Modern Control Engineering

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Section 5–5 / Transient-Response Analysis with MATLAB 193

Plot of Unit-Step Response Curves with (^) n = 1 and = 0, 0.2, 0.4, 0.6, 0.8, 1
Response
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0
t (sec)
012345678910
= 0= 0
0 0.2. 2
0 0.4. 4
0 0.6. 6
0 0.8. 8
1 1.0. 0
(a)
0
1
0.8
0.6
0.4
0.2
0 0
2
4
6
8
10
0.5
1
1.5
2
Response
t Sec
(b)
Three-Dimensional Plot of Unit-Step Response Curves
Figure 5–22
(a) Two-dimensional
plot of unit-step
response curves for
z=0, 0.2, 0.4, 0.6, 0.8,
and 1.0; (b) three-
dimensional plot of
unit-step response
curves.

Obtaining Rise Time, Peak Time, Maximum Overshoot, and Settling Time

with MATLAB. MATLAB can conveniently be used to obtain the rise time, peak time,

maximum overshoot, and settling time. Consider the system defined by

MATLAB Program 5–7 yields the rise time, peak time, maximum overshoot, and settling

time. A unit-step response curve for this system is given in Figure 5–23 to verify the

C(s)

R(s)

=

25

s^2 +6s+ 25