Qingze Zou

A Review of Feedforward Control Approaches in Nanopositioning for High-Speed SPM

Control can enable high-bandwidth nanopositioning needed to increase the operating speed of scanning probe microscopes (SPMs). High-speed SPMs can substantially impact the throughput of a wide range of emerging nanosciences and nanotechnologies. In particular, inversion-based control can find the feedforward input needed to account for the positioning dynamics and, thus, achieve the required precision and bandwidth. This article reviews inversion-based feedforward approaches used for high-speed SPMs such as optimal inversion that accounts for model uncertainty and inversion-based iterative control for repetitive applications. The article establishes connections to other existing methods such as zero-phase-error-tracking feedforward and robust feedforward. Additionally the article reviews the use of feedforward in emerging applications such as SPM-based nanoscale combinatorial-science studies, image-based control for subnanometer-scale studies, and imaging of large soft biosamples with SPMs.

Feedforward control of piezoactuators in atomic force microscope systems

This article describes an inversion-based feedforward approach to compensate for dynamic and hysteresis effects in piezoactuators with application to AFM technology. To handle the coupled behavior of dynamics and hysteresis, a cascade model is presented to enable the application of inversion-based feedforward control. The dynamics, which include vibration and creep, are modeled using linear transfer functions. A frequency-based method is used to invert the linear model to find an input that compensates for vibration and creep. The inverse is noncausal for nonminimum-phase systems. Similarly, the hysteresis is handled by an inverse-Preisach model. To avoid the complexity of finding the inverse-Preisach model, high- gain feedback control can be used to linearize the systems behavior. A feedforward input is then combined with the feedback system to compensate for the linear dynamics to achieve high-speed AFM imaging. Finally, recent efforts in feedforward control for an SPM application including the use of iteration to handle hysteresis as well as uncertainties and variations in the system model is discussed.

Iterative control of dynamics-coupling-caused errors in piezoscanners during high-speed AFM operation

This paper addresses the compensation of the dynamics-coupling effect in piezoscanners used for positioning in atomic force microscopes (AFMs). Piezoscanners are used to position the AFM probe, relative to the sample, both parallel to the sample surface (x and y axes) and perpendicular to the sample surface (z axis). In this paper, we show that dynamics-coupling from the scan axes (x and y axes) to the perpendicular z axis can generate significant positioning errors during high-speed AFM operation, i.e., when the sample is scanned at high speed. We use an inversion-based iterative control approach to compensate for this dynamics-coupling effect. Convergence of the iterative approach is investigated and experimental results show that the dynamics-coupling-caused error can be reduced, close to the noise level, using the proposed approach. Thus, the main contribution of this paper is the development of an approach to substantially reduce the dynamics-coupling-caused error and thereby, to enable high-speed AFM operation.

Iterative Control Approach to Compensate for Both the Hysteresis and the Dynamics Effects of Piezo Actuators

In this brief, the compensation for both the nonlinear hysteresis and the vibrational dynamics effects of piezo actuators is studied. Piezo actuators are the enabling device in many applications such as atomic force microscopy (AFM) to provide nano- to atomic-levels precision positioning. During high-speed, large-range positioning, however, large positioning errors can be generated due to the combined hysteresis and dynamics effects of piezo actuators, making it challenging to achieve precision positioning. The main contribution of this brief is the use of an inversion-based iterative control (IIC) technique to compensate for both the hysteresis and vibrational dynamics effects of piezo actuators. The convergence of the IIC algorithm is investigated by capturing the input-output behavior of piezo actuators with a cascade model consisting of a rate-independent hysteresis at the input followed by the dynamics part of the system. The size of the hysteresis and the vibrational dynamics variations that can be compensated for (by using the IIC method) is quantified. The IIC approach is illustrated through experiments on a piezotube actuator used for positioning on an AFM system. Experimental results show that high-speed, large-range precision positioning can be achieved by using the proposed IIC technique. Furthermore, the proposed IIC algorithm is also applied to experimentally validate the cascade model and the rate-independence of the hysteresis effect of the piezo actuator.

Preview-Based Stable-Inversion for Output Tracking of Linear Systems

Stable Inversion techniques can be used to achieve high-accuracy output tracking. However, for nonminimum phase systems, the inverse is noncausal-hence the inverse has to be precomputed using a prespecified desired-output trajectory. This requirement for prespecification of the desired output restricts the use of inversion-based approaches to trajectory planning problems (for nonminimum phase systems). In the present article, it is shown that preview information of the desired output can be used to achieve online inversion-based output-tracking of linear systems. The amount of preview-time needed is quantified in terms of the tracking error and the internal dynamics of the system (zeros of the system). The methodology is applied to the online output tracking of a flexible structure and experimental results are presented.

