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

Correlation scales have been used in the traditional scheme of three-dimensional variational data assimilation (3DVAR) to estimate the background (or first guess) error covariance matrix (the B matrix in brief) for the numerical forecast and reanalysis of ocean for decades. However, it is challenging to implement this scheme. On the one hand, determining the correlation scales accurately can be difficult. On the other hand, the positive definite of the B matrix cannot be guaranteed unless the correlation scales are sufficiently small. Xie et al. indicated that a traditional 3DVAR only corrects certain wavelength errors, and its accuracy depends on the accuracy of the B matrix. Generally speaking, the shortwave error cannot be sufficiently corrected until the longwave error is corrected. An inaccurate B matrix may mistake longwave errors as shortwave ones, resulting in erroneous analyses.A new 3DVAR data assimilation scheme, called a multigrid data assimilation scheme, is proposed in this paper for quickly minimizing longwave and shortwave errors successively. By assimilating the sea surface temperature and temperature profile observations into a numerical model of the China Seas, this scheme is applied to a retroactive real-time forecast experiment and favorable results are obtained. Compared to the traditional scheme of 3DVAR, this new scheme has higher forecast accuracy and lower root-meansquare errors. Note that the new scheme demonstrates greatly improved numerical efficiency in the analysis procedure.

Abstract-Piezoelectric tube actuators are widely used in atomic force and scanning tunneling microscopy (STM) for nanoscale positioning. There has been a consistent effort to increase the scan speed of these actuators using feedback control techniques. A feedback controller requires a measurement of the scanner's deflection, which is often provided by a capacitive sensor. Such measurements are corrupted by sensor noise, typically in the order of 20 pm/ √ Hz rms. Over a bandwidth of 10 kHz, this translates into an rms noise of 2 nm, clearly inadequate for applications that require subnanometer positioning accuracy, e.g., STM. In this paper, we illustrate how the strain voltage induced in a free electrode of the scanner can be used as an additional displacement signal. The noise level corresponding to the strain signal is about three orders of magnitude less than that of a capacitive sensor, making it an ideal choice for nanopositioning applications. However, it cannot be used for dc and low-frequency measurements. A two-sensorbased controller is designed to use the capacitive sensor signal at low frequencies, and the strain displacement signal at high frequencies. By limiting the capacitive sensor feedback loop bandwidth to less than 100 Hz, the rms value of the noise is reduced to well below 1 nm. For almost the same noise level, the two-sensor-based control structure achieves a closed-loop bandwidth of more than three times that of the single-sensor-based controller.

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