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A closed loop system has the characteristic equation given by s3 + Ks2 + (K + 2)s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?
  • a)
    0 < K < 0.5
  • b)
    0.5 < K < 1
  • c)
    0 < K < 1
  • d)
    K > 1
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A closed loop system has the characteristic equation given by s3+ Ks2+...
Given that characteristic equation is,
s3 + Ks2 + (K + 2)s + 3 = 0
For system to be stable,
K > 0, K (K + 2) - 3 > 0
⇒ K > 0, K2 + 2K - 3 > 0
⇒ K > 0, (K + 3) (K - 1) > 0
⇒ K > 0, K > -3, K > 1 ⇒ K > 1
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Community Answer
A closed loop system has the characteristic equation given by s3+ Ks2+...
The system will be stable if all the roots of the characteristic equation have negative real parts.

Let's analyze the given characteristic equation:

s^3 + Ks^2 + (K+2)s + 3 = 0

For stability, all the roots of this equation should have negative real parts.

To determine the conditions for stability, we can use Routh-Hurwitz criterion.

The Routh-Hurwitz criterion states that a necessary and sufficient condition for a polynomial to have all its roots with negative real parts is that all the coefficients of the characteristic equation are positive.

In our case, the coefficients of the characteristic equation are 1, K, K+2, and 3.

Therefore, the condition for stability is:

1 > 0
K > 0
K+2 > 0
3 > 0

Simplifying the inequalities, we get:

K > 0
K > -2
3 > 0

From these conditions, we can see that the only condition that needs to be satisfied for stability is:

K > 0

So, the correct answer is:

a) 0 < k="" />
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A closed loop system has the characteristic equation given by s3+ Ks2+ (K + 2)s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?a)0 < K < 0.5b)0.5 < K < 1c)0 < K < 1d)K > 1Correct answer is option 'D'. Can you explain this answer?
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