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)

See Also

• syslin linear system definition
• sgrid s-plane grid lines.
• zgrid zgrid plot
• kpure continuous SISO system limit feedback gain
• krac2 continuous SISO system limit feedback gain
• datatips Tool for placing and editing tips along the plotted curves.