Reducing Cross-Coupling in a Compliant XY Nanopositioner for Fast and Accurate Raster Scanning

Abstract

A compliant nanopositioner is presented in this brief. The device is designed to have a very low cross-coupling between the -and -axis. Despite this, during high-speed raster scans, the cross-coupling effect can not be ignored. In this brief, a H controller is designed and implemented to minimize the -to-cross-coupling of the nanoscale positioning stage, particularly at its mechanical resonance frequencies. The controller is augmented with integral action to achieve accurate tracking, as well as sufficient damping. Raster scan results over an area of 10 m 10 m with small positioning errors are demonstrated. High-speed accurate raster scans of up to 100 Hz, with nanoscale resolution are also illustrated. Index Terms-Compliantnanopositioner, cross-coupling, H-infinity control, high-speed scans, raster scanning. I. INTRODUCTIONT HE RAPIDLY growing and ever-increasing applications of nanotechnology have increased the demand for high-speed and high-precision nanopositioning systems. The emergence of compliant, piezoelectric stack-actuated nanopositioners fulfils the requirements of nanotechnology related applications. These applications include scanning probe microscopy (SPM) [1], nano-metrology [2], tracking and analysis of biological cell events [3], nano-indentation for high-density data storage systems [4]-[6], and beam steering for optical communication systems [7].Cross-coupling effect is one of the main complications associated with scanning applications in atomic force microscopy (AFM). AFMs utilize sharp probes of few atoms wide (located at the end of a flexible micro-cantilever) and nanopositioning scanners that move samples relative to the probe to perform raster scans over the sample surface (see Fig. 1). To generate the raster pattern, the fast axis of the AFM nanopositioner is driven by a triangular signal and the slow axis is driven by a synchronized staircase or ramp signal. The triangular waveform contains all odd harmonics of the fundamental frequency. Although the amplitude of these harmonics is attenuated by a factor of , where is the number of the harmonic, a fast triangular Manuscript

Closed-loop control of a 2-D mems micromirror with sidewall electrodes for a laser scanning microscope system

“…2-D MEMS micromirror has been reported to integrate with a MACROscope system for biomedical imaging [9] . To generate the raster scan for imaging applications, the fast axis of the 2-D micromirror is usually driven by a triangle signal, and the slow axis is driven by a ramp signal simultaneously [12] . However, the nonlinear relationship between the tilt angles and the applied voltages results in the distortion of scanning range.…”

“…However, the nonlinear relationship between the tilt angles and the applied voltages results in the distortion of scanning range. On the other hand, when 2-D MEMS micromirror scans in two directions simultaneously, the cross-axis coupling effect between the x and y-axis distorts the scanning patterns and may degrade quality of the reconstructed images [12] .…”

A 2-legged XY parallel flexure motion stage with minimised parasitic rotation

“…For example, a commonly-used parallelogram flexure mechanism produces a transverse primary motion caused by the force acting at the tip of the flexure with the consequence that active rotation compensation is needed to maintain a zero rotation at the tip. In addition, the cross-axis coupling between the X-and Y-axes can introduce the complicated control and measurement uncertainties in the scanning processing [5]. Recent research advances have enabled the desired designs with decoupled configuration and minimised parasitic rotation in XY CPMs.…”

H ∞ Reduced Order Control for Nanopositioning: Numerical Implementability

“…However, higher order model-matching based techniques, such as model reference control (MRC), linear quadratic control (LQR) and H ∞ -control, can in principle allow for higher bandwidth, and can therefore lead to better tracking performance. Model-matching control, especially H ∞ -control, has been widely employed in the nanopositioning literature (Schitter et al, 2001;Salapaka et al, 2002;Salapaka and Sebastian, 2003;Schitter and Stemmer, 2004;Ladjal et al, 2009;Yong et al, 2010). These controllers tend to have a high order, which in turn leads to high computational complexity.…”