An XYZ nanopositioner is designed for fast the atomic force microscopy. The first resonant modes of the device are measured at 8.8, 8.9, and 48.4 kHz along the X-, Y-, and Z-axes, respectively, which are in close agreement to the finite-element simulations. The measured travel ranges of the lateral and vertical axes are 6.5 μm × 6.6 μm and 4.2 μm, respectively. Actuating the nanopositioner at frequencies beyond 1% of the first resonance of the lateral axes causes mechanical vibrations that result in degradation of the images generated. In order to improve the lateral scanning bandwidth, controllers are designed using the integral resonant control methodology to damp the resonant modes of the nanopositioner and to enable fast actuation. Due to the large bandwidth of the designed nanopositioner, a field programmable analog array is used for analog implementation of the controllers. High-resolution images are successfully generated at 200-Hz line rate with 200×200 pixel resolution in closed loop. © 1996-2012 IEEE.

Bharath Bhikkaji

Department of Electrical Engineering

FIELD PROGRAMMABLE ANALOG ARRAYS

FLEXURE-GUIDED POSITIONERS

INTEGRAL RESONANT CONTROLS

NANO-POSITIONER

Atomic force microscopy

Bandwidth

Piezoelectric actuators

Vibrations (mechanical)

Controllers

Fulltext

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IIT Madras

Design, Modeling, and FPAA-Based Control of a High-Speed Atomic Force Microscope Nanopositioner

IEEE/ASME Transactions on Mechatronics

This paper presents a method for designing inputs to identify linear continuous-time multiple-input multiple-output (MIMO) systems. The goal here is to design a T-optimal band-limited spectrum satisfying certain input/output power constraints. The input power spectral density matrix is parametrized as the product ϕu(jω)=12H(jω)HH(jω), where H(jω) is a matrix polynomial. This parametrization transforms the T-optimal cost function and the constraints into a quadratically constrained quadratic program (QCQP). The QCQP turns out to be a non-convex semidefinite program with a rank one constraint. A convex relaxation of the problem is first solved. A rank one solution is constructed from the solution to the relaxed problem. This relaxation admits no gap between its solution and the original non-convex QCQP problem. The constructed rank one solution leads to a spectrum that is optimal. The proposed input design methodology is experimentally validated on a cantilever beam bonded with piezoelectric plates for sensing and actuation. Subspace identification algorithm is used to estimate the system from the input-output data. © 2019, South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature.

Control Theory and Technology

Optimal finite-dimensional spectral densities for the identification of continuous-time MIMO systems

Controller design to compensate vibration, hysteresis and time delay in a high-speed serial-kinematic X-Y nanopositioner is presented in this paper. A high-speed serial-kinematic X-Y nanopositioner, designed in-house, is installed in a commercial AFM and its scanning performance is studied. The impediments to fast scanning are (i) the presence of mechanical resonances in the nanopositioning stage, (ii) nonlinearities due to the piezoelectric actuators and (iii) time delay introduced by finite clock speeds of the signal conditioning circuitry associated with displacement sensors. In this paper an integral resonant controller is designed to mitigate the effect of the resonance along the X axis (fast axis). The control design accommodates for the time delay, thereby ensuring robust stability. A high gain integral controller is wrapped around the damped nanopositioner to ensure sufficient linearity near the region of operation. For actuation along the Y axis (slow axis), where the bandwidth requirement is less demanding, a notch filter is used to increase the gain margin and the nonlinearity is compensated using a high gain feedback controller. Enhancement in the scanning speed up to 200 Hz is observed. Imaging and tracking performance for open loop and closed loop scans up to 200 Hz line rate is compared and presented. Limitations and future work are discussed. © 2014 IOP Publishing Ltd.

Smart Materials and Structures

Control of a piezoelectrically actuated high-speed serial-kinematic AFM nanopositioner

Atomic Force Microscopes (AFM) are used for generating surface topography of samples at micro to atomic resolutions. Many commercial AFMs use piezoelectric tube nanopositioners for scanning. Scanning rates of these microscopes are hampered by the presence of low frequency resonant modes. When inadvertently excited, these modes lead to high amplitude mechanical vibrations causing the loss of accuracy, while scanning, and eventually to break down of the tube. Feedback control has been used to damp these resonant modes. Thereby, enabling higher scanning rates. Here, a multivariable controller is designed to damp the first resonant mode along both the x and y axis. Exploiting the inherent symmetry in the piezoelectric tube, the multivariable control design problem is recast as independent single-input single-output (SISO) designs. This in conjunction with integral resonant control is used for damping the first resonant mode. © 2013 American Institute of Physics.

Review of Scientific Instruments

Diagonal control design for atomic force microscope piezoelectric tube nanopositioners

A transfer-function is said to be negative imaginary if the corresponding frequency response function has a negative definite imaginary part (on the positively increasing imaginary axis). Negative imaginary transfer-functions can be stabilized using negative imaginary feedback controllers. Flexible structures with compatible collocated sensor/actuator pairs have transfer-functions that are negative imaginary. In this paper a model structure that typically represents a collocated structure is considered. An identification algorithm which enforces the negative imaginary constraint is proposed for estimating the model parameters. A feedback control technique, known as integral resonant control (IRC), is proposed for damping vibrations in collocated flexible structures. Conditions for the stability of the proposed controller are derived, and shown that the set of stabilizing IRCs is convex. Finally, a flexible beam with two pairs of collocated piezoelectric actuators/sensors is considered. The proposed identification scheme is used determining the transfer-function and an IRC is designed for damping the vibrations. The experimental results obtained are reported. © 1996-2012 IEEE.

A negative imaginary approach to modeling and control of a collocated structure

Cutting Edge Internal Auditing

Cutting Edge Internal Auditing Wears Many Hats

Design and Control of a Three-Axis Serial-Kinematic High-Bandwidth Nanopositioner

A Low-Cost Flexure-Based Handheld Mechanism for Micromanipulation

Development of a High-Bandwidth XY Nanopositioning Stage for High-Rate Micro-/Nanomanufacturing

Design, modeling, and FPAA-based control of a high-speed atomic force microscope nanopositioner

Journal	IEEE/ASME Transactions on Mechatronics
ISSN	10834435
Open Access	Yes