evans Evans root locus

## Syntax

                evans(H)
                evans(H, kmax)

## Arguments

H

  SISO linear system given by a transfer or a state space representation (see:syslin).

kmax

  real number: maximum gain desired for the plot.

## Description

Gives the Evans root locus for a SISO linear system in state-space or transfer form H(s) (syslin). This is the locus of the roots of `1+k*H(s)=1+k*N(s)/D(s)`, in the complex plane. For a selected sample of gains `k <= kmax` ,the imaginary part of the roots of `D(s)+k*N(s)` is plotted vs the real part.

To obtain the gain at a given point of the locus you can activate the datatips manager and click the desired point on the root locus.

## Examples

    H = syslin('c',352*poly(-5,'s')/poly([0,0,2000,200,25,1],'s','c'));
    clf();
    evans(H,100);
    sgrid()

    // Post-tuning graphical elements
    ch = gca().children;
    curves = ch(2).children;
    curves.thickness = 2;
    asymptotes = ch(ch.type=="Segs");
    asymptotes.segs_color = color("grey70");

    // Completing Evans plot:
    [Ki,s] = kpure(H) // Gains that give pure imaginary closed loop poles
    plot([real(s) real(s)],[imag(s) -imag(s)],'*r')

    [Kr,s] = krac2(H)

H = syslin('c',352*poly(-5,'s')/poly([0,0,2000,200,25,1],'s','c')); clf(); gcf().axes_size = [610 470]; evans(H,100); sgrid() // Post-tuning graphical elements ch = gca().children; curves = ch(2).children; curves.thickness = 2; asymptotes = ch(ch.type=="Segs"); asymptotes.segs_color = color("grey70"); // Completing Evans plot: [Ki,s] = kpure(H) // Gains that give pure imaginary closed loop poles plot([real(s) real(s)],[imag(s) -imag(s)],'*r') [Kr,s] = krac2(H)

## See also

- sgrid
- zgrid
- syslin
- kpure
- krac2
- datatips