Local orbit feedback systems coupled by transfer function errors

In this paper, limit cycle frequency, pulse width and stability analysis are examined using different methods for relay feedback nonlinear control systems with integer or fractional order plant transfer functions. The describing function (DF), A loci, a time domain method formulated in state space notation and Matlab/Simulink simulations are used for the analysis. Comparisons of the results of using these methods are given in several examples. In addition, the work has been extended to fractional order systems with time delay. Programs have been developed in the Matlab environment for all the theoretical methods. In particular, Matlab programs have been written to obtain a graphical solution for the A loci method, which can precisely calculate the limit cycle frequency. The developed solution methods are shown in various examples. The major contribution is to look at finding limit cycles for relay feedback systems having plants with a fractional order transfer function (FOTF). However, en route to this goal new assessments of limit cycle stability have been done for a rational plant transfer function plus a time delay.

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Investigation of Position and Velocity Stability of the Nanometer Resolution Linear Motor Stage with Air Bearings by Shaping of Controller Transfer Function

Symmetry ◽

10.3390/sym12122062 ◽

2020 ◽

Vol 12 (12) ◽

pp. 2062

Author(s):

Artur Piščalov ◽

Edgaras Urbonas ◽

Nikolaj Višniakov ◽

Darius Zabulionis ◽

Artūras Kilikevičius

Keyword(s):

Transfer Function ◽

Dynamic Error ◽

Linear Motor ◽

Symmetric System ◽

Air Bearings ◽

Feedback Systems ◽

Mechatronic Systems ◽

Industrial Enterprises ◽

Dynamic Errors ◽

Moving Platform

Modern industrial enterprises require high accuracy and precision feedback systems to fulfil cutting edge requirements of technological processes. As demand for a highly accurate system grows, a thin gap between throughput and quality exists. The conjunction of ultrafast lasers and modern control strategies of mechatronic systems can be taken into account as an effective solution to reach both throughput and tolerances. In the present paper, the dynamic errors of the moving platform of the one degree of freedom stage, based on linear motor and air bearings, have been analyzed. A precision positioning system is investigated as a symmetric system which is based on symmetric linear motor. The goal of the present article is to investigate the controllers of the different architecture and to find the best controller that can ensure a stable and small dynamic error of the displacement of the stage platform at four different constant velocities of the moving platform. The relations between the controller order, velocity and the displacement dynamic error have been investigated. It is determined that higher-order controllers can reduce the dynamic error significantly at low velocities of the moving platforms: 1 and 5 mm/s. On the contrary, the low order controllers of 4th-degree polynomials of the transfer function can also provide small dynamic errors of the displacement of the platform.

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Derivation of transfer function from relay feedback systems. [Erratum to document cited in CA116(12):109380p]

Industrial & Engineering Chemistry Research ◽

10.1021/ie00012a031 ◽

1992 ◽

Vol 31 (12) ◽

pp. 2807-2807 ◽

Cited By ~ 1

Author(s):

Ren Chiou Chiang ◽

Shih Haur Shen ◽

Cheng Ching Yu

Keyword(s):

Transfer Function ◽

Feedback Systems ◽

Relay Feedback

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Radiation Damage of Support Films

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096862 ◽

1981 ◽

Vol 39 ◽

pp. 28-29

Author(s):

H.A. Cohen ◽

W. Chiu

Keyword(s):

Transfer Function ◽

Low Temperatures ◽

Carbon Support ◽

Contrast Transfer Function ◽

Electron Dose ◽

Imaging Parameters ◽

Negative Stain ◽

Phase Corrections ◽

Two Parameters ◽

Medium Dose

The goal of imaging the finest detail possible in biological specimens leads to contradictory requirements for the choice of an electron dose. The dose should be as low as possible to minimize object damage, yet as high as possible to optimize image statistics. For specimens that are protected by low temperatures or for which the low resolution associated with negative stain is acceptable, the first condition may be partially relaxed, allowing the use of (for example) 6 to 10 e/Å2. However, this medium dose is marginal for obtaining the contrast transfer function (CTF) of the microscope, which is necessary to allow phase corrections to the image. We have explored two parameters that affect the CTF under medium dose conditions.Figure 1 displays the CTF for carbon (C, row 1) and triafol plus carbon (T+C, row 2). For any column, the images to which the CTF correspond were from a carbon covered hole (C) and the adjacent triafol plus carbon support film (T+C), both recorded on the same micrograph; therefore the imaging parameters of defocus, illumination angle, and electron statistics were identical.

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Possible applications of fraunhofer holography in high resolution electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108258 ◽

1978 ◽

Vol 36 (1) ◽

pp. 222-223 ◽

Cited By ~ 1

Author(s):

N. Bonnet ◽

M. Troyon ◽

P. Gallion

Keyword(s):

Electron Microscopy ◽

High Resolution ◽

Transfer Function ◽

Radiation Damage ◽

High Resolution Electron Microscopy ◽

Far Field ◽

Field Region ◽

Crystalline Materials ◽

Resolution Electron ◽

The Ideal

Two main problems in high resolution electron microscopy are first, the existence of gaps in the transfer function, and then the difficulty to find complex amplitude of the diffracted wawe from registered intensity. The solution of this second problem is in most cases only intended by the realization of several micrographs in different conditions (defocusing distance, illuminating angle, complementary objective apertures…) which can lead to severe problems of contamination or radiation damage for certain specimens.Fraunhofer holography can in principle solve both problems stated above (1,2). The microscope objective is strongly defocused (far-field region) so that the two diffracted beams do not interfere. The ideal transfer function after reconstruction is then unity and the twin image do not overlap on the reconstructed one.We show some applications of the method and results of preliminary tests.Possible application to the study of cavitiesSmall voids (or gas-filled bubbles) created by irradiation in crystalline materials can be observed near the Scherzer focus, but it is then difficult to extract other informations than the approximated size.

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Ultimate resolution and information in electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100086787 ◽

1991 ◽

Vol 49 ◽

pp. 496-497

Author(s):

D. Van Dyck

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

Transfer Function ◽

Information Transfer ◽

Communication Channel ◽

Structural Information ◽

Information Rate ◽

Noise Power ◽

Signal Power ◽

Imaging Device

An (electron) microscope can be considered as a communication channel that transfers structural information between an object and an observer. In electron microscopy this information is carried by electrons. According to the theory of Shannon the maximal information rate (or capacity) of a communication channel is given by C = B log2 (1 + S/N) bits/sec., where B is the band width, and S and N the average signal power, respectively noise power at the output. We will now apply to study the information transfer in an electron microscope. For simplicity we will assume the object and the image to be onedimensional (the results can straightforwardly be generalized). An imaging device can be characterized by its transfer function, which describes the magnitude with which a spatial frequency g is transferred through the device, n is the noise. Usually, the resolution of the instrument ᑭ is defined from the cut-off 1/ᑭ beyond which no spadal information is transferred.

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Analytic integration of contrast transfer functions

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010010617x ◽

1988 ◽

Vol 46 ◽

pp. 822-823

Author(s):

Peter Rez

Keyword(s):

Wave Function ◽

Transfer Function ◽

Transfer Functions ◽

Spherical Aberration ◽

Continuous Distribution ◽

Objective Lens ◽

Direction Parallel ◽

Scattering Angle ◽

Analytic Integration ◽

Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

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