Root-Locus

Root-Locus

技术

Introduction

We have demonstrated the importance of the poles and zeros of the closed-loop transfer

function of a linear control sustem on the dynamic performance of 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 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.

The basic properties and the systematic construction of the root loci are first due to

this material we show how to construct these loci by following some simple

plotting the root loci accurately,one can always use a root- locus program and a

digital exanple,the programs ROOTLOCI in the ACSP package,rlplot in the CSAD

toolbox,and ROOT LOCUS of the Program CC,just to name a few,can all be used to generate

the data and plots of the root loci given the loop transfer we were learning to be a

technician,all we have to do is get familiar with the application of one of these

r,it is far more important to learn the basics of the root loci,their

properties,as well as how to interpret the data provided by the root loci for analysis and

design an intelligent engineer, we must know if the data provided by the root

loci are indeed correct,and be able to derive vital information from the root material

is prepared with these objectives in mind.

The root-locus technique is not confined to the study of control general,the

method can be applied to study the behavior of roots of any algebraic equation with variable

general root- locus problem can be formulated by referring to the following

algebraic equation of the complex variable

For the present,we do not place any limitations on the relative magnitudes between n and

m.K in

Eq.

is a real constant that can vary from + to -.

The coefficients a0,a2,…

.,a, b1,b2,

…

.,b are considered t be real and fixed.

Root loci of multiple-variable parameters can be treated by varying one parameter at a

resultant loci are called the root replacing s with z in

Eqs.

through ,we

can construct the root loci of the characteristic equation of a linear discrete-data system in a

similar fashion.

For the purpose of identification,we define the following categorie of root loci based on

the sign of K:

(1)

(2)

(3)

(4)

RL:the portion of the root loci when K is positive;

CRL(complementary root loci):the portion of the root loci when K is negative.

RC(root contours):contour of roots when more than one parameter varies.

Root loci:refers to the total root loci for