High bandwidth nano-positioner: A robust control approach

Abstract

This article presents the design, identification, and control of a nano-positioning device suited to image biological samples as part of an atomic force microscope. The device is actuated by a piezoelectric stack and its motion is sensed by a linear variable differential transformer. It is demonstrated that the conventional proportional-integral control architecture does not meet the bandwidth requirements for positioning. The design and implementation of an H∞ controller demonstrates substantial improvements in the positioning speed and precision, while eliminating the undesirable nonlinear effects of the actuator. The characterization of the resulting device in terms of bandwidth, resolution, and repeatability provided illustrates the effectiveness of the modern robust control paradigm.

A Tutorial on the Mechanisms, Dynamics, and Control of Atomic Force Microscopes

“…Because tube scanners often lack X-Y sensors, much of the original advanced feedback control work was done in the Z direction [59], [86], while feedforward controllers were developed for the X-Y motions [74], [81], [82]. The advent of sensored X-Y stages has led to feedback control methods being developed for X-Y motions as well [87], [88]. Combined feedforward and feedback controllers have also been investigated for both the Z and X motions [89], [90], [91].…”

“…These include efforts geared at increasing the performance of conventional tube scanner-based microscopes through understanding and compensating for the nonlinear effects of hysteresis, creep, and varying voltage response [74], [102]. Many researchers have attacked the speed of measurement problem with approaches including a redesign of the actuator to achieve higher bandwidth [76], and applications of modern control theory to increase the scanning speed [74], [81], [82], [87], [88], [89]. These methods are discussed in more detail in [61].…”

“…In particular, the use of H ∞ in the feedback path only is described in [59], [87], [88] . The use of combined feedforward/feedback controllers is discussed using H ∞ [89], [91], ℓ 1 [90], and model-inverse based methods [68], [74].…”

“…Another cause for loss in precision in piezos is drift due to creep effects, which become significant when positioning is required over extended periods of time (such as during slow operation of AFMs). Modelinversion based controllers [74] have been used to compensate for hysteresis and creep, and both integral and H ∞ controllers [88] have been shown to mitigate these nonlinear effects in the closed-loop system behavior of AFMs.…”

Compensator design for improved counterbalancing in high speed atomic force microscopy

“…[2][3][4][5][6] An important thrust towards the design of faster AFMs has been to capture dynamic processes of biological macromolecules, 2-4 mineral dissolution and growth 5 and polymer crystallization 6 in real time. These efforts have mainly focused on scanner bandwidth enhancement for faster in-plane (referred to as x and y directions), [7][8][9][10][11] and out of plane (referred to as z direction) movement 2,12 of the sample/probe. Probe enhancement for improved sensitivity and speed has also been under investigation.…”