominant harmonics in the experimental tracking error. To resolve this, we develop a novel control scheme involving an internal-model-based control in feedback and an iterative learning control in feedforward. The internal-model-based controller only includes fundamental frequencies of the references while the iterative learning controller rejects the induced higher harmonics by learning from past experiences. The proposed control scheme is employed for tracking the rosette pattern at various scan rates. We investigate the performance of the proposed scanning methods and control techniques in closed-loop experiments. Finally, a series of high-quality images are obtained at high speed using a MEMS nanopositioner and a commercial AFM. A limiting factor toward high-speed atomic force microscopy is the lightly damped nature of the scanners. To increase the imaging bandwidth and scan speed, vibration control techniques have been practiced. Among them, fixed-structure strictly negative imaginary (SNI) controllers ensure robust stability of closed-loop system when the scanner incorporates collocated actuator and sensor pairs. In the third section of this dissertation, we present a convex synthesis of SNI controllers for a class of multi-input multi-output (MIMO) plants satisfying the negative imaginary property. The design procedure is based on the frequency response data of the plant, and the control objective is to minimize the distance between a desired and actual closed-loop frequency response. The controllers are experimentally implemented to augment damping to the fundamental resonant mode of a MEMS nanopositioner in a two-input two-output configuration.