# 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)

### See also

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