Transfer Function Representation Research Articles

Measurement of propagation constant in waveguides with wideband coherent terahertz spectroscopy

A quasi-optical technique for characterizing micromachined waveguides is demonstrated with wideband time-resolved terahertz spectroscopy. A transfer-function representation is adopted for the description of the relation between the signals in the input and output port of the waveguides. The time-domain responses were discretized, and the waveguide transfer function was obtained through a parametric approach in the z domain after describing the system with an autoregressive with exogenous input model. The a priori assumption of the number of modes propagating in the structure was inferred from comparisons of the theoretical with the measured characteristic impedance as well as with parsimony arguments. Measurements for a precision WR-8 waveguide-adjustable short as well as for G-band reduced-height micromachined waveguides are presented.

DIGITAL PID DESIGN FOR MAXIMALLY DEADBEAT AND TIME-DELAY TOLERANCE

This paper presents a new approach to design a digital PID controller for a given LTI plant. By using the Tchebyshev representation of a discrete time transfer function and some new results on root counting with respect to the unit circle, we show how the digital PID stabilizing gains can be directly obtained by solving sets of linear equations. This solution is attractive because it determines the entire set of stabilizing PID gains constructively if exists, Using this characterization of the stabilizing set, we present solutions to two design problems: a) Maximally dead beat design where we determine the smallest circle within the unit circle wherein the closed loop characteristic roots may be placed by PID control, b) Maximal delay tolerance-where we determine the maximal loop delay that can be tolerated under PID control.

Boundary conditions for column flotation —A study by transfer function representation of an axial diffusion model

The boundary conditions for an axial diffusion model were overviewed and then modified concerning the pulp layer boundaries in a flotation column. It has been confirmed through the transfer function representation that the four general boundary conditions for an axial diffusion model correspond to the particular cases of Wehner and Wilhelm's, which considers not only the reaction section itself but also those of its top and bottom sides. Various mathematical models have been proposed for the pulp layer in a flotation column and the most popular one may be an axial diffusion with first order reaction model of one stage. They are, however, unable to estimate the behaviors of free particles which have not attached to bubbles at the pulp-froth interface. In this study, therefore, the authors, represented the transportation of free particles in the pulp layer of a flotation column by the two-stage axial diffusion with first order reaction model. The Wehner and Wilhelm's, as well as Danckwerts' boundary conditions have been partly modified and then applied to the feed point, the pulp-froth interface and the tailing discharge point of the flotation column. The proposed models and their boundary conditions made it possible to estimate the behaviors of free particles at the pulp-froth interface.

Including the Effects of Flexible Bearing Supports in Rotating Machinery

Unbalance response and stability analyses of a flexible rotor on three lobe journal bearings on flexible supports are presented. The influence of the support structure was included in the analyses using polynomial transfer functions. These transfer functions were extracted from measured dynamic compliance data of the support structure, measured at the bearing locations. Numerical predictions using polynomial transfer functions and single mass supports are compared to the experimental data. Predictions using the transfer function representation of the support structure show a clear improvement over the predictions using single mass supports without over-complicating the problem. The predicted critical speeds are within 2.9% of the measured critical speeds. The predicted stability threshold agrees with the measured stability threshold within 1%. The effects of cross talk between supports and cross coupling between horizontal and vertical directions are investigated. The cross talk between supports was found to have a strong influence in the results while the influence of cross coupling between the vertical and horizontal directions is negligible.

Can aftershock studies predict site amplification factors? Northridge, CA, earthquake of 17 January 1994

Three studies of site amplification factors, based on the recorded aftershocks, and one study based on strong motion data, are compared one with another and with the observed distribution of damage from the Northridge, CA, earthquake of 17 January 1994 ( M L=6.4). In the epicentral area, when the peak ground velocities are larger than v m ≈15 cm/s, nonlinear response of soil begins to distort the amplification factors determined from small amplitude (linear) wave motion. Moving into the area of near-field and strong ground motion (v m >30 cm/s), the site response becomes progressively more affected by the nonlinear soil response. Based on the published results, it is concluded that site amplification factors determined from small amplitude waves (aftershocks, small earthquakes, coda waves) and their transfer-function representation may be useful for small and distant earthquake motions, where soils and structures respond to earthquake waves in a linear manner. However in San Fernando Valley, during the Northridge earthquake, the observed distribution of damage did not correlate with site amplification determined from spectra of recorded weak motions. Mapping geographical distribution of site amplification using other than very strong motion data, therefore appears to be of little use for seismic hazard analyses.