Robust Inversion-Based 2-DOF Control Design for Output Tracking: Piezoelectric-Actuator Example

In this paper, a novel robust inversion-based 2-DOF control approach for output tracking is proposed. Inversion-based feedforward control techniques have been successfully implemented in various applications. Usually, to account for adverse effects such as dynamics variations and disturbances, the inverse feedforward control is applied by augmenting it with a feedback control. However, such effects have not been directly addressed in existing system-inversion methods, and the integration of the feedback control with the inversion-based feedforward control is performed in an ad hoc manner, which may not lead to an optimal complement of the inversion-based feedforward control with the feedback control. The contribution of this paper is the development of the following: 1) a robust system-inversion approach to directly account for and then minimize the dynamics-uncertainty effect when finding the inversion-based feedforward controller, and 2) a systematic integration (of such a feedforward controller) with a robust feedback controller. The proposed robust inversion method achieves a guaranteed tracking performance of the feedforward control for bounded dynamics uncertainties. Then, the quantified bound of the feedforward control tracking error is utilized in designing an H infin robust feedback controller to complement the feedforward control. Based on the concept of Bodes integral, it is shown that the feedback bandwidth can be improved from that obtained by using feedback alone. We illustrated the proposed approach by implementing it in experiments on a piezotube actuator of an atomic force microscope for precision positioning.

A Modeling-Free Inversion-Based Iterative Feedforward Control for Precision Output Tracking of Linear Time-Invariant Systems

In this paper, we propose a modeling-free inversion-based iterative feedforward control (MIIFC) approach for high-speed output tracking of single-input single-output linear time-invariant systems. The recently developed inversion-based iterative learning control (IIC) techniques provide a straightforward manner to quantify and account for the effect of dynamics uncertainty on iterative learning control performance, thereby arriving at rapid convergence of the iterative control input. However, dynamics model and thereby the modeling process are still needed, and the model quality directly limits the performance of the IIC techniques. The main contribution of this paper is the development of the MIIFC algorithm to eliminate the dynamics modeling process, and significantly improve the tracking performance. The disturbance (measurement noise) effect on the tracking precision is addressed in the convergence analysis of the MIIFC algorithm. The allowable disturbance/noise level to guarantee the convergence is quantified in frequency domain, and the noise level can be estimated through the noise spectrum measured before the whole operation. The MIIFC technique is demonstrated by applying it to the output tracking of a piezotube scanner on an atomic force microscope. The experimental results showed that precision output tracking of a frequency-rich desired trajectory with power spectrum similar to a band-limited white noise can be achieved.

Macroscopic highly aligned DNA nanowires created by controlled evaporative self-assembly.

By subjecting DNA aqueous solution to evaporate in a curve-on-flat geometry that was composed of either a spherical lens or a cylindrical lens situated on a flat substrate, a set of highly aligned DNA nanowires in the forms of spokes and parallel stripes over a macroscopic area (i.e., millimeter scale) were successfully created. The DNA molecules were stretched and aligned on polymer-coated substrate by the receding meniscus. The imposed curve-on-flat geometry provided a unique environment for controlling the flow within the evaporating solution by eliminating temperature gradient and possible convective instability and, thus, regulated the formation of DNA nanowires. Such controlled evaporative self-assembly is remarkably easy to implement and opens up a new avenue for crafting large-scale DNA-based nanostructures in a simple and cost-effective manner, dispensing with the need for lithography techniques.

A control approach to cross-coupling compensation of piezotube scanners in tapping-mode atomic force microscope imaging

In this article, an approach based on the recently developed inversion-based iterative control (IIC) to cancel the cross-axis coupling effect of piezoelectric tube scanners (piezoscanners) in tapping-mode atomic force microscope (AFM) imaging is proposed. Cross-axis coupling effect generally exists in piezoscanners used for three-dimensional (x-y-z axes) nanopositioning in applications such as AFM, where the vertical z-axis movement can be generated by the lateral x-y axes scanning. Such x/y-to-z cross-coupling becomes pronounced when the scanning is at large range and/or at high speed. In AFM applications, the coupling-caused position errors, when large, can generate various adverse effects, including large imaging and topography distortions, and damage of the cantilever probe and/or the sample. This paper utilizes the IIC technique to obtain the control input to precisely track the coupling-caused x/y-to-z displacement (with sign-flipped). Then the obtained input is augmented as a feedforward control to the existing feedback control in tapping-mode imaging, resulting in the cancellation of the coupling effect. The proposed approach is illustrated through two exemplary applications in industry, the pole-tip recession examination, and the nanoasperity measurement on hard-disk drive. Experimental results show that the x/y-to-z coupling effect in large-range (20 and 45 microm) tapping-mode imaging at both low to high scan rates (2, 12.2 to 24.4 Hz) can be effectively removed.

Precision preview-based stable-inversion for nonlinear nonminimum-phase systems: The VTOL example☆

This article quantifies the importance of the future desired trajectory in determining the exact-output-tracking input for nonlinear, nonminimum-phase systems by using system inversion techniques. It is intuitive that the effect of the desired outputs distant-future values, on the output-tracking input at the current time instant, should be small. Therefore, at a current time instant (tc)(tc), preview information of the desired output in a finite-time window [tc,tc+Tp][tc,tc+Tp] should be sufficient to compute the output-tracking input with an arbitrarily small prescribed error, if the preview time TpTp is sufficiently large. The contribution of this article is the quantification of the needed preview time TpTp by using the benchmark VTOL aircraft model as an example. Additionally, simulation results are presented to evaluate the efficacy of the finite-preview-based stable-inversion approach.