Example 10.6 Examine the stability of s³ + 25 +45³ +85² + 3s + 1 = 0 using Routh's criteria. Solution || در 4 3 S28 1 S³0 2.5 0 5² 8 -Routh's array failed. To remove the above difficulty, the following two methods can be used. Method 1: (i) Replace 0 by E (a small number) and complete the array with E. (ii) Examine the sign change by taking & → 0. The above example is solved below. 4 3 81 2.5 0 کی S2 SE 2 $² 8E-5 3 2.5 8E-5 E 8E-5 E 10 0

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Example 10.6 Examine the stability of s³ +254 + 45³ +85² + 3s +1=0 using Routh's criteria.
Solution
s³|1 4 3
S28 1
$³0 2.5 0
5² 8
←Routh's array failed.
To remove the above difficulty, the following two methods can be used.
Method 1:
3
(i) Replace 0 by E (a small number) and complete the array with E.
(ii) Examine the sign change by taking & → 0.
The above example is solved below.
$$
4 3
S2
$³
8E-5
33
***
E
2.5
***
8ɛ
E
8E-5
E
I
B
81
2.5 0
10
How did he get the final output?
It is possible to explain step by
step and with a clear line
Transcribed Image Text:Example 10.6 Examine the stability of s³ +254 + 45³ +85² + 3s +1=0 using Routh's criteria. Solution s³|1 4 3 S28 1 $³0 2.5 0 5² 8 ←Routh's array failed. To remove the above difficulty, the following two methods can be used. Method 1: 3 (i) Replace 0 by E (a small number) and complete the array with E. (ii) Examine the sign change by taking & → 0. The above example is solved below. $$ 4 3 S2 $³ 8E-5 33 *** E 2.5 *** 8ɛ E 8E-5 E I B 81 2.5 0 10 How did he get the final output? It is possible to explain step by step and with a clear line
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