On Minimum Phase

2013 ◽  
Vol 61 (12) ◽  
pp. 805-817
Author(s):  
Achim Ilchmann ◽  
Fabian Wirth
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Main Tool ◽  
Rational Functions ◽  
Phase System ◽  
Zero Dynamics ◽  
Minimal Realization ◽  
Minimum Phase ◽  
Denominator Polynomial ◽  
The Time Domain

Abstract We discuss the concept of `minimum phase' for scalar semi Hurwitz transfer functions. The latter are rational functions where the denominator polynomial has its roots in the closed left half complex plane. In the present note, minimum phase is defined in terms of the derivative of the argument function of the transfer function. The main tool to characterize minimum phase is the Hurwitz reflection. The factorization of a weakly stable transfer function into an all-pass and a minimum phase system leads to the result that any semi Hurwitz transfer function is minimum phase if, and only if, its numerator polynomial is semi Hurwitz. To characterize the zero dynamics, we use the Byrnes-Isidori form in the time domain and the internal loop form in the frequency domain. The uniqueness of both forms is shown. This is used to show in particular that asymptotic stable zero dynamics of a minimal realization of a transfer function yields minimum phase, but not vice versa.

PROCESSING AND INTERPRETATION OF MAGNETOTELLURIC SOUNDINGS

Geophysics ◽  
1972 ◽  
Vol 37 (6) ◽  
pp. 1005-1021 ◽  
Author(s):  
G. Kunetz
Keyword(s):  
Transfer Function ◽  
Time Domain ◽  
Transfer Functions ◽  
Seismic Analysis ◽  
Magnetotelluric Soundings ◽  
Automatic Interpretation ◽  
Uniqueness Of The Solution ◽  
Experimental Values ◽  
The Time Domain ◽  
Analytical Expressions

A few methods in the processing and interpretation of magnetotelluric soundings over a stratified earth are investigated, with emphasis on the less commonly used time‐domain procedures. Analytical expressions of the theoretical transfer function between the magnetic‐ and electric‐field variations, both in frequency and time domain, are derived. Their properties are studied, and recursive algorithms are given for their numerical computation. On the other hand, a procedure is outlined which leads directly in the time domain to the experimental values of this transfer function. It is similar to the methods used in seismic analysis for signal determination and makes use of the auto‐ and crosscorrelation functions of the measured field variations. Finally, methods of interpretation, based either on a visual or on an automatic comparison of these theoretical and experimental transfer functions, are proposed. For the case of automatic interpretation, complementary geologic data should be used where possible to take care of the lack of uniqueness of the solution.

scholarly journals Evaluation of Equivalent Circuit Diagrams and Transfer Functions for Modeling of Lithium-Ion Batteries

2013 ◽  
Vol 2 (1) ◽  
pp. 34-39 ◽  
Author(s):  
Ahmad Rahmoun ◽  
Helmuth Biechl ◽  
Argo Rosin
Keyword(s):  
Energy Storage ◽  
Lithium Ion Batteries ◽  
Equivalent Circuit ◽  
Transfer Functions ◽  
Lithium Ion ◽  
Life Time ◽  
Rational Functions ◽  
Model Parameters ◽  
Energy Storage Devices ◽  
The Time Domain

AbstractThe rapid developments in the field of electrochemistry, enabled lithium-ion batteries to achieve a very good position among all the other types of energy storage devices. Therefore they became an essential component in most of the modern portable and stationary energy storage applications, where the specific energy and the life time play an important role. In order to analyze and optimize lithium-ion batteries an accurate battery model for the dynamic behavior is required. At the beginning of this paper four different categories of electrical models for li-ion cells are presented. In the next step a comparison between equivalent circuit diagrams and fractional rational functions with the complex variable s is shown for lithium-ion battery modeling. It is described how to identify the parameters of the models in the time domain and also in frequency domain. The validation of the different models is made for high and low dynamic current profiles. In the first step the dependency of all model parameters on the temperature and on the battery age is neglected. These effects will be taken into account in the continuation of this work

A Class of Transfer Functions With Non-Negative Impulse Response

1991 ◽  
Vol 113 (2) ◽  
pp. 313-315 ◽  
Author(s):  
S. Jayasuriya ◽  
M. A. Franchek
Keyword(s):  
Transfer Function ◽  
Impulse Response ◽  
Closed Loop ◽  
Transfer Functions ◽  
Phase Transfer ◽  
Minimum Phase ◽  
Step Input ◽  
Input Disturbance ◽  
Negative Impulse ◽  
Poles And Zeros

Presented in this note is a class of stable, minimum phase transfer functions whose impulse response is non-negative. A simple sufficiency criterion based on the relative locations of the poles and zeros characterizes the class. When the transfer function is in a factored form the sign of its impulse response may either be obtained by inspection or is inconclusive. A need for identifying such transfer functions was recently established by Jayasuriya (1989) who showed that a controller designed on the basis of maximizing a step input disturbance will reject a persistent disturbance bounded by the size of the maximized step if and only if the closed-loop system’s impulse response is of one sign.

