Browsing by Author "Hoon Hong, Committee Member"

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Advanced Modulation, Control and Application for Multilevel Inverters
(2009-11-13) Liu, Yu; Alex Huang, Committee Chair; Hoon Hong, Committee Member; Subhashish Bhattacharya, Committee Member; Mesut Baran, Committee Member
LIU, YU. Advanced Modulation, Control and Application for Multilevel Inverters. (Under the direction of Alex Huang.) The purpose of the research has been to develop advanced modulation, control and application for multilevel inverters. A new series of modulations has been proposed to achieve minimal THD (Total Harmonic Distortion) for multilevel inverters. The first minimal THD modulation is a real-time algorithm used to calculate optimal values of switching angles for given DC voltages and a modulation index. The second one is an algorithm used to calculate optimal values of DC voltages and switching angles for a given modulation index. The third one used an algorithm to calculate optimal values of DC voltages, switching angles and a modulation index. Another new optimal combination modulation strategy has been proposed for the 10 MVA 5-level cascade multilevel inverter based STATCOM (Static Synchronous Compensator) system. In this thesis, I also proposed several advanced controls for cascade multilevel inverters to be used in STATCOM applications. A new feedback control strategy for balancing individual DC capacitor voltages is proposed. The key part of the control strategy is a compensator used to cancel the variable parts in the model. I have also proposed the solutions for enhancing ride-through capability of the STATCOM during faults conditions.
Approximate Factorization of Polynomials in Many Variables and Other Problems in Approximate Algebra via Singular Value Decomposition Methods
(2005-07-20) May, John P; Erich Kaltofen, Committee Chair; Hoon Hong, Committee Member; Agnes Szanto, Committee Member; Pierre Gramaud, Committee Member; Mark Giesbrecht, Committee Member
Aspects of the approximate problem of finding the factors of a polynomial in many variables are considered. The idea is that an polynomial may be the result of a computation where a reducible polynomial was expected but due to introduction of floating point coefficients or measurement errors the polynomial is irreducible. Introduction of such errors will nearly always cause polynomials to become irreducible. Thus, it is important to be able to decide whether the computed polynomial is near to a polynomial that factors (and hence should be treated as reducible). If this is the case, one would like to be able to find a closest polynomial that does indeed factor. Though this problem is computable there is no known polynomial time algorithm to find the nearest polynomial that factors. However, there are a number of methods that can be used to find a nearby polynomial that factors if the original polynomial was very close to being factorizable. This dissertation gives a method to find a lower bound on the distance to the nearest polynomial that factors. If this lower bound is quite large, one can conclude that the polynomial does not have approximate factors. As part of finding this bound, a linear condition for irreducibility of polynomials from bivariate polynomials is generalized to polynomials with many variables, and a general theory of low rank approximation to extend bounds results to many different polynomial norms is given. The singular value decomposition methods used to find the above lower bound can be used to create another method to find a nearby polynomial that factors. This method is studied, and is shown to be practical. Similar methods are also shown to work for approximate division and approximate greatest common divisor computation. The results on bounding the distance to the nearest polynomial that factors can be applied to functional decomposition of univariate polynomials. Results on functional decomposition from the 1970's together with approximate factorization results allow for a method to compute a lower bound on the distance to the nearest polynomial that has a non-trivial functional decomposition and a new algorithm to compute approximate decompositions.
Black Box Linear Algebra with the LinBox Library
(2002-07-02) Turner, William J.; Erich Kaltofen, Committee Chair; Carl D. Meyer, Committee Member; Ralph C. Smith, Committee Member; B. David Saunders, Committee Member; Hoon Hong, Committee Member
Black box algorithms for exact linear algebra view a matrix as a linear operator on a vector space, gathering information about the matrix only though matrix-vector products and not by directly accessing the matrix elements. Wiedemann's approach to black box linear algebra uses the fact that the minimal polynomial of a matrix generates the Krylov sequences of the matrix and their projections. By preconditioning the matrix, this approach can be used to solve a linear system, find the determinant of the matrix, or to find the matrix's rank. This dissertation discusses preconditioners based on Benes networks to localize the linear independence of a black box matrix and introduces a technique to use determinantal divisors to find preconditioners that ensure the cyclicity of nonzero eigenvalues. This technique, in turn, introduces a new determinant-preserving preconditioner for a dense integer matrix determinant algorithm based on the Wiedemann approach to black box linear algebra and relaxes a condition on the preconditioner for the Kaltofen-Saunders black box rank algorithm. The dissertation also investigates the minimal generating matrix polynomial of Coppersmith's block Wiedemann algorithm, how to compute it using Beckermann and Labahn's Fast Power Hermite-Pade Solver, and a block algorithm for computing the rank of a black box matrix. Finally, it discusses the design of the LinBox library for symbolic linear algebra.
Computation of the Exact and Approximate Radicals of Ideals: Techniques Based on Matrices of Traces, Moment Matrices and Bezoutians
(2008-07-07) Janovitz-Freireich, Itnuit; Agnes Szanto, Committee Chair; Hoon Hong, Committee Member; Erich Kaltofen, Committee Member; Michael Singer, Committee Member
Solving homogeneous linear differential equations of order 4 in terms of equations of smaller order.
(2002-08-20) Person, Axelle Claude; Gabriel Caloz, Committee Member; Michael Singer, Committee Chair; Felix Ulmer, Committee Co-Chair; Kailash Misra, Committee Member; Hoon Hong, Committee Member; Ernie Stitzinger, Committee Member
In this thesis we consider the problem of deciding if a fourth order linear differential equation can be solved in terms of solutions of lower order equations. There is a group theoretic criteria which can be turned into a decision procedure for solving this problem. Once the decision has been made that a certain type of equation can be solved in terms of lower order equations we also give methods for producing the lower order equations used for solving it.
Standardization and Integration of Body Scan Data for Use in the Apparel Industry - Body Scan Data Connectivity with Apparel CAD
(2005-04-21) Hwang, Su-Jeong; Cynthia L. Istook, Committee Chair; Hoon Hong, Committee Member; Traci May-Plumlee, Committee Member; Trevor Little, Committee Co-Chair
The purpose of this research was to provide a methodology for standardization and connectivity of body measurement data for apparel applications between body scanning systems and CAD systems to support further research of system integration in the apparel industry. This research has led to the development of standardization of the body measurement terminology and a data file format to connect the apparel CAD and 3D body scanning systems for the exchange of body measurement data for use in pattern design or alteration. A Metaphor Matching Process (MMP) was designed for developing a set of Identification Codes with syntax to match and identify body measurements. And, an exchangeable body measurement data in XML (eXtensible Markup Language) format, called MMP XML, was developed for achieving standardization of the body measurement terminology for bi-directional interpretation and transmission of data generated by 3D body scanning systems and 2D CAD pattern generation systems. Then, validation was accomplished by format data exchange testing with Gerber Technology, Inc. and [TC]². XML format data was gathered from an apparel CAD system and a body scan system. The XML format data was converted into a database system to demonstrate the connectivity between apparel pattern data and body scan data for standardization and integration. A logical IDEF1X model of data flow structure was developed for the body scan data connectivity with apparel CAD.