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Analytic Solution To Inner-Outer & Spectral Factorization Problems And Its MATLAB Simulation

Posted on:2008-03-17Degree:MasterType:Thesis
Country:ChinaCandidate:L WangFull Text:PDF
GTID:2178360215476991Subject:Control theory and control engineering
Abstract/Summary:PDF Full Text Request
The inner-outer and spectral factorization problem is a very important subject in the realm of control theory with an extensive application range. It has been playing a pivotal role in many fields.In this paper, the three major application realms of inner-outer and spectral factorization are introduced, respectively,in Chapter 1, which are robust filter problem, linear quadratic control problem and H 2/ H∞optimal control problem, and how crucial functions it performs in these realms.Then, in Chapter 2, significant inner-outer factorization methods and spectral factorization methods that emerged historically on the international stage are presented, respectively, as well as the advantages and disadvantages of their own under certain circumstances. Taking them as the step stones, both the traits and fundamental conception of the novel algorithm for inner-outer and spectral factorization that is about to be presented are given. The fundamental conception is that the zero-pole distribution and the partial fraction expansion of its inverse matrix have a close relationship.In Chapter 3, basic concepts both in the field of control theory and in that of mathematics are provided for better and deeper understanding of the algorithm derivation, analysis and testification procedures that are presented later in this paper.The core of this paper-------a novel analytic algorithm for inner-outer and spectral factorization problems and its derivation and proof-seeking procedures are proposed in Chapter 4. Through complex analysis techniques, the algorithm is applied to systems with simple open right half plane zeros and those with multiple open right half plane zeros separately (Note: the former systems can be considered as the special cases of the latter ones as well), and analytic formulas are obtained as a result. The proposed method is very simple and efficient for computation in contrast to those numerical ones. In the entire computation procedures, all that needs efforts is to find the open right half plane zeros and their corresponding zero directions, and the rest is to follow the steps. To highlight this, numerical examples are presented for illustration.Another prominent merit of the proposed method lies in the easy combination with mathematics software package (for example: MATLAB). What's more, the resulting method bears even more efficiency and simplicity in computation procedures. In Chapter 5, this point is demonstrated not only by presenting the MATLAB program list that is rigorously based on the novel algorithm, but also by applying it to the numerical examples that appear in Chapter 4, for the sake of proving the MATLAB program correct and efficient in a intuitive and vivid way.Finally, in Chapter 6, the preceding content in this paper is summarized, and the subject waiting for further researches is looked out, which is to narrow the gap between the proposed inner-outer and spectral factorization method and the practical applications, making its value and functions fulfilled. For instance, when deriving optimal controllers taking advantage of IMC structure, totally analytic derivation procedures might be received by applying the novel algorithm into them. These are the focus of our major attentions and efforts in the near future.
Keywords/Search Tags:inner-outer and spectral factorization, zero, zero direction, Lyapunov equation
PDF Full Text Request
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