Tracking Control of a Nanopositioner Using Complementary Sensors

Abstract

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.

Tracking of Triangular References Using Signal Transformation for Control of a Novel AFM Scanner Stage

“…Together with the input impedance of the preamplifier, the cutoff frequency of the high-pass filter is reduced to 0.5 Hz. Although the cutoff frequency is low, accurate positioning at low frequencies using the strain-induced voltage alone could be difficult [19].…”

“…Piezoelectric tube scanners are the most commonly used mechanism in commercial AFM to position a sample close to the cantilever probe and to move the sample in a raster pattern during scanning [18], [19]. The tube is fixed at one end and free at the other.…”

“…The high-frequency content in a fast triangular waveform can excite the tube's resonance and subsequently distort the scanned image. Accurate tracking of a fast triangular waveform is one of the major challenges not only in SPM [19]- [29] but also in other scanner-based devices such as optical scanners and selective laser sintering (SLS) machines [30], [31]. The performance of the piezoelectric tube scanner is often quantified by its positioning resolution (which is governed by measurement noise), tracking bandwidth and robustness to disturbances [5].…”

“…There has been a significant effort to improve the tracking accuracy and speed of piezoelectric tube scanners using feedback control techniques. To track a fast triangular signal, high bandwidth closed-loop controllers have been implemented in many nanopositioning devices [19], [23], [24], [26], [28], [32]- [34]. However, the scanning speed is limited in feedback control systems due to hysteresis, thermal drift, sensor noise, uncertainty, and mechanical vibrations when piezoelectric tubes are used to follow non-smooth triangular trajectories [18].…”

Control Methods in Data-Storage Systems

“…In this case, the tracking controllers are designed in such a way that frequency separation is enforced. It is worth observing that a similar situation arises, very naturally, in piezoelectric tube scanners, which has made it possible to use the concept of frequency separation for high-precision high-speed nanopositioning for AFM-type piezoelectric tube scanners [265], [266]. Two other track-following methods are proposed and discussed in [267].…”