Transfer Function Reduction

1976 ◽  
Vol 190 (1) ◽  
pp. 643-651 ◽  
Author(s):  
R. Whalley
Keyword(s):  
Transfer Function ◽  
Series Expansion ◽  
Laurent Series ◽  
Hankel Matrix ◽  
Rational Functions ◽  
Reduced Form ◽  
Reduced Order Models ◽  
Minimum Phase ◽  
Reduced Order

SYNOPSIS A method of generating reduced order models from the Laurent series expansion of a transfer function is examined by means of the Hankel Matrix and its correspondence to the field of rational functions. The approach enables particularly simple results to be derived regarding the composition of the reduced form and the avoidance of non minimum phase characteristics therein.

scholarly journals Selective quantification of the cardiac sympathetic and parasympathetic nervous systems by multisignal analysis of cardiorespiratory variability

2008 ◽  
Vol 294 (1) ◽  
pp. H362-H371 ◽  
Author(s):  
Xiaoxiao Chen ◽  
Ramakrishna Mukkamala
Keyword(s):  
Nervous System ◽  
Transfer Function ◽  
Parasympathetic Nervous System ◽  
Transfer Functions ◽  
Low Frequency ◽  
Sympathetic Blockade ◽  
Nervous Systems ◽  
Autonomic Nervous ◽  
Arterial Blood ◽  
The Time Domain

Heart rate (HR) power spectral indexes are limited as measures of the cardiac autonomic nervous systems (CANS) in that they neither offer an effective marker of the β-sympathetic nervous system (SNS) due to its overlap with the parasympathetic nervous system (PNS) in the low-frequency (LF) band nor afford specific measures of the CANS due to input contributions to HR [e.g., arterial blood pressure (ABP) and instantaneous lung volume (ILV)]. We derived new PNS and SNS indexes by multisignal analysis of cardiorespiratory variability. The basic idea was to identify the autonomically mediated transfer functions relating fluctuations in ILV to HR (ILV→HR) and fluctuations in ABP to HR (ABP→HR) so as to eliminate the input contributions to HR and then separate each estimated transfer function in the time domain into PNS and SNS indexes using physiological knowledge. We evaluated these indexes with respect to selective pharmacological autonomic nervous blockade in 14 humans. Our results showed that the PNS index derived from the ABP→HR transfer function was correctly decreased after vagal and double (vagal + β-sympathetic) blockade ( P < 0.01) and did not change after β-sympathetic blockade, whereas the SNS index derived from the same transfer function was correctly reduced after β-sympathetic blockade in the standing posture and double blockade ( P < 0.05) and remained the same after vagal blockade. However, this SNS index did not significantly decrease after β-sympathetic blockade in the supine posture. Overall, these predictions were better than those provided by the traditional high-frequency (HF) power, LF-to-HF ratio, and normalized LF power of HR variability.

scholarly journals Frequency model of an essentially nonlinear steering drive with a digital microcontroller

2020 ◽  
Vol 23 (3) ◽  
pp. 52-62
Author(s):  
S. V. Gryzin
Keyword(s):  
Transfer Function ◽  
Frequency Band ◽  
Dynamic Characteristics ◽  
Phase System ◽  
Minimum Phase ◽  
Stabilization System ◽  
Bending Vibrations ◽  
Frequency Model ◽  
Simple Description ◽  
The Stability

When designing a stabilization system for highly maneuverable unmanned aerial vehicles (UAVs), one of the relevant tasks is to study the operation of the steering drive in the frequency band corresponding to the flexural vibrations of the UAV body. To ensure the stability of the UAV stabilization system, quite conflicting requirements may be imposed on the dynamic characteristics of the drive. In particular, the requirement for a sharp suppression of the amplitude-frequency characteristic at the frequency of UAV bending vibrations with minimal phase distortions in the control band of the longitudinal and lateral channels of the stabilization system can significantly complicate the task of researching the stability of the UAV motion control system. The article discusses an electric drive prototype with a digital microcontroller, designed for a highly maneuverable UAV. Adaptive algorithms of the digital controller make it possible to provide the necessary phase delays in the control frequency band and at the same time almost completely suppress the harmonic components of the control signals at the frequencies of the bending vibrations of the UAV body. The algorithms are essentially nonlinear in nature and are based on a change in the gain of the direct circuit of the drive depending on the frequency of the input signal, which greatly complicates the calculation of the transfer function of the steering drive for use in the frequency model of the stabilization system. Generally, the steering drive is described by a linear minimum-phase system, presented as a transfer function of one of the typical blocks of the first or second order, but for the specified steering drive with given dynamic characteristics, this approach is untenable. As a result of the study, a method for obtaining a frequency model of the steering drive is proposed, which is implemented as a non-minimum phase system, the main property of which is the independence of the amplitude-frequency and phase-frequency characteristics. In the process of research, the results obtained on the proposed model are compared with the results of experiments on a drive prototype and its complete non-linear time model. The main advantage of the proposed frequency model is a fairly simple description of the steering drive in the frequency domain, convenient for use as part of the frequency model of the stabilization system in the study of problems of ensuring the stability of UAV flight.

