Santosh Devasia

A Survey of Control Issues in Nanopositioning

Nanotechnology is the science of understanding matter and the control of matter at dimensions of 100 nm or less. Encompassing nanoscale science, engineering, and technology, nanotechnology involves imaging, measuring, modeling, and manipulation of matter at this level of precision. An important aspect of research in nanotechnology involves precision control and manipulation of devices and materials at a nanoscale, i.e., nanopositioning. Nanopositioners are precision mechatronic systems designed to move objects over a small range with a resolution down to a fraction of an atomic diameter. The desired attributes of a nanopositioner are extremely high resolution, accuracy, stability, and fast response. The key to successful nanopositioning is accurate position sensing and feedback control of the motion. This paper presents an overview of nanopositioning technologies and devices emphasizing the key role of advanced control techniques in improving precision, accuracy, and speed of operation of these systems.

Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application

Structural vibrations and hysteresis nonlinearities in piezoactuators have been fundamental limitations when using these actuators for high-speed precision-positioning applications. Positioning speed (bandwidth) is limited by structural vibrations, typically, to about one-tenth the fundamental vibrational frequency of the piezoprobe. Further, precision in positioning is limited by hysteresis nonlinearities, which can result in signie cant errors for large-range positioning applications. This paper shows that signie cant improvements in precision and bandwidth can be achieved by using an inversion-based approach to compensate for hysteresis and vibrations in the piezodynamics. Theapproach decouplestheinversion into 1 )inversion of thehysteresisnonlinearity and 2 )inversion ofthe structuraldynamics,toe ndaninputvoltageproe lethatachievesprecisiontracking ofa desiredpositiontrajectory. Theapproachisappliedtoapiezoactuator,andexperimentalresultsshowthatanorderofmagnitudeimprovement in positioning speed is achieved, while maintaining precision tracking of the desired position trajectory. I. Introduction P IEZOACTUATORS can achieve nanometer resolution positioning and are hence increasingly being used for ultraprecision positioning in aerospace applications, 1;2 vibration control, scanning probe microscopy for surface characterization, and nanofabrication. 3i5 Two major limitations of present positioning techniquesusing piezoactuatorsare 1 )lowoperating bandwidthdue to positioning errors caused by structural vibrations at high speeds and 2) low precision for relatively large-range displacements (due to errors caused by hysteresis nonlinearities ), resulting in restricted positioning range. This paper presents a method to improve both the accuracy and the speed of piezoactuators by using an inversionbased approach to e nd the voltage input to the piezoactuators that compensates for the hysteresis nonlinearities and the structural vibrations. This approach e rst decouples the system dynamics into two separate subsystems that model 1 ) the hysteresis nonlinearity

Nonlinear inversion-based output tracking

An inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory. In the case of minimum phase systems, the trajectory produced agrees with that generated by Hirschorns inverse dynamic system; however, the preimage trajectory is noncausal (rather than unstable) in the nonminimum phase case. In addition, the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case. With the addition of stabilizing feedback to the preimage trajectory, asymptotically exact output tracking is achieved. Tracking is demonstrated with a numerical example and compared to the well-known Byrnes-Isidori regulator. Rather than solving a partial differential equation to construct a regulator, the inverse is calculated using a Picard-like interaction. When preactuation is not possible, noncausal inverse trajectories can be truncated resulting in the tracking-error transients found in other control schemes.

Feedback-Linearized Inverse Feedforward for Creep, Hysteresis, and Vibration Compensation in AFM Piezoactuators

In this brief, we study the design of a feedback and feedforward controller to compensate for creep, hysteresis, and vibration effects in an experimental piezoactuator system. First, we linearize the nonlinear dynamics of the piezoactuator by accounting for the hysteresis (as well as creep) using high-gain feedback control. Next, we model the linear vibrational dynamics and then invert the model to find a feedforward input to account vibration - this process is significantly easier than considering the complete nonlinear dynamics (which combines hysteresis and vibration effects). Afterwards, the feedforward input is augmented to the feedback-linearized system to achieve high-precision highspeed positioning. We apply the method to a piezoscanner used in an experimental atomic force microscope to demonstrate the methods effectiveness and we show significant reduction of both the maximum and root-mean-square tracking error. For example, high-gain feedback control compensates for hysteresis and creep effects, and in our case, it reduces the maximum error (compared to the uncompensated case) by over 90%. Then, at relatively high scan rates, the performance of the feedback controlled system can be improved by over 75% (i.e., reduction of maximum error) when the inversion-based feedforward input is integrated with the high-gain feedback controlled system.

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.

Should model-based inverse inputs be used as feedforward under plant uncertainty?

Bounds on the size of the plant uncertainties are found such that the use of the inversion-based feedforward input improves the output-tracking performance when compared to the use of feedback alone. The output-tracking error is normalized by the size of the desired output and used as a measure of the output tracking performance. The worst-case performance is compared for two cases: (1) with the use of feedback alone and (2) with the addition of the feedforward input. It is shown that inversion-based feedforward controllers can lead to performance improvements at frequencies w where the uncertainty /spl Delta/ (jw) in the nominal plant is smaller than the size of the nominal plant G/sub 0/(jw) divided by its condition number K/sub G0/ (jw), i.e., /spl par//spl Delta/(jw)/spl par//sub 2/ < /spl par/G/sub 0/(jw) /spl par//sub 2//k/sub G0/ (jw). A modified feedforward input is proposed that only uses the model information in frequency regions where plant uncertainty is sufficiently small. The use of this modified inverse with (any) feedback results in improvement of the output tracking performance, when compared to the use of the feedback alone.

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.

Vibration compensation for high speed scanning tunneling microscopy

Low scanning speed is a fundamental limitation of scanning tunneling microscopes (STMs), making real time imaging of surface processes and nanofabrication impractical. The effective scanning bandwidth is currently limited by the smallest resonant vibrational frequency of the piezobased positioning system (i.e., scanner) used in the STM. Due to this limitation, the acquired images are distorted during high speed operations. In practice, the achievable scan rates are much less than 1/10th of the resonant vibrational frequency of the STM scanner. To alleviate the scanning speed limitation, this article describes an inversion-based approach that compensates for the structural vibrations in the scanner and thus, allows STM imaging at high scanning speeds (relative to the smallest resonant vibrational frequency). Experimental results are presented to show the increase in scanning speeds achievable by applying the vibration compensation methods.

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.