Modern Control Engineering

aa

Section 5–5 / Transient-Response Analysis with MATLAB 191

MATLAB Program 5–5

% ------------- Unit-step response -------------

num = [25];

den = [1 4 25];

t = 0:0.01:3;

[y,x,t] = step(num,den,t);

plot(t,y)

grid

title('Unit-Step Response of G(s)=25/(sˆ2+4s+25)')

xlabel('t Sec')

ylabel('Output')

1.4

1.2

1

0.8

0.6

0.4

0.2

0

0 0.5 1 1.5 2 2.5 3

t Sec

Unit-Step Response of G(s)= 25/(s^2 + 4 s+25)

Output

Figure 5–21
Unit-step response
curve.

Obtaining Three-Dimensional Plot of Unit-Step Response Curves with

MATLAB. MATLAB enables us to plot three-dimensional plots easily. The commands

to obtain three-dimensional plots are “mesh” and “surf.” The difference between the

“mesh” plot and “surf” plot is that in the former only the lines are drawn and in the lat-

ter the spaces between the lines are filled in by colors. In this book we use only the

“mesh” command.

EXAMPLE 5–4 Consider the closed-loop system defined by

(The undamped natural frequency vnis normalized to 1.) Plot unit-step response curves c(t)when

zassumes the following values:

z=0, 0.2, 0.4, 0.6. 0.8, 1.0

Also plot a three-dimensional plot.

C(s)

R(s)

=

1

s^2 + 2 zs+ 1