Four methods are proposed for estimating the dominant time constant and dead time of a given process from a knowledge of its moments, s-plane, frequency or transient response data. The methods are faster and simpler and, in terms of accuracy and reliabiltiy, are comparable to the time domain least squares procedure for parameter estimation. Applications of the methods are illustrated with the aid of a dispersion model. A comparison is also made with other known techniques to demonstrate the superiority of the suggested methods.

Estimation of time delay time constant parameters in time, frequency, and laplace domains

This report presents a survey of methods for the Distributed Parameter System Identification Problem. Fundamental concepts such as ‘ System Identification ’ and ‘ Distributed Parameter Systems ’ are briefly summarized in order to make precise what kind of problem will be considered here. The various identification methods are grouped into three disjoint classes, namely : ‘ Direct Method ’, ‘ Reduction to a Lumped Parameter System ’ and ‘ Reduction to an Algebraic Equation ’. Under this classification we give a general survey of the main approaches to the problem of identification in distributed systems

Distributed parameter system indentification A survey

Parameter estimation from tracer response measurements

This study compares residence time distributions in a helically coiled tube and a spatially chaotic system. The chaotic system consists of an array of bends, the plane of curvature of each one makes a 90° angle with that of its neighbors. Chaotic trajectories are obtained by the switch in the symmetry plane of the Dean vortices which appear in the bends. Mixing in the two configurations is compared by modeling the residence time distributions, experimentally determined by means of a two-measurement-point technique, using the axial dispersion plug-flow model. For Reynolds numbers greater than 2500, axial dispersion in the chaotic system is more than 20% less than in a helically coiled tube having the same number of bends. The decrease in axial dispersion is due to the generation of chaotic trajectories, which also contribute to an increase in transverse dispersion. Thus, the chaotic curved pipes system appears very promising in producing good mixing, especially in a laminar flow regime.

Residence time distribution in twisted pipe flows: helically coiled system and chaotic system

Response to perturbations of concentration and temperature have been used since the early part of the century [l, 21 to describe mathematically the transient behavior of process equipment. Beginning two decades ago [3, 41, evaluation of rate parameters, such as mass transfer coefficients, diffusivities, and chemical kinetic constants from response measurements, has developed into a useful tool in applied science. Kubin [5, 61 and Kucera [7] made a major contribution in pointing out that experimentally measurable moments of the response curves (peaks) to pulse inputs could be expressed explicitly in terms of the rate and equilibrium parameters used to describe the chemical and physical processes occurring in the equipment, For example, in a fixed-bed, continuously operating adsorber the moments of the response peak, in the effluent stream, to a pulse of concentration introduced in the feed could be expressed in terms of an axial dispersion rate coefficient, fluid-to-particle mass transfer coeffici...

Rate Parameters in Heterogeneous Catalysis by Pulse Techniques

A note on determination of the parameters of the longitudinal dispersion model from experimental data

An important problem in the mathematical modeling of dynamic systems is the testing of model applicability and the determination of the best model parameters through the minimization of the squared difference of the observed and predicted responses. This paper discusses the advantages of the transformation of the expression for the integral of the squared deviations ϕ to the frequency domain by the use of parseval's theorem. Two important advantages of the minimization of ϕ in the frequency domain are the ease with which the transform of the predicted response can be obtained and the algebraic nature of frequency domain operations. Other advantages are discussed and techniques for the numerical transformation and inversion of the observed and predicted responses are given.

William C. Clements

Papers

A note on determination of the parameters of the longitudinal dispersion model from experimental data

The frequency domain evaluation of mathematical models for dynamic systems

A distributed-parameter model for liquid extraction