# evans

Evans root locus

## Calling Sequence

    evans(H [,kmax])

## Arguments

H

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

kmax

  real (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()
        [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();evans(H,100);sgrid() [Ki,s]=kpure(H) plot([real(s) real(s)],[imag(s) -imag(s)],'*r') [Kr,s]=krac2(H)

## See Also

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