The reduction of complex transfer function models to simple models using the method of moments

Gibilaro, L.G.; Lees, F.P.

doi:10.1016/0009-2509(69)80011-4

Cited by 84 publications

(15 citation statements)

References 2 publications

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“…Other methods for accomplishing this same result have also been proposed and it will be helpful to place the minimum realization in proper perspective in relation to these other methods. In particular, the two most frequently used techniques are moment and frequency response analysis, (see Kropholler, 1970;Gibilaro and Lees, 1969;Buffham and Gibilaro, 1970).…”

Section: Comparison With Other Identification Methodsmentioning

confidence: 99%

Minimum realizations and system modeling. I. Fundamental theory and algorithms

Rossen

Lapidus

1972

AIChE Journal

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This review article surveys representative literature on minimum re&-zations and system modeling. This theory makes possible the construction of minimum size state-space models directly from experimental input/output data. Theoretical developments, numerical algorithms, and the connection with other methods of identification of linear systems are covered. Partial minimum realizations which are extensions of the concepts developed are also included. A numerical example illustrates many of the techniques. SCOPEOne of the most important and interesting problems of concern to the chemical engineer is the modeling or identification of real dynamical systems. Such modeling must be done in the face of significant nonlinearities and high dimensionality, both items being major components in chemical engineering systems. The results of such analysis can, of course, be used in a descriptive and/or predictive sense for optimizing and controlling the actual behavior of a system.There currently exists a relevant theory for linear, constant, dynamical systems which makes possible the construction of state-space models directly from input/output experimental data. This theory, termed realization theory, has generated a more fundamental understanding of the relationships between state-space, transfer function, and input/output descriptions of linear systems.Underlying many, if not all, of the important principles of realization theory are the dual concepts of controllability and observability. The importance of these concepts, first recognized by Kalman (1963) and Gilbert (1963), in the construction of state-space representations of minimum dimension and in the stability analysis of physical processes has been documented (Kalman, 1965a, b;Roberts, 1969). Techniques developed within the last few years have allowed the extension to the construction of linear, constant-coefficient, dynamical models of nonlinear systems. Although subject to many of the same limitations that restrict other linearization procedures, these techniques have proven to be quite useful in the modeling of many varieties of chemical engineering processes (Kallina, 1970;Rossen, 1972).In this paper, realization techniques which operate in the state or output space and yield linear models from input/output data will be developed. The methods will not only furnish a linear representation of a system but will also develop a minimal model in the sense of specifying the minimum number of system parameters, a minimal realization. The black box approach is used in these methods because only the innut/output data are used in the construction of the models.It is important to realize that such model construction methods can form the basis for a rational choice of model size for real linear systems. In the second paper in this series, new developments which can be auplied to nonlinear lumped and distributed parameter systems will be outlined. As such, the theory forms a viable algorithm for real chemical engineering systems. CONCLUSIONS AND SIGNIFICANCETo help the reader...

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Section: Comparison With Other Identification Methodsmentioning

confidence: 99%

Minimum realizations and system modeling. I. Fundamental theory and algorithms

Rossen

Lapidus

1972

AIChE Journal

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“…It is evident that (11) is the solution to (12). Now consider the identification problems for the four low-order models by using the moments of input and output of a stable LTI system.…”

Section: Momentsmentioning

confidence: 99%

“…Note that the parameters c 1 , c 2 , and c 3 are known constants because m g i can be calculated by means of the moments of input and output using (11).…”

Section: Proposition 2 For the Sodf Model Inmentioning

confidence: 99%

“…As an alternative open-loop identification method,Åström and Hägglund [10] suggested that FOTD and SOTD models can be obtained by using the method of moments. Gibilaro and Lees [11] reported that for a simple transfer function model defined by a time constant with n multiplicity and a time delay, three parameters of the model can be obtained explicitly by matching the first three moments of the impulse response of the complex and simple models. Moment matching is widely used to reduce the model order [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Robust identification of continuous-time low-order models using moments of a single rectangular pulse response

Kim

Jin

2013

Journal of Process Control

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“…The classical Pade approximant (in particular the N -liN) has also been used by Teasdale (1953) and others. Gibilaro and Lees (1969) followed the same objective by using moment approximants.…”

Section: Introductionmentioning

confidence: 99%

Squared amplitude frequency response and Chebyshev techniques applied to continued fraction transfer-function approximates

Calfe¹,

Healey²

1976

International Journal of Control

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A continued fraction {Peele] approximant is discussed. based on the' arnpfit.udosquared frequency response 1 of the original system. A study is also made of modificabions to the Pede approximant, due to Meehly. based on Chebyshev rather than Maclaurin series. By introducing the concept of ' shifting' allied to the amplitude. squared technique, the reduced model can be made an approximant over a specified range of frequencies, including band-pees systems.It is concluded that these techniques offer some interesting extensions to tho continued fraction mod'el reduction methods but fail to provide t.he all-purpose solution sought after; the Chebyshev techniques, already established in numerical analysis, are not so successful in model reduction.

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The reduction of complex transfer function models to simple models using the method of moments

Cited by 84 publications

References 2 publications

Minimum realizations and system modeling. I. Fundamental theory and algorithms

Minimum realizations and system modeling. I. Fundamental theory and algorithms

Robust identification of continuous-time low-order models using moments of a single rectangular pulse response

Squared amplitude frequency response and Chebyshev techniques applied to continued fraction transfer-function approximates

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