On the selection of the eigenvalues to be retained in the reduced order models
TL;DR: In this article, a new model order selection criterion was proposed to overcome the deficiencies of the earlier methods for Davison's and Marshall's reduced order models, which are not applicable in many of the practical cases.
Abstract: This note points out that the model order selection criteria proposed earlier for Davison's and Marshall's reduced order models are not applicable in many of the practical cases. A new criterion is proposed to overcome the deficiencies of the earlier methods.
Citations
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TL;DR: Two model-reduction methods for discrete systems related to balanced realizations are described, a technique which utilizes the least controllable and observable subsystem in deriving a balanced discrete reduced-order model and a frequency-weighting technique for discrete- and continuous-time systems.
Abstract: Two model-reduction methods for discrete systems related to balanced realizations are described. The first is a technique which utilizes the least controllable and observable subsystem in deriving a balanced discrete reduced-order model. For this technique as L/sup infinity / norm bound on the reduction error is given. The second method is a frequency-weighting technique for discrete- and continuous-time systems where the input-normal or output-normal realizations are modified to include a simple frequency weighting. For this technique, L/sup infinity / norm bounds on the weighted reduction errors are obtained. >
143 citations
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TL;DR: An Linftybound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing for continuous-time systems for algorithmsbased on balancing.
Abstract: The design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction. In order for the design based on the order reduction to include a guarantee of stability, it is sufficient to have a bound on the model error. Previous work has provided such a bound for continuous-time systems for algorithms based on balancing. In this note an Linftybound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing.
135 citations
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TL;DR: The theory of model simplification is presented as a means of increasing model understanding, issues in the application to nonlinear models are considered, and software that facilitates model Simplification is discussed.
Abstract: The theory of model simplification is presented as a means of increasing model understanding. Simplification is based on a selection of the behavior modes defined by the linearized representation of the model and results in a smaller and more easily understood model. To allow understanding, the variables in the simplified model must be easy to interpret relative to those in the original model. This interpretation is complete in an exact simplification, a concept used to derive measures of the importance of different variables in generating selected behavior modes. These measures are used to select which variables to retain and which to omit in forming the simplified model. Issues in the application to nonlinear models are considered, and software that facilitates model simplification is discussed.
46 citations
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TL;DR: The denominator of a reduced-order model (ROM) is obtained by clustering the poles of the original high-order system using the Fuzzy C-Means clustering technique retaining some dominant poles to determine the denominator polynomial.
Abstract: In this paper, a mixed method of model order reduction for a continuous-time single-input single-output system is presented. The denominator of a reduced-order model (ROM) is obtained by clustering...
19 citations
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TL;DR: In this article, the input and output normal representations of stable systems are generalized for unstable systems, and the generalized normal representations are then modified to include a frequency weighting resulting in frequency weighted generalized normal representation.
Abstract: The input and output normal representations of stable systems are generalized for unstable systems These are then used to reduce the order of unstable discrete-time linear multivariable systems resulting in reduced order models with the same number of unstable poles as the full order model and with an a priori upper bound on the reduction error The generalized normal representations are then modified to include a frequency weighting resulting in frequency weighted generalized normal representations These are used to derive frequency weighted reduced order models for unstable discrete systems with the same number of unstable poles as the full order model and with an a priori upper bound on the frequency weighted reduction error
12 citations
References
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TL;DR: A method is proposed for reducing large matrices by constructing a matrix of lower order which has the same dominant eigenvalues and eigenvectors as the original system.
Abstract: Often it is possible to represent physical systems by a number of simultaneous linear differential equations with constant coefficients, \dot{x} = Ax + r but for many processes (e.g., chemical plants, nuclear reactors), the order of the matrix A may be quite large, say 50×50, 100×100, or even 500×500. It is difficult to work with these large matrices and a means of approximating the system matrix by one of lower order is needed. A method is proposed for reducing such matrices by constructing a matrix of lower order which has the same dominant eigenvalues and eigenvectors as the original system.
595 citations
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TL;DR: In this paper, a criterion for selecting the order of the reduced-order model of a given high-order system is presented, where the eigenvalues of the system are not restricted to be real only.
Abstract: A criterion is presented for selecting the order of the reduced-order model of a given high-order system. The eigenvalues of the system are not restricted to be real only.
32 citations
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TL;DR: In this paper, a criterion is defined to select the size of the low-order system after simplifying the given high-order plant by Davison and Chidambara's technique which gives satisfactory dynamic and correct steady-state responses.
Abstract: A criterion is wesented in this note to select the size of the low-order system after simplifying the given high-order plant by Davison and Chidambara's technique which gives satisfactory dynamic and correct steady-state responses.
19 citations
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TL;DR: In this article, a new criterion for selecting a low-order system to approximate a high-order model has been proposed, which is rigorously justified and is also applicable when eigenvalues of the system are nonreal.
Abstract: A technique for selecting a low-order system to approximate a high-order model has been suggested by Davison [2]. A critical component in this technique is the criterion used to select the most appropriate order and modes for the low-order approximation. Criteria have been discussed and analyzed by Mahapatra [5], [6], Rao, Lamba, and Rao [7], and Elrazaz and Sinha [3]. In this note we overcome deficiencies in the criteria that have been proposed and we introduce a new criterion which is rigorously justified. The criterion we suggest is also applicable when eigenvalues of the system are nonreal.
19 citations
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TL;DR: In this paper, a criterion is presented in this correspondence to select the low-order system after simplifying the given high-order systems by Davison's model simplification technique.
Abstract: A criterion is presented in this correspondence to select the low-order system after simplifying the given high-order system by Davison's model simplification technique. The criterion is judged by a numerical example.
16 citations
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