Stability and performance analysis in an uncertain world

Classical control systems design uses fixed plant transfer functions, yet engineers have known for many years that there is often considerable uncertainty regarding the parameters used in a transfer function representation. A major breakthrough on systems with uncertain parameters was achieved by the Russian mathematician V.L. Kharitonov (1979), who extended the Routh stability criterion to interval polynomials, that is where the polynomial coefficients may be assumed to lie within a specific range rather than being fixed. Recently these ideas have been extended to frequency response representations, such as Nyquist and Bode plots, for interval plant transfer functions. This paper reviews some of these results, which can be easily understood and used by practising engineers.

カラム浮選における境界条件について 一軸拡散モデルの伝達関数表示による考察

Abstract The boundary conditions for an axial diffusion model were overviewed and then modified concerning the pulp layer boundaries in a flotation column. It has been confirmed through the transfer function representation that the four general boundary conditions for an axial diffusion model correspond to the particular cases of Wehner and Wilhelm's, which considers not only the reaction section itself but also those of its top and bottom sides. Various mathematical models have been proposed for the pulp layer in a flotation column and the most popular one may be an axial diffusion with first order reaction model of one stage. They are, however, unable to estimate the behaviors of free particles which have not attached to bubbles at the pulp-froth interface. In this study, therefore, the authors, represented the transportation of free particles in the pulp layer of a flotation column by the two-stage axial diffusion with first order reaction model. The Wehner and Wilhelm's, as well as Danckwerts' boundary conditions have been partly modified and then applied to the feed point, the pulp-froth interface and the tailing discharge point of the flotation column. The proposed models and their boundary conditions made it possible to estimate the behaviors of free particles at the pulp-froth interface.

資源処理プロセスの伝達関数表示とその応用

Transfer function representations of various plants still have significant positions in design and analysis of control systems, because new frequency-domain control techniques, such as H∞ control theory, are now easily available. This paper describes applications of transfer function representations of resources processing plants. The authors at first have showed examples of processes when the idea proposed in a paper of Åström et al. (1992) is applied to resources processing plants.The authors have, subsequently, calculated 4 transfer functions of one-dimensional reactive-diffusive models, which are typically found in resources processing plants, under 4 types of boundary conditions. Then, behaviors under Bo → ∞, 0 have been established based on the transfer functions calculated above. The transfer function representation of a free-flow flotation process proposed by Niemi (1966) seems to be lack of generality, because of the boundary conditions adopted. The authors have showed a new transfer function representation of the flotation process, under appropriate boundary conditions. The new transfer function model has been investigated to validate the idea of Åström et al. (1992), which attempts to apply Ziegler Nichols's PID tuning method through analyzing dimensionless numbers. The main results are summarized as follows : · Achievable performance of the PID control system is not affected by normalized reaction constant K, but by Bodenstein number Bo. · Relation between normalized process gain κ and normalized deadtime θ can empirically be described by an equation κ = 1 + 0.46 / θ 1.67. Relation κ = 2 (11 θ + 13) / (37 θ - 4) for finite-dimensional systems also gives rather a good approximation. · Within recommended region 0.1< θ < 0.6 of Ziegler-Nichols's ultimate gain method, crude approximations κ λ ≈ 1.4 and τ ≈ 1 hold.The latter half of the second term and the whole of the third term mentioned above show the validity of the idea of Åström et al. (1992), while the reactive-diffusive models are infinite-dimensional. This suggests usefulness of dimensionless numbers.Relations between other tuning methods and dimensionless numbers, applications to back-mixing models which are also familiar models in resources processing plants are the remaining themes to be studied.

Selection of Best Orthonormal Rational Basis

This contribution deals with the problem of structure determination for generalized orthonormal basis models used in system identification. The model structure is parameterized by a prespecified set of poles representing a finite-dimensional subspace of ${\cal H}^2$. Given this structure and experimental data, a model can be estimated using linear regression techniques. Since the variance of the estimated model increases with the number of estimated parameters, one objective is to find coordinates, or a basis, for the finite-dimensional subspace giving as compact or parsimonious a system representation as possible. In this paper, a best basis algorithm and a coefficient decomposition scheme are derived for the generalized orthonormal rational bases. Combined with linear regression and thresholding this leads to compact transfer function representations. The methods are demonstrated with several examples.

