H. Habibullah

Tracking of Triangular Reference Signals Using LQG Controllers for Lateral Positioning of an AFM Scanner Stage

This paper presents the design of an internal reference model-based optimal linear quadratic Gaussian (LQG) controller for the lateral positioning of a piezoelectric tube actuator (PTA) used in an atomic force microscope (AFM). In this control design, internal modeling of the reference signal and system error are considered. As a result, the steady-state tracking error is minimized. In addition to the LQG controller, a vibration compensator is incorporated with the plant to suppress the vibration of the PTA at the resonance frequency. It achieves a high closed-loop bandwidth and significant damping of the resonant mode of the PTA, which enables a reference triangular signal to be tracked. Comparison of performance of the optimal LQG controller augmented with a vibration compensator and a PI controller demonstrates that the proposed controller shows significant improvements over the existing AFM PI controller.

High-speed spiral imaging technique for an atomic force microscope using a linear quadratic Gaussian controller

This paper demonstrates a high-speed spiral imaging technique for an atomic force microscope (AFM). As an alternative to traditional raster scanning, an approach of gradient pulsing using a spiral line is implemented and spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes to the X and Y-axes of the AFMs piezoelectric tube scanner (PTS). Due to these single-frequency sinusoidal input signals, the scanning process can be faster than that of conventional raster scanning. A linear quadratic Gaussian controller is designed to track the reference sinusoid and a vibration compensator is combined to damp the resonant mode of the PTS. An internal model of the reference sinusoidal signal is included in the plant model and an integrator for the system error is introduced in the proposed control scheme. As a result, the phase error between the input and output sinusoids from the X and Y-PTSs is reduced. The spirals produced have particularly narrow-band frequency measures which change slowly over time, thereby making it possible for the scanner to achieve improved tracking and continuous high-speed scanning rather than being restricted to the back and forth motion of raster scanning. As part of the post-processing of the experimental data, a fifth-order Butterworth filter is used to filter noises in the signals emanating from the position sensors and a Gaussian image filter is used to filter the images. A comparison of images scanned using the proposed controller (spiral) and the AFM PI controller (raster) shows improvement in the scanning rate using the proposed method.

High-precision spiral positioning control of a piezoelectric tube scanner used in an atomic force microscope

This paper considers a high-speed spiral scanning method using an atomic force microscope (AFM). In it, spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes in the X and Y-axes, respectively, of the AFMs piezoelectric tube (PZT) scanner. Due to these single-frequency sinusoidal input signals, the scanning process can be faster than that of conventional raster scanning. A linear quadratic Gaussian (LQG) controller is designed to track the reference sinusoidal signal. An internal model of the reference sinusoidal signal is included in the plant model and an integrator for the system error is introduced in the proposed control scheme. As a result, the phase error between the input and output sinusoid from the X and Y-PZTs is reduced. The spirals produced have particularly narrow-band frequency measures which change slowly over time, thereby making it possible for the scanner to achieve improved tracking and continuous high-speed scanning rather than being restricted to the back and forth motion of raster scanning. Also, a fifth-order Butterworth filter is used to filter noises in the signals emanating from the position sensors. A comparison of images scanned using the proposed controller (spiral) and the AFM proportional integral (PI) controller (raster) provide evidence of the efficacy of the proposed method.

A Novel Control Approach for High-Precision Positioning of a Piezoelectric Tube Scanner

An optimal controller for high-precision spiral positioning of a piezoelectric tube scanner used in an atomic force microscope (AFM) is proposed in this paper. In the proposed control scheme, a second-order vibration compensator is incorporated with the piezoelectric tube scanner (PTS) to suppress the vibration of the PTS at the resonant frequency. An internal model of a reference sinusoidal signal is included with the augmented plant model and an integrator is introduced with a linear quadratic Gaussian controller which reduces the phase error between the input and output sinusoids. The proposed method allows a commercial AFM to scan at high scanning speeds as an alternative to the raster scanning approach. The performance of this controller is assessed with closed-loop frequency response, tracking accuracy, and a set of spiral scanned images. The raster scanned images obtained using the standard AFM PI controller is also presented for comparison with the spiral images. Experimental results prove the effectiveness of the proposed method.

Limiting factor for a piezoelectric tube scanner

In most nanotechnology applications, speed and precision are important requirements for obtaining good topographical maps of material surfaces using atomic force microscopes (AFMs), many of which use piezoelectric tube scanners (PTSs) for scanning and positioning at nanometric resolutions. However, PTS suffers from various intrinsic problems that degrade its positioning performance, such as: (i) lightly damped low-frequency resonant modes due to its mechanical structure; (ii) nonlinear behavior due to hysteresis and creep; and (iii) the cross-coupling effect between its axes (in 3D positioning systems such as AFMs). This paper presents a survey of the literature on the PTS, an overview of a few emerging innovative solutions for its nanopositioning and future research directions.

Design of a robust controller for vibration control of a piezoelectric tube scanner

This paper presents an approach for designing a robust vibration control system for a piezoelectric tube scanner (PTS) used in an atomic force microscope (AFM). In this control design, an uncertainty system model is constructed by measuring modeling error between the measured and model frequency response data. Then a minimax linear quadratic Gaussian (LQG) control technique is used to design a controller which minimizes scanner vibration at its resonant mode. This controller is robust against uncertainties introduced as a result of truncating higher order modes of the scanner, variation of plant transfer function due to temperature and humidity and measurement noise from the position sensors. The experimental results show that the proposed controller is able to reduce the vibration at its resonant mode and track the reference signal.

Design and application of a data driven controller using the small-gain constraint for positioning control of a nano-positioner

In this paper, the design of a data driven controller using a small-gain theorem approach for improving the positioning accuracy of a piezoelectric tube scanner (PTS) is demonstrated. Open-loop frequency responses of both the X-PTS and Y-PTS are measured using a band-limited sweep sine signal and are used as primary data for this control design. The frequency response of the controllers is synthesized by the application of the small-gain theorem constraints over the entire frequency range for both the axes. The experimental implementation of this feedback data driven controller provides significant vibration reduction, with 19 dB and 15 dB damping at the resonance frequencies of the X and Y-axes of the PTS, respectively. A comparison between the open-loop and closed-loop tracking performance for triangular signals shows significant improvement up to the scanning frequency of 150 Hz. Moreover, the design of this data driven controller is less complex than conventional controller design methods as it does not need a system model.

Robust spiral positioning control of a piezoelectric tube scanner

In this paper, a robust spiral positioning of a piezoelectric tube scanner (PTS) used in an atomic force microscope (AFM) is proposed. A minimax linear quadratic Gaussian (LQG) controller is designed based on an uncertainty system model which is constructed by measuring the modeling error between the measured and model frequency response. This controller is robust against uncertainties introduced as a result of spillover dynamics of the scanner at frequencies after the first resonance frequency (900 Hz) of the scanner and variation in plant transfer functions due to temperature and humidity. The proposed scheme provides sufficient damping at resonant modes to track the reference sinusoidal signal. The experimental results demonstrate that sufficiently high positioning accuracy is achieved using the proposed control scheme.