Get Analytic Curve Frequency-Sweeping Stability Tests for PDF

By Xu-Guang Li, Silviu-Iulian Niculescu, Arben Cela

ISBN-10: 3319157167

ISBN-13: 9783319157160

ISBN-10: 3319157175

ISBN-13: 9783319157177

In this short the authors determine a brand new frequency-sweeping framework to resolve the whole balance challenge for time-delay structures with commensurate delays. The textual content describes an analytic curve point of view which permits a deeper figuring out of spectral homes concentrating on the asymptotic habit of the attribute roots situated at the imaginary axis in addition to on homes invariant with appreciate to the hold up parameters. This asymptotic habit is proven to be comparable by means of one other novel idea, the twin Puiseux sequence which is helping make frequency-sweeping curves beneficial within the learn of basic time-delay structures. The comparability of Puiseux and twin Puiseux sequence results in 3 vital results:

  • an particular functionality of the variety of volatile roots simplifying research and layout of time-delay platforms in order that to a point they are handled as finite-dimensional systems;
  • categorization of all time-delay structures into 3 varieties based on their final balance homes; and
  • a uncomplicated frequency-sweeping criterion permitting asymptotic habit research of serious imaginary roots for all optimistic severe delays by means of observation.

Academic researchers and graduate scholars attracted to time-delay structures and practitioners operating in numerous fields – engineering, economics and the existence sciences regarding move of fabrics, power or info that are inherently non-instantaneous, will locate the implications awarded the following helpful in tackling the various complex difficulties posed by way of delays.

Show description

Read Online or Download Analytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays PDF

Similar system theory books

Read e-book online Architecture of Systems Problem Solving PDF

One criterion for classifying books is whether or not they're written for a unmarried pur­ pose or for a number of reasons. This ebook belongs to the class of multipurpose books, yet certainly one of its roles is predominant-it is basically a textbook. As such, it may be used for a spread ofcourses on the first-year graduate or upper-division undergraduate point.

Download e-book for kindle: Digital Repetitive Control under Varying Frequency by Germán A. Ramos

The tracking/rejection of periodic signs constitutes a large box of study within the regulate conception and functions zone. Repetitive keep watch over has confirmed to be an effective strategy to face this subject. besides the fact that, in a few functions the frequency of the reference/disturbance sign is time-varying or doubtful.

New PDF release: Virtual Reality Excursions with Programs in C

Digital truth tours: With courses in C makes the present functions accessiable to the computer person. The authors have built software program that allows readers to create their very own digital environments. The booklet is written at a degree applicable to researchers and academicians, in addition to to desktop fanatics.

Additional resources for Analytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays

Sample text

39]. Only a few attempts have been made to employ the frequency-sweeping curves to the asymptotic behavior analysis. For instance, in [64], the (single) frequency-sweeping curve is used for analyzing the asymptotic behavior of the critical imaginary roots. However, the scenario considered therein is specific and it is not easy to extend the approach to the general case. In the sequel, we give a motivating example to show that the frequency-sweeping curves of a time-delay system may possess some involved characteristics, even if the time-delay system under consideration has only simple critical imaginary roots.

2 discussed below. 2 The analysis of the asymptotic behavior of a critical imaginary root with respect to all the infinitely many positive critical delays. 2 (though has not been explicitly proposed in the literature) has been noticed and solved for some specific time-delay systems. If a critical imaginary root is simple for all the critical delays, it was proved in [97] together with [109] that the way the critical imaginary root moves as τ increases near each positive critical delay always has the same effect on NU (τ ).

In this way, we obtain a discrete set of points with nonnegative integral coordinates in the coordinate plane, called the Newton diagram of Φ(y, x). We draw a line through the point (0, ordx ) (this point belongs to the Newton diagram) coinciding with the ordinate axis and we rotate this line counterclockwise around the point (0, ordx ) until it touches other points from the Newton diagram. Among the touched points from the Newton diagram, we select the one with the greatest abscissa, say (M1 , N1 ).

Download PDF sample

Analytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays by Xu-Guang Li, Silviu-Iulian Niculescu, Arben Cela


by William
4.2

Rated 4.45 of 5 – based on 27 votes