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Article
Publication date: 10 April 2007

Marissa Condon and Rossen Ivanov

The paper is aimed at the development of novel model reduction techniques for nonlinear systems.

Abstract

Purpose

The paper is aimed at the development of novel model reduction techniques for nonlinear systems.

Design/methodology/approach

The analysis is based on the bilinear and polynomial representation of nonlinear systems and the exact solution of the bilinear system in terms of Volterra series. Two sets of Krylov subspaces are identified which capture the most essential part of the input‐output behaviour of the system.

Findings

The paper proposes two novel model‐reduction strategies for nonlinear systems. The first involves the development, in a novel manner compared with previous approaches, of a reduced‐order model from a bilinear representation of the system, while the second involves reducing a polynomial approximation using Krylov subspaces derived from a related bilinear representation. Both techniques are shown to be effective through the evidence of a standard test example.

Research limitations/implications

The proposed methodology is applicable to so‐called weakly nonlinear systems, where both the bilinear and polynomial representations are valid.

Practical implications

The suggested methods lead to an improvement in the accuracy of nonlinear model reduction, which is of paramount importance for the efficient simulation of state‐of‐the‐art dynamical systems arising in all aspects of engineering.

Originality/value

The proposed novel approaches for model reduction are particularly beneficial for the design of controllers for nonlinear systems and for the design and analysis of radio‐frequency integrated circuits.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 26 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 1 June 2004

Marissa Condon and Rossen Ivanov

This paper presents the application in circuit simulation of a method for model reduction of nonlinear systems that has recently been developed for chemical systems. The…

Abstract

This paper presents the application in circuit simulation of a method for model reduction of nonlinear systems that has recently been developed for chemical systems. The technique is an extension of the well‐known balanced truncation method that has been applied extensively in the reduction of linear systems. The technique involves the formation of controllability and observability gramians either by simulated results or by measurement data. The empirical gramians are subsequently employed to determine a subspace of the full state‐space that contains the most significant dynamics of the system. A Galerkin projection is used to project the system onto the subspace to form a lower‐dimensional nonlinear model. The method is applied to a nonlinear resistor network which is a standard example for exemplifying the effectiveness of a nonlinear reduction strategy.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 23 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 1 March 2005

Marissa Condon and Rossen Ivanov

Nonlinear dynamical systems may, under certain conditions, be represented by a bilinear system. The paper is concerned with the construction of the controllability and…

Abstract

Purpose

Nonlinear dynamical systems may, under certain conditions, be represented by a bilinear system. The paper is concerned with the construction of the controllability and observability gramians for the corresponding bilinear system. Such gramians form the core of model reduction schemes involving balancing.

Design/methodology/approach

The paper examines certain properties of the bilinear system and identifies parameters that capture important information relating to the behaviour of the system.

Findings

Novel approaches for the determination of approximate constant gramians for use in balancing‐type model reduction techniques are presented. Numerical examples are given which indicate the efficacy of the proposed formulations.

Research limitations/implications

The systems under consideration are restricted to the so‐called weakly nonlinear systems, i.e. those without strong nonlinearities where the essential type of behaviour of the system is determined by its linear part.

Practical implications

The suggested methods lead to an improvement in the accuracy of model reduction. Model reduction is a vital aspect of modern system simulation.

Originality/value

The proposed novel approaches for model reduction are particularly beneficial for the design of controllers for nonlinear systems and for the design of radio‐frequency integrated circuits.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 24 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 1 March 1995

Lisa Johnson

What is it about academia anyway? We profess to hate it, spend endless amounts of time complaining about it, and yet we in academia will do practically anything to stay…

Abstract

What is it about academia anyway? We profess to hate it, spend endless amounts of time complaining about it, and yet we in academia will do practically anything to stay. The pay may be low, job security elusive, and in the end, it's not the glamorous work we envisioned it would be. Yet, it still holds fascination and interest for us. This is an article about American academic fiction. By academic fiction, I mean novels whosemain characters are professors, college students, and those individuals associated with academia. These works reveal many truths about the higher education experience not readily available elsewhere. We learn about ourselves and the university community in which we work.

Details

Reference Services Review, vol. 23 no. 3
Type: Research Article
ISSN: 0090-7324

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