S. O. Reza Moheimani

Design, Identification, and Control of a Flexure-Based XY Stage for Fast Nanoscale Positioning

The design, identification, and control of a novel, flexure-based, piezoelectric stack-actuated XY nanopositioning stage are presented in this paper. The main goal of the design is to combine the ability to scan over a relatively large range (25times25 mum) with high scanning speed. Consequently, the stage is designed to have its first dominant mode at 2.7 kHz. Cross-coupling between the two axes is kept to -35 dB, low enough to utilize single-input--single-output control strategies for tracking. Finite-element analysis (FEA) is used during the design process to analyze the mechanical resonance frequencies, travel range, and cross-coupling between the X- and Y-axes of the stage. Nonlinearities such as hysteresis are present in such stages. These effects, which exist due to the use of piezoelectric stacks for actuation, are minimized using charge actuation. The integral resonant control method is applied in conjunction with feedforward inversion technique to achieve high-speed and accurate scanning performances, up to 400 Hz.

Resonant controllers for smart structures

In this paper we propose a special type of colocated feedback controller for smart structures. The controller is a parallel combination of high-Q resonant circuits. Each of the resonant circuits is tuned to a pole (or the resonant frequency) of the smart structure. It is proven that the parallel combination of resonant controllers is stable with an infinite gain margin. Only one set of actuator–sensor can damp multiple resonant modes with the resonant controllers. Experimental results are presented to show the robustness of the proposed controller in damping multimode resonances.

Invited Review Article : Accurate and fast nanopositioning with piezoelectric tube scanners: Emerging trends and future challenges

Piezoelectric tube scanners have emerged as the most widely used nanopositioning technology in modern scanning probe microscopes. Despite their impressive properties, their fast and accurate operations are hindered due to complications such as scan induced mechanical vibrations, hysteresis nonlinearity, creep, and thermal drift. This paper presents an overview of emerging innovative solutions inspired from recent advances in fields such as smart structures, feedback control, and advanced estimation aimed at maximizing positioning precision and bandwidth of piezoelectric tube scanners. The paper presents a thorough survey of the related literature and contains suggestions for future research prospects.

Integral resonant control of collocated smart structures

This paper introduces integral resonant control, IRC, a simple, robust and well-performing technique for vibration control in smart structures with collocated sensors and actuators. By adding a direct feed-through to a collocated system, the transfer function can be modified from containing resonant poles followed by interlaced zeros, to zeros followed by interlaced poles. It is shown that this modification permits the direct application of integral feedback and results in good performance and stability margins. By slightly increasing the controller complexity from first to second order, low-frequency gain can be curtailed, alleviating problems due to unnecessarily high controller gain below the first mode. Experimental application to a piezoelectric laminate cantilever beam demonstrates up to 24 dB modal amplitude reduction over the first eight modes.

A New Method for Robust Damping and Tracking Control of Scanning Probe Microscope Positioning Stages

This paper demonstrates a simple second-order controller that eliminates scan-induced oscillation and provides integral tracking action. The controller can be retrofitted to any scanning probe microscope with position sensors by implementing a simple digital controller or operational amplifier circuit. The controller is demonstrated to improve the tracking bandwidth of an NT-MDT scanning probe microscope from 15 Hz (with an integral controller) to 490 Hz while simultaneously improving gain-margin from 2 to 7 dB. The penalty on sensor induced positioning noise is minimal. A unique benefit of the proposed control scheme is the performance and stability robustness with respect to variations in resonance frequency. This is demonstrated experimentally by a change in resonance frequency from 934 to 140 Hz. This change does not compromise stability or significantly degrade performance. For the scanning probe microscope considered in this paper, the noise is marginally increased from 0.30 to 0.39 nm rms. Open and closed-loop experimental images of a calibration standard are reported at speeds of 1, 10, and 31 lines per second (with a scanner resonance frequency of 290 Hz). Compared with traditional integral controllers, the proposed controller provides a bandwidth improvement of greater than 10 times. This allows faster imaging and less tracking lag at low speeds.

An optimization approach to optimal placement of collocated piezoelectric actuators and sensors on a thin plate.

