Page 161 - MATLAB an introduction with applications
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146 ——— MATLAB: An Introduction with Applications
Solution:
>> %MATLAB Program
>>numg=40*[1 –5 7];
>> deng =poly ([–1 –2 –4 –5]);
>> G=tf (numg, deng);
>> T=feedback (G, 1)
Transfer function:
∧
40s 2 – 200s + 280
∧
∧
∧
s 4 + 12s 3 + 89s 2 – 122s + 320
>> step (T)
Computer response:
Figure E3.6 (a) shows the response.
Step Response
8
7
6
5
Amplitude 4
3
2
1
0
- –1
0 0.5 1 1.5 2 2.5 3 3.5
Time (sec)
Fig. E3.6(a)
Simulation shows over 30% overshoot and non minimum-phase behaviour. Hence, the second-order
approximation is not valid.
Example E3.7: Determine the accuracy of the second-order approximation using MATLAB to simulate the
unity feedback system shown in Fig. E3.7 where
12(s + 3s + 9)
2
() =
Gs
(s + 3s + 9)(s + 1)(s + 5)
2
F:\Final Book\Sanjay\IIIrd Printout\Dt. 10-03-09
