Identifying a Transfer Function From a Frequency Response

2008 ◽  
Vol 3 (2) ◽  
pp. 021207 ◽  
Author(s):  
Duarte Valério ◽  
Manuel Duarte Ortigueira ◽  
José Sá da Costa
Keyword(s):  
Transfer Function ◽  
Frequency Response

A Method of Model Reduction

1986 ◽  
Vol 108 (4) ◽  
pp. 368-371 ◽  
Author(s):  
Jium-Ming Lin ◽  
Kuang-Wei Han
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Model Reduction ◽  
Control Systems ◽  
Response Curve ◽  
Nonlinear Control Systems ◽  
Frequency Response Curve ◽  
Stability Boundaries ◽  
Parameter Variations ◽  
The Stability

In this brief note, the effects of model reduction on the stability boundaries of control systems with parameter variations, and the limit-cycle characteristics of nonlinear control systems are investigated. In order to reduce these effects, a method of model reduction is used which can approximate the original transfer function at S=0, S=∞, and also match some selected points on the frequency response curve of the original transfer function. Examples are given, and comparisons with the methods given in current literature are made.

Evaluation of an Articulation-Index Based Model for Predicting the Effects of Adaptive Frequency Response Hearing Aids

1990 ◽  
Vol 33 (4) ◽  
pp. 676-689 ◽  
Author(s):  
David A. Fabry ◽  
Dianne J. Van Tasell
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Hearing Aids ◽  
Background Noise ◽  
Speech Intelligibility ◽  
Hearing Aid ◽  
Hearing Impaired ◽  
Articulation Index ◽  
Intelligibility Ratings ◽  
High Pass

The Articulation Index (AI) was used to evaluate an “adaptive frequency response” (AFR) hearing aid with amplification characteristics that automatically change to become more high-pass with increasing levels of background noise. Speech intelligibility ratings of connected discourse by normal-hearing subjects were predicted well by an empirically derived AI transfer function. That transfer function was used to predict aided speech intelligibility ratings by 12 hearing-impaired subjects wearing a master hearing aid with the Argosy Manhattan Circuit enabled (AFR-on) or disabled (AFR-off). For all subjects, the AI predicted no improvements in speech intelligibility for the AFR-on versus AFR-off condition, and no significant improvements in rated intelligibility were observed. The ability of the AI to predict aided speech intelligibility varied across subjects. However, ratings from every hearing-impaired subject were related monotonically to AI. Therefore, AI calculations may be used to predict relative—but not absolute—levels of speech intelligibility produced under different amplification conditions.

On the Determination of the Transfer Function of Infinite Line Pressure Probes for Turbomachinery Applications

2012 ◽  
Author(s):  
Nicolas Van de Wyer ◽  
Jean-François Brouckaert ◽  
Rinaldo L. Miorini
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Pressure Fluctuations ◽  
Axial Compressor ◽  
Fast Response ◽  
Experimental Results ◽  
Geometrical Parameters ◽  
Electrical Transmission ◽  
Infinite Line ◽  
Line Pressure

This paper deals with the use of the infinite line pressure probes (ILP) to measure fluctuating pressures in hot environments in turbomachinery applications. These probes, sometimes called waveguide measuring systems, and composed of a series of lines and cavities are using a remote pressure sensor. Ideally they should form a non-resonant system. This is however not always the case and the frequency response of these systems is of course limited by the tubing (diameter and length) but is also highly dependent on other geometrical parameters like sudden expansions or discontinuities in the tubing, or parasite cavities. The development of a new model for ILP simulation, based on the analogy between the propagation of the pressure waves in a line-cavity system and the electrical transmission line, is presented. Unlike the models based on the Bergh and Tijdeman equations, this approach allows the simulation of systems presenting parallel branches. This makes the model appropriate for the prediction of the frequency response of ILP. The model is validated by a comparison of the results with the theory of Bergh and Tijdeman, and with experimental results from the literature and from shock tube tests. Finally, the model is applied for the optimization of ILPs, representative of the systems used in the aeronautics industry, and compared to the experimental results performed on an axial compressor. In those tests, a typical ILP geometry is installed on the compressor casing to measure static pressure fluctuations in the rotor tip gap. Simultaneous measurements with a fast response flush-mounted sensor provided data for comparison and validation of the predicted transfer function.

