Modern Control Engineering

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Section 5–5 / Transient-Response Analysis with MATLAB 201

Obtaining Response to Arbitrary Input. To obtain the response to an arbitrary

input, the command lsimmay be used. The commands like

lsim(num,den,r,t)

lsim(A,B,C,D,u,t)

y = lsim(num,den,r,t)

y = lsim(A,B,C,D,u,t)

will generate the response to input time function roru. See the following two examples.

(Also, see Problems A–5–14throughA–5–16.)

EXAMPLE 5–6 Using the lsimcommand, obtain the unit-ramp response of the following system:

We may enter MATLAB Program 5–12 into the computer to obtain the unit-ramp response. The

resulting plot is shown in Figure 5–28.

C(s)

R(s)

=

2 s+ 1

s^2 +s+ 1

MATLAB Program 5–12

% ------- Ramp Response -------

num = [2 1];

den = [1 1 1];

t = 0:0.1:10;

r = t;

y = lsim(num,den,r,t);

plot(t,r,'-',t,y,'o')

grid

title('Unit-Ramp Response Obtained by Use of Command "lsim"')

xlabel('t Sec')

ylabel('Unit-Ramp Input and System Output')

text(6.3,4.6,'Unit-Ramp Input')

text(4.75,9.0,'Output')

Unit-Ramp Response Obtained by use of Command “Isim”

t Sec

012345678910

Un

it-Ramp Input and System Output

12

0

4

2

6

8

10

Output

Unit-Ramp Input

Figure 5–28
Unit-ramp response.