New analysis and design tool for achieving low variability process designs

A new process analysis and design tool was developed. The analysis tool consists of a systematic algorithm for analyzing a block diagram representation of a process flowsheet and identifying different paths between a given input and output variable. Transfer function representations of different paths are calculated to determine the contribution of each path to the overall attenuation characteristics of the process. To improve these attenuation characteristics, the paths that contribute the most to the overall variability must be identified and addressed. The design tool consists of a set of guidelines that the engineer can use to develop alternate process designs or control strategies to eliminate these identified paths, reduce their contribution to overall variability, or negate their effects by adding new paths. Although the ingenuity of the design engineer is critical, this tool provides the engineer with a means to identify problems in a process design, to help develop design alternatives, and a quantitative basis for comparing and evaluating these alternatives. This new tool was applied to a standard design for a stock preparation system in a pulp and paper mill.

Representation of sound localizatin transfer function and psychoacoustical evaluation.

A method is proposed for determining representatives of the sound localization transfer function (SLTF) aiming at a compromise between feasibility and localization accuracy. This method is based on principal components analysis (PCA). The magnitudes of SLTF measured at both ears of 56 subjects for 24 targets were modelled by linear combination of six principal components (PC). For each target and ear, the representative was determined to be the SLTF whose weights of PC contributing to the magnitude best approximated the average over subjects. The effectiveness of the representatives was evaluated both statistically and psychoacoustically. The statistical analysis indicates that the individual distribution of the weights of PC is assumed to be a six-dimensional normal distribution that is densest around the average. The discrepancy of the representatives from the average is within 1.5 percent of the individual accumulation. The psychoacoustical evaluation for 28 of the subjects indicates that the increase in the front/back confusion rate in the use of the representatives is significant for frontal targets, but not for other targets. The lateral judgement is robust against SLTFs for all targets tested. However, considerable individual dispersion of the front/back confusion rate hindered from determining the allowance of the discrepancy between individual SLTFs and the representatives for acceptable localization accuracy.

Unitary Colligations, Reproducing Kernel Hilbert Spaces, and Nevanlinna–Pick Interpolation in Several Variables

Recently J. Agler studied the class Sdof scalar-valued, analytic functions ofdcomplex variablesffor whichf(T1, …, Td) has norm at most 1 for any collection ofdcommuting contractions (T1, …, Td) on a Hilbert space H. Among other results he obtained a characterization of such functions in terms of a positivity property and in terms of a representation as the transfer function of a certain type of d-variable linear system, as well as a Nevanlinna–Pick interpolation theorem for this class of functions. In this note we examine the system theory aspects and uniqueness of the transfer function representation, and give a simpler proof of the Nevanlinna–Pick interpolation theorem for the class Sdand obtain ad-variable version of the Toeplitz corona theorem. By using ideas of Arov and Grossman introduced for 1-variable problems, as a bonus we obtain a collection of linear fractional maps which parametrize the set of all Sdsolutions of an interpolation problem.

Simple method for determining slowly varying refractive-index profiles from in situ spectrophotometric measurements

Reliable control of the deposition process of optical films and coatings frequently requires monitoring the refractive-index profile throughout the layer. In the present research a simple in situ approach is proposed that uses a WKBJ matrix representation of the optical transfer function of a single thin film on a substrate. Mathematical expressions are developed that represent the minima and the maxima envelopes of the curves transmittance versus time and reflectance versus time. The refractive index and the extinction coefficient depth profiles of different films are calculated from simulated spectra as well as from experimental data obtained during the PECVD (plasma-enhanced chemical vapor deposition) of silicon-compound films. Variation in the deposition rate with time is also evaluated from the position of the spectra extrema as a function of time. The physical and mathematical limitations of the method are discussed.

A simple predictive controller for use on large scale arrays of parabolic trough collectors

Efficient operation of a distributed collector field requires effective regulation of the outlet temperature. Control schemes utilising PI based controllers, whether adaptive or fixed parameter, have been shown to be unsuitable for this application. The reason for this is that such collector fields possess resonance dynamics at a low frequency which tend to restrict the bandwidth of such controllers. In this article a predictive controller is proposed whose purpose is to effectively counter such dynamics. This control technique is based upon a simple transfer function representation of the resonance dynamics which can be tuned using easily obtained experimental data and is computationally efficient. When applied to a validated non-linear computer model of the collector field the controller is seen to exhibit a fast well damped control response superior to that achievable using PI control.