Abstract The purpose of this paper is to suggest a criterion for the optimal placement of collocated piezoelectric actuator–sensor pairs on a thin flexible plate using modal and spatial controllability measures. Consideration is given to the reduction of control spillover effect by adding an extra spatial controllability constraint in the optimization procedure. The spatial controllability is used to find the optimal placement of collocated actuator–sensor pairs for effective average vibration reduction over the entire structure, while maintaining modal controllability and observability of selected vibration modes. It is found that the methodology for optimal actuator placement can be used for a collocated system without damaging the observability performance of the collocated sensors. Experimental validation of our optimal placement is done on a simply supported thin plate with a collocated piezoelectric actuator–sensor pair.

A New Scanning Method for Fast Atomic Force Microscopy

In recent years, the atomic force microscope (AFM) has become an important tool in nanotechnology research. It was first conceived to generate 3-D images of conducting as well as nonconducting surfaces with a high degree of accuracy. Presently, it is also being used in applications that involve manipulation of material surfaces at a nanoscale. In this paper, we describe a new scanning method for fast atomic force microscopy. In this technique, the sample is scanned in a spiral pattern instead of the well-established raster pattern. A constant angular velocity spiral scan can be produced by applying single frequency cosine and sine signals with slowly varying amplitudes to the x-axis and y -axis of AFM nanopositioner, respectively. The use of single-frequency input signals allows the scanner to move at high speeds without exciting the mechanical resonance of the device. Alternatively, the frequency of the sinusoidal set points can be varied to maintain a constant linear velocity (CLV) while a spiral trajectory is being traced. Thus, producing a CLV spiral. These scan methods can be incorporated into most modern AFMs with minimal effort since they can be implemented in software using the existing hardware. Experimental results obtained by implementing the method on a commercial AFM indicate that high-quality images can be generated at scan frequencies well beyond the raster scans.

Making a commercial atomic force microscope more accurate and faster using positive position feedback control

This paper presents experimental implementation of a positive position feedback (PPF) control scheme for vibration and cross-coupling compensation of a piezoelectric tube scanner in a commercial atomic force microscope (AFM). The AFM is a device capable of generating images with extremely high resolutions down to the atomic level. It is also being used in applications that involve manipulation of matter at a nanoscale. Early AFMs were operated in open loop. Consequently, they were susceptible to piezoelectric creep, thermal drift, hysteresis nonlinearity, and scan-induced vibration. These effects tend to distort the generated image and slow down the scanning speed of the device. Recently, a new generation of AFMs has emerged that utilizes position sensors to measure displacements of the scanner in three dimensions. These AFMs are equipped with feedback control loops that work to minimize the adverse effects of hysteresis, piezoelectric creep, and thermal drift on the obtained image using proportional-plus-integral (PI) controllers. These feedback controllers are often not designed to deal with the highly resonant nature of an AFMs scanner nor with the cross coupling between various axes. In this paper we illustrate the improvement in accuracy and imaging speed that can be achieved by using a properly designed feedback controller such as a PPF controller. Such controllers can be incorporated into most modern AFMs with minimal effort since they can be implemented in software with the existing hardware. Experimental results show that by implementing the PPF control scheme, relatively good images in comparison with a well-tuned PI controller can still be obtained up to line scan of 60 Hz.

Integral Resonant Control for Vibration Damping and Precise Tip-Positioning of a Single-Link Flexible Manipulator

In this paper, we propose a control design method for single-link flexible manipulators. The proposed technique is based on the integral resonant control (IRC) scheme. The controller consists of two nested feedback loops. The inner loop controls the joint angle and makes the system robust to joint friction. The outer loop, which is based on the IRC technique, damps the vibration and makes the system robust to the unmodeled dynamics (spill-over) and resonance frequency variations due to changes in the payload. The objectives of this work are: 1) to demonstrate the advantages of IRC, which is a high-performance controller design methodology for flexible structures with collocated actuator-sensor pairs and 2) to illustrate its capability of achieving precise end-point (tip) positioning with effective vibration suppression when applied to a typical flexible manipulator. The theoretical formulation of the proposed control scheme, a detailed stability analysis and experimental results obtained on a flexible manipulator are presented.

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

A compliant XY nanopositioner is presented in this brief. The device is designed to have a very low cross-coupling between the X- and Y-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 X-to- <;i>Y<;/i> 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 μm × 10 μm with small positioning errors are demonstrated. High-speed accurate raster scans of up to 100 Hz, with nanoscale resolution are also illustrated.