Comment on the stability of a control system whose characteristic equation is given b:
\({s^5} + 24{s^4} + 24{s^3} + 48{s^2} - 25s - 50 = 0\)
(AMIE Summer 2021)
Solution
|
s5 |
1 |
24 |
-25 |
|
s4 |
2 |
48 |
-50 |
|
s3 |
a = 0 |
b = 0 |
|
|
s2 |
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|
s1 |
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s0 |
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\(\begin{array}{l}a = \frac{{1x48 - 24x2}}{2}\\b = \frac{{1x( - 50) - ( - 25x2)}}{2}\end{array}\)
If all elements in a row are zero, then differentiate the coefficients of the above row.
\(\begin{array}{l}\frac{{d(2{s^4} + 48{s^2} - 50)}}{{ds}}\\ = 8{s^3} + 96s\end{array}\)
|
s5 |
1 |
24 |
-25 |
|
s4 |
2 |
48 |
-50 |
|
s3 |
a = 0 (8) |
b = 0 (96) |
|
|
s2 |
-24 |
50 |
|
|
s1 |
-112.66 |
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|
|
s0 |
-50 |
|
|
There is a sign change in the first column of the Routh table, hence the system is unstable.
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