Bharath Bhikkaji

High-Performance Control of Piezoelectric Tube Scanners

In this paper, a piezoelectric tube of the type typically used in scanning tunneling microscopes (STMs) and atomic force microscopes (AFMs) is considered. Actuation of this piezoelectric tube is hampered by the presence of a lightly damped low-frequency resonant mode. The resonant mode is identified and damped using a positive velocity and position feedback (PVPF) controller, a control technique proposed in this paper. Input signals are then shaped such that the closed-loop system tracks a raster pattern. Normally, piezoelectric tubes are actuated using voltage amplifiers. Nonlinearity in the form of hysteresis is observed when actuating the piezoelectric tubes at high amplitudes using voltage amplifiers. It has been known for some time that hysteresis in piezoelectric actuators can be largely compensated by actuating them using charge amplifiers. In this paper, high-amplitude actuation of a piezoelectric tube is achieved using a charge amplifier.

Minimizing Scanning Errors in Piezoelectric Stack-Actuated Nanopositioning Platforms

Piezoelectric stack-actuated parallel-kinematic nanopositioning platforms are widely used in nanopositioning applications. These platforms have a dominant first resonant mode at relatively low frequencies, typically in the hundreds of hertz. Furthermore, piezoelectric stacks used for actuation have inherent nonlinearities such as hysteresis and creep. These problems result in a typically low-grade positioning performance. Closed-loop control algorithms have shown the potential to eliminate these problems and achieve robust, repeatable nanopositioning. Using closed-loop noise profile as a performance criterion, three commonly used damping controllers, positive position feedback, polynomial-based pole placement, and resonant control are compared for their suitability in nanopositioning applications. The polynomial-based pole placement controller is chosen as the most suitable of the three. Consequently, the polynomial-based control design to damp the resonant mode of the platform is combined with an integrator to produce raster scans of large areas. A scanning resolution of approximately 8 nm, over a 100 mum times 100 mum area is achieved.

Experimental implementation of extended multivariable PPF control on an active structure

This paper reports experimental implementation of an extended positive position feedback (PPF) controller on an active structure consisting of a cantilevered beam with bonded collocated piezoelectric actuators and sensors. Stability conditions for PPF control are rederived to allow for a feed-through term in the model of the structure. This feed-through term is needed to ensure that the systems in-bandwidth zeros are captured with reasonable accuracy. The set of stabilizing PPF controllers is shown to be a convex set characterized by a set of linear matrix inequalities. A number of multivariable PPF controllers are designed and successfully implemented on the structure.

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.

A Negative Imaginary Approach to Modeling and Control of a Collocated Structure

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.

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

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.

Precise Tip Positioning of a Flexible Manipulator Using Resonant Control

A single-link flexible manipulator is fabricated to represent a typical flexible robotic arm. This flexible manipulator is modeled as an SIMO system with the motor torque as the input and the hub angle and the tip position as the outputs. The two transfer functions are identified using a frequency-domain system identification method, and the resonant modes are determined. A feedback loop around the hub angle response with a resonant controller is designed to damp the resonant modes. A high-gain integral controller is also implemented to achieve zero steady-state error in the tip position response. Experiments are performed to demonstrate the effectiveness of the proposed control scheme.

Fast scanning using piezoelectric tube nanopositioners: A negative imaginary approach

Most commercially available Atomic Force Microscopes (AFMs) use piezoelectric tube nano-positioners for scanning. Current scanning frequencies are less than 0.01 ƒr, where ƒr is the frequency of the first resonant mode of the piezoelectric tube used. An improvement in the scanning rates without losing the nano-scale precision is desired. Here, a prototype of the scanning unit of an AFM is considered. The dynamics of the piezo tube, used in the prototype, is approximated by a model that satisfies the negative imaginary property. The resonant mode that hampers the fast scanning is identified from the model and damped using a feedback control technique known as the Integral Resonant Control (IRC). The piezoelectric tube is then actuated to have fast and accurate scans.

PPF Control of a Piezoelectric Tube Scanner

Piezoelectric tubes are commonly used in Scanning Tunnelling Microscopes and Atomic Force Microscopes to scan material surfaces. In general, scanning using a piezoelectric tube is hampered by the presence of low-frequency mechanical modes that are easily excited to produce unwanted vibration. In this work, a Positive Position Feedback controller is designed to mitigate the undesired mechanical resonance. Experimental results reveal a significant damping of the mechanical dynamics, and consequently, an improvement in tracking performance.

Multivariable integral control of resonant structures

Integral resonant control (IRC) is a feedback control technique used for damping active structures with a collocated sensor/actuator pair. This paper extends this control technique to structures having several collocated sensor/ actuator pairs. Conditions for the closed loop stability are derived, and the set of such stabilizing IRC controllers is shown to be a convex set. An experimental implementation of an IRC controller on an active structure (cantilever beam) with two pairs of bonded collocated piezoelectric sensors/actuators is also presented.