Phase-locked Loop-based Proportional Integral Control for Spiral Scanning in an Atomic Force Microscope

Habibullah, Habibullah; Pota, Hemanshu R.; Petersen, Ian R.

doi:10.3182/20140824-6-za-1003.00388

Cited by 17 publications

(10 citation statements)

References 18 publications

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“…3(a)) can be found in [22] and the first resonant mode is at about 683 Hz and the second mode is at 1090 Hz. Similarly, the state-space model to be the best fit for the Y-PTS (Fig.…”

Section: Modeling Of the Ptsmentioning

confidence: 95%

“…Similarly, the state-space model to be the best fit for the Y-PTS (Fig. 3(b)) can be found in [22] where the first resonant mode of the PTS is at about to 683 Hz and second mode at 1100 Hz. In Fig.…”

Section: Modeling Of the Ptsmentioning

confidence: 99%

“…An experimental frequency response is obtained using a dual-channel HP35665A dynamic signal analyzer (DSA). The experimental setup details and detail modeling procedure can be found in [10,22]. The frequency responses generated in the DSA are processed in MATLAB and using the prediction error method (PEM), a system model is obtained [31].…”

Section: Modeling Of the Ptsmentioning

confidence: 99%

“…For example, a square lattice becomes rhombohedral and since this is a well-known structure one can draw the wrong conclusions [10]. To avoid this, spiral scanning approaches have been introduced in [17][18][19][20][21][22][23] for fast imaging using the AFM. In [24], a spiral scanning method is reported as a replacement for raster scanning and in this scanning method two challenges are mentioned: the first challenge is to achieve uniform distribution of sampling points in the 2-D plane and the second is to have a relatively constant linear speed.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Reduction of phase error between sinusoidal motions and vibration of a tube scanner during spiral scanning using an AFM

Habibullah

Pota

Petersen

2016

Int. J. Control Autom. Syst.

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The design of a phase-locked loop (PLL)-based proportional integral (PI) controller for compensating the phase error between motions from the lateral axes of a piezoelectric tube scanner (PTS) during spiral scanning for an atomic force microscope (AFM) is proposed in this paper. Spiral motion of the PTS for scanning of material surfaces or biological samples using an AFM is achieved by applying two sinusoidal signals with a 90 degree phase-shift and of varying amplitudes to the X and Y-axes of the scanner. The phase error between the X and Y-axes positions and scanner's vibration due to its mechanical properties increase with increasing scanning speeds which reduce the imaging performance of the AFM at high frequencies. In the proposed control scheme, a vibration compensator is used with the X and Y-PTS to damp the vibration of the PTS at its resonant frequency and the phase error between the displacements of the two lateral axes of the scanner is measured by a phase detector and a PI controller is used to reduce the error. Comparisons of experimental results for reference tracking and imaging performance with the AFM PI controller demonstrate the efficiency of the proposed control method.

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“…3(a)) can be found in [22] and the first resonant mode is at about 683 Hz and the second mode is at 1090 Hz. Similarly, the state-space model to be the best fit for the Y-PTS (Fig.…”

Section: Modeling Of the Ptsmentioning

confidence: 95%

Section: Modeling Of the Ptsmentioning

confidence: 99%

Section: Modeling Of the Ptsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Reduction of phase error between sinusoidal motions and vibration of a tube scanner during spiral scanning using an AFM

Habibullah

Pota

Petersen

2016

Int. J. Control Autom. Syst.

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show abstract

“…The tracking behavior as well as the stability of such a system is largely dependent on the phase detector (PD) characteristics. In many literatures (see [3][4][5][6][7][8] and references therein), the nonlinear nature of the PD is bypassed, which is typically a reasonable approximation when considering the PLL to be close to its lock state. While this is convenient during the initial phases of modern PLL designs, the linear assumption of the PD is only valid when the phase difference between the output and input remains sufficiently small [9], [10].…”

Section: Introductionmentioning

confidence: 99%

Robust stability analysis and improved design of phase‐locked loops with non‐monotonic nonlinearities: LMI‐based approach

Ahmad

2017

Circuit Theory & Apps

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Due to nonlinear nature of several phase detectors, linear approximation method often leads to performance degradation in many phase-locked loops (PLLs), particularly when the phase errors are sufficiently large. A third or higher order PLL, in spite of the ability to track a wider variety of inputs and having higher operatingfrequency range, requires more design attention in order to ensure stable tracking. In this work, with the nonlinearities inserted into the system's model, suitable criteria that take into account the nonlinearities' non-monotonicity, sector and slope bounds are employed to establish robust stability conditions. The result is applicable to any PLLs without order and type restrictions. For Type-1 PLLs, the resulting condition can be used to search for the maximum stable loop gain, which is also linked to the lock-in range of the system. In the later part of this work, the focus is devoted towards designing PLLs with high lock-in range, which is performed via mixing the proposed method with H ∞ synthesis. The searches for the parameters in both PLL analysis and design are expressed in terms of convex linear matrix inequalities, which are computationally tractable. To illustrate the improvement introduced via this approach, several numerical examples and simulations are included with comparisons over conventional methods. Remark 2Solving the optimization problem in (13) with c set to unity gives K L = k 0 . The significance of this is that it directly reduces the complexity of the LMI search for higher values of c where the solution is only k 0 c . This is useful particularly when n is large, which often leads to numerical issues.

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A Novel Application of Minimax LQG Control Technique for High‐speed Spiral Imaging

Habibullah

Pota

Petersen

2017

Asian Journal of Control

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Over the last two decades, increasing the scanning speed of an atomic force microscopy (AFM) has been attempted either by applying novel controllers, using alternative scanning methods, or by modifying the hardware setup. This paper demonstrates, the first two approaches to achieve high-speed AFM image scanning. A robust minimax linear quadratic Gaussian (LQG) controller is designed and spiral scanning is considered as an alternative scanning method rather than conventional raster scanning. The minimax LQG controller is designed based on an uncertain system model which is constructed by measuring the plant variations due to variations in sample mass and also modeling error between the measured and model frequency responses. This controller is also robust against uncertainties introduced as a result of variations of sample mass, spillover dynamics of the scanner at frequencies higher than the first resonance frequency of the scanner, and variation in plant transfer functions due to temperature and humidity. The designed controller is experimentally implemented on an AFM using a dSPACE ds-1103 real-time prototyping system and open-loop and closed-loop spiral imaging performances are evaluated. The proposed controller provides sufficient damping at the resonant modes to accurately track the sinusoidal reference signal and generate vibration free images. Also, creep, hysteresis, and cross-coupling effects are significantly reduced. The experimental results show that the proposed scheme outperforms the open-loop case and some other existing approaches.

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Phase-locked Loop-based Proportional Integral Control for Spiral Scanning in an Atomic Force Microscope

Cited by 17 publications

References 18 publications

Reduction of phase error between sinusoidal motions and vibration of a tube scanner during spiral scanning using an AFM

Reduction of phase error between sinusoidal motions and vibration of a tube scanner during spiral scanning using an AFM

Robust stability analysis and improved design of phase‐locked loops with non‐monotonic nonlinearities: LMI‐based approach

A Novel Application of Minimax LQG Control Technique for High‐speed Spiral Imaging

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