Rational Function Model Research Articles

Two-Dimensional Exact Model Matching With Application to Repetitive Control

This paper concerns matching a system with time-delayed feedback to a rational transfer function model and its application to repetitive controller design. Necessary and sufficient conditions on the order of the plant, reference model, and controller are obtained for the existence of causal and stabilizing exact model matching solutions. The results are applied to robust repetitive controller design, in which a delayed feedback is introduced in the repetitive controller for rejecting periodic disturbances while simultaneously achieving input-output model matching. Furthermore, the 2-D model matching method also renders computationally efficient solutions. Also addressed are some subtle points on the selection of a low-pass filter required for robust stability. Finally, the approach is experimentally applied for turning noncircular shapes.

Dielectric measurements using a rational function model

A recently proposed rational function model for the aperture admittance of 50 ohm Teflon filled coaxial lines in contact with a homogeneous dielectric is experimentally validated. A calibration technique of the automatic network analyzer utilizing standard terminations and time domain gating is used. Uncertainties in the dielectric properties of reference liquids do not enter the calibration procedure. Experimental results for water and methanol are compared with estimated values. A model expression for the sensitivity of the probe is validated. The sensitivities of two coaxial line probes for the measurements made are determined. Results obtained using the new model are compared with those of other workers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Identification of parametric models for ultrasonic wave propagation in the presence of absorption and dispersion

Acoustic wave propagation in an absorptive and dispersive medium is usually described using models derived from a nearly local form of the Kramers-Kronig relationship, e.g., Q- and relaxation models. A modeling approach based on rational transfer function models for the generalized Hooke's law is presented. The assumptions and restrictions of models based on the nearly local absorption-dispersion relations and rational transfer function models are discussed. Using identification techniques, it is experimentally shown that the rational transfer function models explain the ultrasonic wave propagation in an absorptive-dispersive medium much better than the classical Q-models.

Use of frequency-derivative information in two-dimensional electromagnetic scattering problems

The use of frequency-derivation information incorporated with model-based parameter estimation (MBPE) to predict the scattering from conducting and dielectric two-dimensional tragets over a frequency band is summarised. Instead of computing a method of moment solution using a point-by-point approach, a rational function model is used to approximate the current as a function of frequency. The model coefficients are computed using frequency-derivative information at one frequency within the band to improve efficiency of conventional moment method approaches. Results show that the model based approach gives excellent results over a limited frequency band, and is much more efficient than the converntional point-by-point approach.

Phonon spectra and isothermal elastic constants forf-shell metals: A dynamical treatment

The two-body interaction is written as the sum of s-s,d-d overlap, d-d attractive, f-f overlap, and f-f attractive contributions. The free-electron part of the pair potential is obtained in second-order perturbation theory using a rational dielectric function and Heine-Abarenkov model pseudopotential. The overlap between d and f states of different ions and the effect of s-d and s-f hybridization are included in an approximate manner, as has been suggested by Wills and Harrison and by Harrison. The temperature dependence has been included through an asymptotic factor. The effective pair potential so defined is fast converging. It is then used to calculate the phonon spectra of rare-earth and actinide elemental metals in the fcc phase. The agreement between predicted and observed values is found to be reasonably good for all the metals. The binding energy and elastic constants of these metals are also calculated.

Using model-based parameter estimation to increase the efficiency of computing electromagnetic transfer functions

Two main ideas are introduced: (1) the use of model-based parameter estimation based on rational function approximations, which reduces the number of frequencies at which solutions or samples are required; (2) a sampling approach that uses frequency derivatives of the response and a novel analytical technique based on differentiating the moment method impedance equation, which provides derivative information in a time proportional to N/sup 2/ in contrast with the N/sup 3/ dependence in solving the original problem. Antenna input admittances are modeled using frequency samples and derivatives. The rational function model is shown to offer a large advantage over polynomial interpolation of a frequency response. Application of the frequency-derivative approach is demonstrated for problems having well-defined resonances such as a dipole antenna, and for more challenging problems having narrow resonances. >

A simple method for the estimation of rational distributed lag models

In an earlier paper we suggested a method for the identification and estimation of linear transfer function models. The method was claimed to be especially suitable for polynomial transfer function models. In this paper we shall consider the case of rational transfer function models (distributed lag models) in more detail. A simple method for the estimation of the parameters of multiple input rational distributed lag models is suggested. The method is based on simple linear identities that the parameters always fulfill. The asymptotic distribution of the proposed estimator is derived. Two illustrative examples of the use of the new method are given.

