Modern Control Engineering

Example Problems and Solutions 363

The MATLAB program to plot the root loci of G(s)and the asymptotes is given in MATLAB

Program 6–17. Note that the numerator and denominator for G(s)are

num = [1]

den = [1 4 11 14 10]

For the numerator and denominator of the asymptotes we used

numa = [1]

dena = [1 4 6 4 1]

Figure 6–72 shows the plot of the root loci and asymptotes.

Since the characteristic equation for the system is

(s^2 + 2 s+ 2 )(s^2 + 2 s+ 5 )+K= 0

slimSqG(s)

MATLAB Program 6–17

% Root-locus plot

num = [1];

den = [1 4 11 14 10];

numa = [1];

dena = [1 4 6 4 1];

r = rlocus(num,den);

plot(r,'-')

hold

Current plot held

plot(r,'o')

rlocus(numa,dena);

v = [-6 4 -5 5]; axis(v); axis('square')

grid

title('Plot of Root Loci and Asymptotes')

− 6 − 4 − 2 0 2 4

0

1

5

3

2

4

− 2

− 1

− 5

− 4

− 3

Real Axis

Imag Axis

Plot of Root Loci and Asymptotes

Figure 6–72
Plot of root loci and
asymptotes.