TAILIEUCHUNG - Ebook Automatic control systems (9th edition): Part 2

(BQ) Part 2 book "Automatic control systems" has contents: Root locus analysis, frequency-domain analysis, design of control systems, state variable analysis. | CHAPTER 1 Root Locus Analysis 7-1 INTRODUCTION In the preceding chapters, we have demonstrated the importance of the poles and zeros of the closed-loop transfer function of a linear control system on the dynamic performance of the system. The roots of the characteristic equation, which are the poles of the closed-loop transfer function, determine the absolute and the relative stability of linear SISO systems. Keep in mind that the transient properties of the system also depend on the zeros of the closed-loop transfer function. An important study in linear control systems is the investigation of the trajectories of the roots of the characteristic equation—or, simply, the root loci—when a certain system parameter varies. In Chapter 5, several examples already illustrated the usefulness of the root loci of the characteristic equation in the study of linear control systems. The basic properties and the systematic construction of the root loci are first due to W. R. Evans [1,3]. In general, root loci may be sketched by following some simple rules and properties. For plotting the root loci accurately, the MATLAB root-locus tool in the Control Systems Toolbox component of ACSYS can be used. See Chapter 9 for examples. As a design engineer, it may be sufficient for us to learn how to use these computer tools to generate the root loci for design purposes. However, it is important to learn the basics of the root loci and their properties, as well as how to interpret the data provided by the root loci for analysis and design puiposes. The material in this text is prepared with these objectives in mind; details on the properties and construction of the root loci are presented in Appendix E. The root-locus technique is not confined only to the study of control systems. In general, the method can be applied to study the behavior of roots of any algebraic equation with one or more variable parameters. The general root-locus problem can be formulated by referring to the .

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