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A system has a characteristic equation s3 + 2s2 + (K + 1)s + 6 = 0. The range of K for a stable system will be

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UPPSC AE Electrical 29 May 2022 Official Paper I
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  1. K > 2
  2. 0.5 < K < 1.5
  3. 1< K < 2
  4. K < 2

Answer (Detailed Solution Below)

Option 1 : K > 2
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Detailed Solution

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Concept:

The stability of the system is given by the Routh table.

s3 1 k + 1
s2 2 6
s1    
s0    

If there are no sign changes in the first column of the Routh table, then the system is said to be stable.

s3 1 k + 1
s2 2 6
s1  
s0 1  

For the system to be stable, 

6 - 2k - 2 > 0

k > 2

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Q1.The Routh Array is as below : \(\begin{array}{lllll} \mathrm{S}^{6} & 1 & 8 & 20 & 16 \\ \mathrm{S}^{5} & 2 & 12 & 16 & \\ \mathrm{S}^{4} & 2 & 12 & 16 & \\ \mathrm{S}^{3} & 0 & 0 & & \end{array}\) The row of zero of this array will be replaced by coefficients of 
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