M. S. Rana

Performance of Sinusoidal Scanning With MPC in AFM Imaging

An atomic force microscope (AFM) is an extremely versatile investigative tool in the field of nanotechnology, the performance of which is significantly influenced by its conventional zig-zag raster pattern scanning method. In this paper, in order to increase its imaging speed, we consider the use of a sinusoidal scanning method, i.e., a spiral scanning method with an improved model predictive control (MPC) scheme. In this approach, spirals are generated by applying waves, each with a single frequency and slowly varying amplitude, in the X-piezo (sine wave) and Y-piezo (cosine wave) of the piezoelectric tube scanner (PTS) of the AFM. As these input signals are single frequencies, the scanning can proceed faster than traditional raster scanning, without exciting the resonant mode of the PTS. The proposed MPC controller reduces the phase error between the reference position input and measured output sinusoids and provides better tracking of the reference signal. Also, a notch filter is designed and included in the feedback loop to suppress vibrations of the PTS at the resonant frequency. The experimental results show that, using the proposed method, the AFM is able to scan a 6 μm radius image within 2.04 s with a quality better than that obtained using the conventional raster pattern scanning method.

High-Speed AFM Image Scanning Using Observer-Based MPC-Notch Control

This paper presents the design and experimental implementation of an observer-based model predictive control scheme with a notch filter to achieve accurate tracking and fast scanning for an atomic force microscope (AFM). The proposed controller reduces the tracking error by improving the damping of the resonant modes of the AFM piezoelectric tube scanner (PTS). The design of this controller is based on an identified model of the PTS. A Kalman filter is used to obtain full-state information in the presence of position sensor noise. A comparison of the experimentally obtained scanned images using the proposed controller and the existing AFM PI controller is given. The experimental results demonstrate the efficacy of the proposed controller.

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.

Spiral Scanning With Improved Control for Faster Imaging of AFM

One of the key barriers to an atomic force microscope (AFM) achieving high scanning speeds is its use of the traditional zig-zag raster pattern scanning technique. In this paper, we consider the use of a high-speed spiral imaging technique with an improved multi-input multi-output (MIMO) model predictive control (MPC) scheme with a damping compensator for faster scanning by an AFM. The controllers design is based on an identified MIMO model of the AFMs piezoelectric tube scanner (PTS) and it achieves a higher closed-loop bandwidth, significant damping of the resonant mode of the PTS, and reduces the cross-coupling effect between the PTSs axes. 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. To evaluate the performance improvement using this proposed control scheme for spiral scanning, an experimental comparison of its scanned images with those of the open-loop condition is performed. Experimental results show that, by using the proposed method, the AFMs scanning speed is significantly increased up to 180 Hz.

Creep, Hysteresis, and Cross-Coupling Reduction in the High-Precision Positioning of the Piezoelectric Scanner Stage of an Atomic Force Microscope

This paper presents the high-precision lateral positioning of a piezoelectric tube scanner (PTS) used in an atomic force microscope (AFM). The operation of the PTS is affected by various nonlinearities depending upon its operating conditions. An internal reference model-based optimal linear quadratic Gaussian (LQG) controller with a vibration compensator is designed and implemented on the AFM to reduce creep, hysteresis, induced vibration, and cross coupling. This proposed controller has integral action on the error state which makes it possible to track the reference signal and the vibration compensator achieves significant damping of the resonant modes of the PTS in the X- and Y-axes. It also compensates the cross coupling between the X-Y axes dynamics of the AFM system, reducing the artifacts instigated by the system dynamic behavior at high scan rates. The closed-loop frequency responses for both the axes have a high bandwidth. The experimental results are presented which demonstrate the efficacy of the proposed method.

Nonlinearity Effects Reduction of an AFM Piezoelectric Tube Scanner Using MIMO MPC

The design of a controller which compensates for the effects of creep, hysteresis, vibration, and cross-coupling in a piezoelectric tube scanner (PTS) is presented in this paper. The PTS is a key nanopositioning component installed in a commercial atomic force microscope (AFM) to perform scanning. The impediments to fast scanning due to PTS dynamics are: 1) the presence of mechanical resonances; 2) nonlinearities due to the piezoelectric characteristics; and 3) the cross-coupling effect between x- and y-axes in the PTS. In this paper, a multi-input multi-output model predictive control (MPC) scheme is designed to counteract the effects of creep, hysteresis, vibration, and cross-coupling in a PTS. Also, a damping compensator is included to suppress the vibration effect at its resonance frequency. The proposed controller achieves a high closed-loop bandwidth and significant damping of the resonant mode. To evaluate the performance improvement using the proposed control scheme, an experimental comparison with the existing AFM proportional-integral (PI) controller and a single-input single-output (SISO) MPC is conducted. Enhancement in the scanning speed up to 125 Hz is observed with the proposed controller.

Model predictive control of atomic force microscope for fast image scanning

This article presents the design of a model predictive control (MPC) scheme for fast tracking and accurate scanning of an atomic force microscope (AFM). The design of this controller is based on an identified model of the AFM piezoelectric tube (PZT) scanner. Total development of the AFM imaging and scanning speed has been illustrated through this paper by proper design and implementation of the MPC controller. Experimental results show that the MPC can increase the scanning speed significantly in contrast with the existing PI controller.

The design of model predictive control for an AFM and its impact on piezo nonlinearities

An atomic force microscope (AFM) is an extremely versatile investigative tool in the field of nanotechnology, the performance of which is significantly influenced due to the nonlinear behavior of its scanning unit; i.e., the piezoelectric tube scanner (PTS). In order to increase the imaging speed of the AFM, a model predictive control (MPC) scheme is applied in both the X and Y-piezo axes of the PTS to reduce its nonlinearity effects and to improve in damping of the resonant mode. The proposed controller provides an AFM with the capability to achieve improved tracking and it results in the reduction of the hysteresis, creep, vibration, and cross-coupling effects in piezoactuators. The experimental results demonstrate the effectiveness of the proposed control scheme.

Reduction of cross-coupling between X-Y axes of piezoelectric scanner stage of atomic force microscope for faster scanning

In this paper we describe the cross-coupling effect between X-Y axes of piezoelectric tube (PZT) scanner used in an atomic force microscope (AFM). During raster scanning X-Y axes induced cross-coupling effect in the lateral positioning of the scanner stage of the AFM and as a result, it produces blurred or distorted images. To address this effect, an LQG controller is designed and implemented on AFM which minimizes the cross-coupling effect between the axes mainly at the resonance frequency of the scanner tube. The proposed controller has an integral action with the error signal which makes it possible to track the reference signal and a significant damping of the resonant modes of the PZT in the X and Y axes. This controller compensates the cross-coupling between X-Y axes dynamics of the AFM system, reducing the artifacts instigating by the system dynamic behavior at high scan rates. The closed-loop frequency responses for both the axes have achieved high bandwidth. Consequently, scanned results are evaluated as a better one than the open-loop of the AFM.

Improvement of the tracking accuracy of an AFM using MPC

Tracking a reference signal is one of the major problems of an atomic force microscope (AFM). This article presents the design and experimental implementation of a model predictive control (MPC) scheme, with a vibration compensator for achieving accurate tracking for an AFM at higher scanning rates. To evaluate the improvement in performance attained by this control scheme, an experimental comparison of its tracked signals against different reference signals at different scanning rates is conducted. The experimental results demonstrate the effectiveness of the proposed controller.