Page 188 - MATLAB an introduction with applications

Control Systems ——— 173

The characteristic equation with K = 2.0535 is then
s(s + 3)(s + 5) + 2.0535 = 0
2
3
or s + 8s + 15s + 2.0535 = 0
(c) The closed-loop poles can be obtained by the following MATLAB program.
% MATLAB Program
p = [1 8 15 2.0535];
roots(p)
ans =
–5.1817
–2.6699
–0.1484
Hence, the closed-loop poles are located at
s = –5.1817, s =–2.6699, s = –4.1565.

(d) The unit-step response of the system for K = 2.0535 can be obtained from the following MATLAB
program. The resulting unit-step response curve is shown in Fig. E3.21(c).
% MATLAB Program
num = [0 0 0 2.0535];
den = [1 8 15 2.0535];
step(num,den)
grid
title(‘Unit-Step Response’)
xlabel(‘t Sec’)
ylabel(‘Output’).
Step Response
1
0.9
0.8

0.7

Amplitude 0.6
0.5
0.4
0.3
0.2

0.1
0
0 5 10 15 20 25 30 35 40
Time (sec)
Fig. E3.21 (c)

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