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186 Chapter 5 / Transient and Steady-State Response Analyses
To: Y2
1.5
2
1
0.5
0
04812
Time (sec)
1.5
2
1
0.5
0
04812
To: Y1
0.4
0.6
0.2
−0.2
00
−0.4
0.4
0.6
0.2
−0.2
−0.4
04812 04812
From: U1 From: U2
Step Response
Amplitude
Figure 5–18
Unit-step response
curves.
MATLAB Program 5–1
A = [–1 –1;6.5 0];
B = [1 1;1 0];
C = [1 0;0 1];
D = [0 0;0 0];
step(A,B,C,D)
signalu 1 as the input, we assume that signal u 2 is zero, and vice versa. The four transfer functions
are
Assume that u 1 andu 2 are unit-step functions. The four individual step-response curves can then
be plotted by use of the command
step(A,B,C,D)
MATLAB Program 5–1 produces four such step-response curves. The curves are shown in Figure 5–18.
(Note that the time vector tis automatically determined, since the command does not include t.)
Y 2 (s)
U 2 (s)
=
6.5
s^2 +s+6.5
Y 2 (s)
U 1 (s)
=
s+7.5
s^2 +s+6.5
,
Y 1 (s)
U 2 (s)
=
s
s^2 +s+6.5
Y 1 (s)
U 1 (s)
=
s- 1
s^2 +s+6.5
,
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