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The closed loop transfer function of a system is
The system is said to be
  • a)
    Unstable with a pair of complex conjugate poles on imaginary axis
  • b)
    Unstable with two pairs of complex conjugate poles on imaginary axis
  • c)
    Marginal stable with all poles on imaginary axis
  • d)
    Marginal stable with a pair of complex conjugate poles on imaginary axis
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The closed loop transfer function of a system isThe system is said to...
Given
Routh Hurwitz array
Hence Auxiliary equation -2s4 - 6s2 -4 = 0
For non-zero row we must differentiate above equation with respect to s.
⇒ -8s3 - 12s = 0
⇒ -4s3 - 6s = 0
To find locations of dominant poles :
Auxiliary equation : A(s) = -2s4 - 6s2 - 4 = 0
Finding roots of A(s) to know locations of dominant poles :
s4 + 3s2 +2 = 0
Let s2 = x
x = -1, x = -2
Since, the auxiliary equation is of 4th order.
Hence, two pairs of complex conjugate poles lie on imaginary axis.
Also number of sign changed in the first column of Routh Hurwitz array = 1
Hence, the given system is unstable with two pair of complex conjugate poles on imaginary axis.
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The closed loop transfer function of a system isThe system is said to bea)Unstable with a pair of complex conjugate poles on imaginary axisb)Unstable with two pairs of complex conjugate poles on imaginary axisc)Marginal stable with all poles on imaginary axisd)Marginal stable with a pair of complex conjugate poles on imaginary axisCorrect answer is option 'B'. Can you explain this answer?
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