scholarly journals Python app for drawing Bode diagram asymptotes of transfer function for minimum and non-minimal phase systems

2021 ◽  
Author(s):  
Magno Enrique Mendoza Meza
Keyword(s):  
Transfer Function ◽  
Phase Curve ◽  
Phase System ◽  
Minimum Phase ◽  
Transport Delay ◽  
Phase Systems ◽  
Bode Diagram ◽  
Response Method ◽  
Quadratic Factor ◽  
Minimal Phase

The purpose of this article is to introduce an application to draw the asymptotes of Bode diagram module and phase from each constituent elementary factors of any transfer function for minimum and non-minimal phase systems without transport delay. The Bode diagram is the most used tool in the frequency response method. Python was used to program the application to perform the operations as well as the Qt5 Design for the simple graphical interface for the application and all this in the Linux operating system. The application purpose is to assist students in learning the concept and drawing of Bode diagram. For students the non-minimum phase system Bode diagram is more difficult to draw than a minimum phase system due to the presence of zeros and/or poles on right half of s-plane. The phase asymptotes of a quadratic factor was closest to the real phase curve around the corresponding undamped natural frequency and this can be observed in the example showed in this article. This example must be used as a help and not a simply to solve a problem.

scholarly journals Fitting of Generic Process Models by an Asymmetric Short Relay Feedback Experiment—The n-Shifting Method

2021 ◽  
Vol 11 (4) ◽  
pp. 1651
Author(s):  
José Sánchez Moreno ◽  
Sebastián Dormido Bencomo ◽  
José Manuel Díaz Martínez
Keyword(s):  
Time Delay ◽  
Transfer Function ◽  
Dynamic Systems ◽  
Transfer Functions ◽  
Process Models ◽  
Transfer Function Model ◽  
Minimum Phase ◽  
Relay Feedback ◽  
Function Model ◽  
Generic Process

This paper presents the generalization of the shifting method for relay feedback identification of dynamic systems of any order. The original shifting method enables the fitting of a maximum of five parameters of a transfer function model from the information obtained from a short relay test and without prior knowledge of the process to identify. The generalization, known as n-shifting, allows the estimation of the parameters of transfer functions of any order by applying one short relay test to the process to identify. Without loss of generality, the n-shifting approach is applied to fit an n-order plus time delay (n-OPTD) model but the approach can be also developed to identify models with other structures (non-minimum phase, unstable, integrators). Some examples of estimations are presented.

Comparison of transfer functions using estimated rational functions to detect winding mechanical faults in transformers

2012 ◽  
Vol 61 (1) ◽  
pp. 85-99 ◽  
Author(s):  
Mehdi Bigdeli ◽  
Mehdi Vakilian ◽  
Ebrahim Rahimpour
Keyword(s):  
Transfer Function ◽  
Evaluation Method ◽  
Transfer Functions ◽  
Rational Functions ◽  
Accurate Method ◽  
High Potential ◽  
Feasible Method ◽  
Transformer Winding ◽  
Intact Condition ◽  
Mechanical Faults

Comparison of transfer functions using estimated rational functions to detect winding mechanical faults in transformers As it is found in the related published literatures, the transfer function (TF) evaluation method is the most feasible method for detection of winding mechanical faults in transformers. Therefore, investigation of an accurate method for evaluation of the TFs is very important. This paper presents three new indices to compare the transformer TFs and consequently to detect the winding mechanical faults. These indices are based on estimated rational functions. To develop the method, the necessary measurements are carried out on a 1.3 MVA transformer winding, under intact condition, as well as different fault conditions (axial displacement of winding). The obtained results demonstrate the high potential of proposed method in comparison with two other well-known indices. Additionally, two important methods for describing TFs by rational functions are studied and compared in this paper.

scholarly journals Research on improving measurement accuracy of acoustic transfer function of underwater vehicle

2021 ◽  
Vol 336 ◽  
pp. 01006
Author(s):  
Jiangqiao Li ◽  
Li Jiang ◽  
Fujian Yu ◽  
Ye Zhang ◽  
Kun Gao
Keyword(s):  
Transfer Function ◽  
Impulse Response ◽  
Time Domain ◽  
Transfer Functions ◽  
Least Squares Method ◽  
Signal To Noise Ratio ◽  
Random Noise ◽  
Phase Compensation ◽  
Acoustic Transfer Function ◽  
The Time Domain

To address the problem that acoustic transfer functions with underwater platforms cannot be measured accurately, this paper presents a method based on phase compensation to improve the accuracy of acoustic transfer function measurements on underwater platforms. The time-domain impulse response signals with multiple cycles are first collected and intercepted, and then their phase differences are estimated using the least-squares method, and phase compensation is used to align the phases of all the signals, and then the impulse response signals are weighted and averaged over all the impulse response signals to cancel out the random noise. The water pool test proves that this method reduces the measurement random noise while obtaining a high-fidelity time domain transfer function, which effectively improves the signal-to-noise ratio of the measurement. The method adopts only one measurement signal, and without changing the measurement system, the random noise is cancelled out by the in-phase superposition of the multi-cycle impulse response signals to avoid the nonlinear distortion of the measurement results.

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