Transfer Functions of One-Dimensional Distributed Parameter Systems by Wave Approach

2006 ◽  
Vol 129 (2) ◽  
pp. 193-201 ◽  
Author(s):  
B. Kang
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Wave Reflection ◽  
Transfer Functions ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Complex Frequency ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Analysis Technique

An alternative analysis technique, which does not require eigensolutions as a priori, for the dynamic response solutions, in terms of the transfer function, of one-dimensional distributed parameter systems with arbitrary supporting conditions, is presented. The technique is based on the fact that the dynamic displacement of any point in a waveguide can be determined by superimposing the amplitudes of the wave components traveling along the waveguide, where the wave numbers of the constituent waves are defined in the Laplace domain instead of the frequency domain. The spatial amplitude variations of individual waves are represented by the field transfer matrix and the distortions of the wave amplitudes at point discontinuities due to constraints or boundaries are described by the wave reflection and transmission matrices. Combining these matrices in a progressive manner along the waveguide using the concepts of generalized wave reflection and transmission matrices leads to the exact transfer function of a complex distributed parameter system subjected to an externally applied force. The transient response solution can be obtained through the Laplace inversion using the fixed Talbot method. The exact frequency response solution, which includes infinite normal modes of the system, can be obtained in terms of the complex frequency response function from the system’s transfer function. This wave-based analysis technique is applicable to any one-dimensional viscoelastic structure (strings, axial rods, torsional bar, and beams), in particular systems with multiple point discontinuities such as viscoelastic supports, attached mass, and geometric/material property changes. In this paper, the proposed approach is applied to the flexural vibration analysis of a classical Euler–Bernoulli beam with multiple spans to demonstrate its systematic and recursive formulation technique.

scholarly journals Transfer Function with Nonlinear Characteristics Definition Based on Multidimensional Laplace Transform and its Application to Forced Response Power Systems

Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4061
Author(s):  
Villalón ◽  
Medina-Rios
Keyword(s):  
Transfer Function ◽  
Power Systems ◽  
Power System ◽  
Laplace Transform ◽  
Frequency Response ◽  
Transfer Functions ◽  
Volterra Series ◽  
Forced Response ◽  
Nonlinear Characteristics ◽  
Test Power

In this research, the concept of nonlinear transfer function with nonlinear characteristics is introduced through the multidimensional Laplace transform and modal series (MS) method. The method of modal series is applied to the power systems dynamics analysis in order to consider nonlinear oscillations and modal interactions, which contribute to the response of the system's dynamic following disturbances. The method of MS allows the inclusion of input excitation functions obtained as Laplace domain kernels superposed to obtain a transfer function. Applying the Volterra series expansion through kernels decomposition, a transfer function with nonlinear characteristics is obtained which incorporates some of the main modal characteristics of the nonlinear system. Following the same schematic procedure, it is possible to determine second and higher order transfer functions. Once the transfer functions both linear and with nonlinear characteristics are determined, a time domain and frequency response analyses can be performed. The methodology is exemplified by denoting the numerical and analytical properties with the application to a synchronous machine-infinite busbar test power system and to a three synchronous machines–nine buses test power system. Bode and Nyquist analysis are utilized to demonstrate the transfer functions accuracy and frequency response.

Alternative Analytical Mean-Square Calculations for Dynamic Systems Subject to Random Inputs

2001 ◽  
Author(s):  
Robin C. Redfield
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Dynamic Systems ◽  
Analytical Techniques ◽  
System Response ◽  
Mean Square ◽  
Random Inputs ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Insight Into

Abstract Output variables of linear dynamic systems subject to random inputs are often quantified by mean square calculations. Computationally, these involve integration of the frequency response magnitude squared over all frequency. Numerically, this is an easy task and analytically, methods exist to find mean square values as functions of transfer function (frequency response) coefficients. This paper develops further analytical techniques to calculate mean-square values as functions of system pole-zero locations and as functions of eigenproperties and system matrices. These other analytical representations may provide paths to further insight into dynamic system response and optimal design/tuning of dynamic systems.

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