evans

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

• sgrid — draws a s-plane grid
• zgrid — zgrid plot
• syslin — linear system definition
• 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