Use of a nonquadratic model in a conjugate-gradient method of optimization with inexact line searches

An algorithm for unconstrained minimization is developed which uses a rational function model, rather than a quadratic, as a basis for conjugate directions. The algorithm is similar to one previously proposed by the authors, but inexact linear searches are investigated in the present paper.

Estimation of rational transfer function models

In the estimation of rational transfer function models, it has been recommended that starting values of a transfer function component be assumed to be zero (or a constant) in the recursive computation of the transfer function response. It is demonstrated that such algorithms may lead to serious bias in the estimation of moving average parameters. This paper discusses several other algorithms that may rectify this problem. It is found that the starting-value-free (SVF) method is a more reliable algorithm. For computer programs using the traditional algorithm, i.e., the zero-starting-value (ZSV) method, the bias problem can be easily remedied using a short-cut method that omits appropriate number of values at the beginning of the residual series.

Plant rational transfer approximation from input-output data

A rational transfer function model of the plant is generally desirable in feedback system design, when only plan input and output data are available over finite, sometimes incomplete, time intervals. This is especially so in a recent exact design technique for highly uncertain time-varying and non-linear plants. Here, the plants are replaced rigorously by an equivalent linear time-invariant plant set. Existing numerical techniques were found inadequate, especially in the high-frequency range, which is important in the design of feedback systems with large plant uncertainty. A technique was developed with excellent results, even for noisy data, unstable and non-minimum phase plants and severely truncated time intervals. The transfer function is calculated directly, without derivation of the input, output signal transforms. The operations involve repeated integrations of the data. Numerous examples are included.

Parametric time domain analysis of the multiple input/scalar output problem: The source identification problem

A multiple input/scalar output stationary time series identification problem is considered from a parametric model time domain point of view. Particular emphasis is on the source identification problem. Closed form formula estimates of the individual source power contributions are expressed in terms of sample correlations that are obtained from the observed input and output time series and from parametric models fitted to that data. The estimates of the noise power contributions are asymptotically jointly normally distributed. The mean values and covariance matrix of those estimates yield confidence interval estimates of the individual and joint power contributions. The motivation for developing a rational polynomial transfer function or ARMA model of the multi-input scalar output plus additive noise situation is given. A two correlated input/single output version of this model is considered for a Monte Carlo simulation study. Parametric ARMA and approximate AR models are fitted to the simulated data. The asymptotic normality, and the distribution of the mean and covariances of the source power contribution computed from the ARMA and AR models are appraised. Several facets of the relative performance of windowed periodogram and AR model spectral analysis are examined for the multiple input/scalar output identification problem. The points that are emphasized are that conventional windowed periodogram spectral analysis is subjective, not particularly satisfactory for the sharp spectral peak situation that is commonly encountered in vibration data analysis and very likely not as good as “objective” Akaike criterion order AR modelled spectral analysis.

Normal hemoglobin-oxygen affinity.

Hemoglobin-xoygen affinity is known to vary in a number of disease states. The authors measured the continuous affinity of blood from healthy subjects and, using mathematical data reduction techniques, calculated coefficients for rational function models of average normal affinity, plus or minus 2 standard deviations, and 95 per cent confidence limits. Average normal P50 was 27.10 torr, with a two-standard-deviation range of 25.85 to 28.35; P50s of the 95 per cent confidence limits were 26.69 and 27.53 torr. The affinity usually accepted as standard lay between or very near to the 95% confidence limits of normal throughout its range. It is concluded that the range of normal affinity is narrow and that, for most practical purposes, standard affinity adequately represents normal affinity. There should be little difficulty in distinguishing from normal the shifts that occur in certain disease conditions.

Method for identifying linear dynamic systems

In this correspondence we consider parameter estimation from output observations of a rational pulse transfer function model excited by Gaussian input. The method proposed here is to compute only a few sample covariances and then estimate the parameter by a two-stage process. Algorithms are described and simulation results verify the efficacy of the method.