Analysis of
MODEL REDUCTION BY MOMENT MATCHING FOR LINER AND NONLINEAR SYSTEMS
Control department Measure and control major
Michael 宋扬
School number: U200914324
This paper is published by Journal of Control Theory and Practice.
The Control Theory and Practice is to publish papers that use experimental and theoretical (analytical and computer-aided) methods, approaches, and techniques to address and solve various mechanical, materials, and reliability problems encountered in the analysis, design, manufacturing, testing, and operation of electronic, and photonics components, devices, and systems. Liner and nonlinear systems analysis belong to this famous magazine, which is published in 2003. Systems integration, flexible electronics, materials with nano structures and in general small scale systems are areas of growing interest for the Journal. Originality, scientific merit and high engineering relevance are the major criteria for the acceptance of a submitted paper.
Its ISSN number is 1084-12. This journal is published quarterly and the paper is picked out from the volume of year 2003.
The aim of the paper is to introduce Modern nonlinear system analysis and design technology, and provides analysis tools of nonlinear system. Mainly includes the phase-plane, describing function analysis, feedback linearization, etc.
Abstract:
The linear theory directly determines the linear system control reliability. This research presented a quantitative analysis of the relationship between the nonlinear and the linear, and demonstrated that
the nonlinear measurement also plays an important role.[1]
In this paper’s abstract, the authors used about 150 words to give his general idea of their study.The model reduction problem for (single-input,single-output) linear and nonlinear systems is addressed using the notion of moment. The paper expounds the core direction the nonlinear system and linear system for matching.
The text explains the research content of theme, and to other related problems involved. As we know, in a paper, 200 words should be a sensible maximum for a relatively long paper or report, but never more than 500 words; and this abstract is also confined within one paragraph. As to the category of the abstract, in my opinion, it is a descriptive abstract, which gives you a simple linear and nonlinear system description. By using many graphics, the author mentions that data and the wide use of linear recordings is important in this field.
Just like the function of abstract , this paper precedes the whole paper and appears separately. So it will be more widely read than the document itself. It can be circulated much wider and farther then the paper itself. And this paper gives us a general impression of linear and nonlinear control system.
Keywords: Nonlinear Systems Analysis,single-input single-output
(SISO), Phase Plane Analysis, Concepts of Phase Plane Analysis , Constructing Phase Portraits, Determining Time from Phase
Portraits,Phase Plane Analysis of Linear Systems, Phase Plane Analysis of Nonlinear Systems, Existence of Limit Cycles, Sliding Control, Adaptive Control
As we all know, the use of the key words is to give the readers the key points of the paper. This paper’s key words successfully give us a overall view of all the length. By learning the key words, readers will be easy to learn the paper and theory.
Parts of Body
The paper is logically divided into two parts. In the first part , the
problem of model reduction by moment matching for linear systems is re-visited from a point of view that allows for the nonlinear theory to be developed in the second part (Section III).I. INTRODUCTION
II. MODEL REDUCTION BY MOMENT MATCHING FOR LINEAR SYSTEMS—REVISITED 1. Introduction
Using:Assumption2, Definition2 , Theorem7, Proof, Remark10, Example8.
The writer use these to make this strewn at random have send, structure clarity. Title to the use of more have administrative levels feeling, such as:Matching With Prescribed Relative Degree and Matching With Prescribed Zero Dynamic.
2. Discussion
“We complete this section with a property which is instrumental to derive a nonlinear enhancement of the notion of moment.” The writer give his proves .However, to the best of the author’s knowledge, they have not been presented in this form, see however a similar discussion in [1,Section 6.1], the paper [65], in which Sylvester equations are used to compute the Krylov subspaces arising in the construction of the
projectors which define the reduced order model, and the early results [66] (and references therein), in which the relation between least-square interpolation and moment matching (at and ) is discussed.
Acknowledgment
The authors would like to acknowledge the support of the Ministry of Science and Technology of the People’s Republic of China _PRC_ with Contract No. 2005AA260.”
In this acknowledge part, the author expressed his acknowledgement to the Ministry of Science and Technology of the People’s Republic of China.
Reference
As to the reference part, it is obviously in a APA style.
Firstly, the author used “References” as the title of this part, it is the main symbol of a paper’s reference part style.
Secondly, the author used a reference list at the end of article, in which
references are listed alphabetically.
The reference part of this article is not very formal. Normally, the reference list must be double-spaced, and it is arranged in alphabetical order. Entries should start with a paragraph indent. But the authors of this paper don’t arrange the order in a sequence by the alphabetical order of the references’ authors’ names.
We can see that the materials the author picked of this passage are almost come from the proceedings of several main international conferences. The first 11 references all come in this way. The 12th reference comes from a journal “Vacuum Physics”, followed by the name of the publisher, the location and the page number.
The 13th reference is a rare phenomenon, this reference comes from a passage written by the group “ Science ”. Reference list
[1]~[9] are all from the original paper. References
● Colvin, R, J .,(19).TUTOR :MATHS READING ● MICHAEL.LEE& JHON.(1992).RESEARCH ON LINEAR ●PICA,T., Holliday ,l.,(1999) Model Reduction by Moment Matching ● MCGEE,. D.(1977). Linear and Nonlinear Systems Research.
