A contribution to root-locus techniques for the analysis of transient responses

Author

Matkowsky, B.J. ; Zemanian, A.

Author_Institution

New York University, New York, NY, USA

Volume

7

Issue

3

fYear

1962

fDate

4/1/1962 12:00:00 AM

Firstpage

69

Lastpage

73

Abstract

A method involving root-locus techniques is developed by which one can analyze transient responses by ascertaining bounds on them. In particular, the following questions are considered: 1) Given a rational system function $W(s)$ , can another rational $M(s)$ (of simpler form) be constructed such that, for sufficiently large values of the constant multiplier $B$ of $M(s)$ , the corresponding transient responses satisfy the condition, $m(t) \\geq w(t)? 2)$ If so, can a range of values for $B$ be determined for which the same condition holds? Necessary conditions for an affirmative answer to question 1) are first developed and then sufficient conditions are obtained. Then, a general method using root-locus techniques is developed for answering question 2). Certain special cases are studied in detail and necessary and sufficient conditions are obtained, thus leading to the best possible bound for the given form of $M(s)$ . Finally, a number of examples are given.

Keywords

Board of Directors; Poles and zeros; Senior members; Sufficient conditions; Time domain analysis; Transfer functions; Transient analysis; Transient response;

fLanguage

English

Journal_Title

Automatic Control, IRE Transactions on

Publisher

ieee

ISSN

0096-199X

Type

jour

DOI

10.1109/TAC.1962.1105446

Filename

1105446