Computer-aided root -locus numerical technique

The existing technique of manual calculation and plotting of root-locus of a control system for stability studies is laborious and time consuming. computer-aided root-locus numerical technique based on simple fast mathematical iteration is developed to eliminate this rigour. Alternative iteration formulas were formed and tested for convergence. A pair of complementary formulas with highest rate of convergence was selected. The process of automatic determination of roots and plotting of root-locus were divided into steps which were analyzed, simplified and coded into computer programs. The geometric properties of the root-loci obtained with this technique are found to conform to those root described in the literature. Root-loci are drawn to scale instead of rough sketches.Keywords: control system, stability, transient response, root-locus, iteratio

Extending the Root-Locus Method to Fractional-Order Systems

The well-known root-locus method is developed for special subset of linear time-invariant systems known as fractional-order systems. Transfer functions of these systems are rational functions with polynomials of rational powers of the Laplace variable s. Such systems are defined on a Riemann surface because of their multivalued nature. A set of rules for plotting the root loci on the first Riemann sheet is presented. The important features of the classical root-locus method such as asymptotes, roots condition on the real axis, and breakaway points are extended to fractional case. It is also shown that the proposed method can assess the closed-loop stability of fractional-order systems in the presence of a varying gain in the loop. Three illustrative examples are presented to confirm the effectiveness of the proposed algorithm

Simple answers to usual questions about unusual forms of the Evans' root locus plot

After a first contact with Evans' root locus plots, in an introductory course about classical control theory, students usually pose questions for which the answers are not trivially found in the usual textbooks. Examples of such questions are: Can a branch intersect itself? Can two or more branches be coincident? Can a branch intersect its asymptote? In this paper devoted to helping teaching, numerical examples and an incremental property are used for answering some questions about unusual forms of root loci related to closed-loop control systems. In some cases, answering to these questions can be fundamental for making a correct sketch of a root locus.Após um primeiro contato com gráficos de Evans de lugar das raízes, num curso introdutório sobre teoria de controle clássico, os estudantes normalmente fazem perguntas para as quais as respostas não são encontradas trivialmente nos livros-textos usuais. Exemplos de tais questões são: Um ramo pode se auto-interseccionar? Dois ou mais ramos podem ser coincidentes? Um ramo pode interseccionar sua assíntota? Neste artigo com fins didáticos, usam-se exemplos numéricos e uma propriedade incremental para responder algumas questões sobre formas incomuns de lugar das raízes relacionadas a sistemas de controle em malha fechada. Em alguns casos, responder a essas questões pode ser fundamental para fazer um esboç o correto de um lugar das raízes

Imaginary-axis crossing points in root loci that depend polynomially on the gain

This technical note discusses the crossing with the stability boundary for the root loci that polynomially depend on the gain. A simple calculation method based on reflected polynomials is provided. The trend of the roots is also determined, which allows studying the gain margin as well as the minimum gain so that all the roots are within the stable region. Finally, these concepts are illustrated with two case studies

The steady state stability of synchronous machine as affected by direct and quadrature axis excitation regulators

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Hard hexagon partition function for complex fugacity

We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site computed by Baxter in the thermodynamic limit for positive real values of the fugacity is not sufficient to describe the analyticity in the full complex fugacity plane. We also obtain a new algebraic equation for the low density partition function per site.Comment: 49 pages, IoP styles files, lots of figures (png mostly) so using PDFLaTeX. Some minor changes added to version 2 in response to referee report

Crosscaps in Gepner Models and the Moduli space of T2 Orientifolds

We study T^2 orientifolds and their moduli space in detail. Geometrical insight into the involutive automorphisms of T^2 allows a straightforward derivation of the moduli space of orientifolded T^2s. Using c=3 Gepner models, we compare the explicit worldsheet sigma model of an orientifolded T^2 compactification with the CFT results. In doing so, we derive half-supersymmetry preserving crosscap coefficients for generic unoriented Gepner models using simple current techniques to construct the charges and tensions of Calabi-Yau orientifold planes. For T^2s we are able to identify the O-plane charge directly as the number of fixed points of the involution; this number plays an important role throughout our analysis. At several points we make connections with the mathematical literature on real elliptic curves. We conclude with a preliminary extension of these results to elliptically fibered K3s.Comment: LaTeX, 59 pages, 21 figures (uses axodraw

Control Engineering

Control means a speci?c action to reach the desired behavior of a system. In the control of industrial processes generally technological processes, are considered, but control is highly required to keep any physical, chemical, biological, communication, economic, or social process functioning in a desired manner

Classical phase transitions in a one-dimensional short-range spin model

Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost to insert domain walls in such systems is outweighed by entropy excess so that symmetry cannot be spontaneously broken. An archetypal way around the no-go theorems is to augment interaction energy by increasing the range of interaction. Here we introduce new ways around the no-go theorems by investigating entropy depletion instead. We implement this for the Potts model with invisible states.Because spins in such a state do not interact with their surroundings, they contribute to the entropy but not the interaction energy of the system. Reducing the number of invisible states to a negative value decreases the entropy by an amount sufficient to induce a positive-temperature classical phase transition. This approach is complementary to the long-range interaction mechanism. Alternatively, subjecting positive numbers of invisible states to imaginary or complex fields can trigger such a phase transition. We also discuss potential physical realisability of such systems.Comment: 29 pages, 11 figure