Frequency response of sampled-data systems

This paper introduces the concept of frequency response for sampled-data systems and explores some basic properties as well as its computational procedures. It is shown that 1) by making use of the lifting technique, the notion of frequency response can be naturally introduced to sampled-data systems in spite of their time-varying characteristics, 2) it represents a frequency domain steady-state behaviour, and 3) it is also closely related to the original transfer function representation via an integral formula. It is shown that the computation of the frequency response can be reduced to a finite-dimensional eigenvalue problem, and some examples are presented to illustrate the results.

Optimal capacitance assignment of switched-capacitor biquads

An algorithm is presented for the optimal capacitance assignment of conventional switched-capacitor biquads. It maximizes the dynamic range and minimizes the total capacitance simultaneously, with results presented in analytical forms. This is made possible by the development of a canonical representation of second-order transfer functions in the z-domain, which gives simple relations among three sets of parameters: (1) the pole-and zero-frequencies, and pole- and zero-Q's of the s-domain prototype; (2) the key parameters of the bilinear-transformed z-domain transfer function; and (3) the capacitance ratios of the final switched-capacitor realization. Analytical results are derived and compared with those from using existing assignment techniques. This shows a reduction of 12% in total capacitance for some biquads. An extension of the algorithm to very large time-constant biquads is also discussed; the improvement is even larger for these circuits.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Transfer-Function Representation for Flux Responses of a Controlled Metabolic Pathway to Influx and Efllux Rates

The flux response of a metabolic pathway undergoing the end-product feedback inhibition to changes around a steady state in influx rate of the substrate and efflux rate of the end product is validly approximated with respective transfer functions of the constituent enzymatic reactions. The transfer function for input-output relation between reaction velocity and the flux rates may be expressed as first-order system for a Michaelis-Menten-type reaction, and as second-order system for an allosteric reaction of Monod-Wyman-Changeux dimeric model, respectively, in contrast to higher-order systems derived from linearization of the rate equation of the pathway.

構造物の固有振動特性に及ぼす動的相互作用効果に関する研究

In order to grasp the dynamic characteristics of structure considering soil structure interaction, the eigenproperty of structure having identical stiffenss and mass distribution is evaluated. As evaluation methods, two approaches are introduced. The first is based on explicitly representing the determinant of dynamic stiffness matrix by the polynomial expression using the property of the cofactor expansion of tridiagonal matrix having common elements. The another method is based on explicit representation of transfer function using the transfer matrix method which is powerful for periodic structures. The dependency of the eigenfrequencies and damping ratios on the analysis model, story and size of structure and stiffness of soil are studied. First, the effect of soil-structure interaction on the eigenfrequencies for undamped models are studied. Secondly, the effect of damping on the eigenproperty is studied through the complex eigenvalues and transfer functions and it is clarified that the soil-structure interaction gives a large influences on the dynamic property of structures, which points out the limitage of conventional real eigenanalysis and the importance of proper selection of damping model.

Phantom zeros in curve-fitted frequency response functions

For complete models, there is an exact equivalence between pole/zero and pole/residue representations of transfer functions, but in practice truncation is almost inevitably necessary, in which case the equivalence breaks down. This paper discusses how extra zeros are typically added into a truncated model to compensate for the effects of out-of-band modes, and illustrates their effects. Because compensation is primarily required on the magnitude of the FRF, these extra zeros, named 'phantom zeros', are typically arranged in pairs around the frequency axis, so that half of them have maximum phase properties even when the physical model is minimum phase. The number of phantom zeros required depends on the separation of the excitation and response points. For a driving point measurement, where there are virtually as many zeros as poles, the effects of truncation are very small, whereas at the other extreme, with no actual zeros, a correspondingly greater number of phantom zeros is required to correct the slope of the magnitude of the FRF.

The Bilinear Transform in Control System Simulation

Digital computer simulation of a continuous control system furnishes the designer with a convenient means of assessing the effects of control strategies and can also provide an independent check on the transient and frequency responses obtained from a theoretical analysis. Although commercial packages are widely available, it is instructive to build an initial simulation using a discrete transfer function representation of the dynamic elements. The bilinear transform can be used to derive a suitable transfer function, with the necessary algebraic manipulations being performed by the computer. The method produces an inherently flexible simulation and is equally applicable to linear and nonlinear systems.