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Quiz: LCS-Root Locus

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Number of Questions: 17

Question: 11 -

Which one of the following options correctly describes the locations of the roots of the equation s4+s2+1=0 on the complex plane?

Options:

  1. Four left half plane (LHP) roots

  2. Two RHP roots and two LHP roots

  3. One right half plane (RHP) root, one LHP root and two roots on the imaginary axis

  4. All four roots are on the imaginary axis

    5. Answer:

    Two RHP roots and two LHP roots
    Solution not available.

Question: 12 -

Which of the following points is NOT on the root locus of a system with the open–loop transfer function

G(s)H(s) = K/s(s+1)(s+3)

Options:

  1. -∞

  2. -j√3

  3. -1.5

  4. -3

    5. Answer:

    -1.5
    Solution:

    Count for ODD number of poles and zeros on RHS.

Question: 13 -

The number of open right half plane poles of

G(s) = 10/(s5+2s4+3s3+6s2+5s+3) is

Options:

  1. 2

  2. 1

  3. 0

  4. 3

    5. Answer:

    2
    Solution:

    Use Routh's Array and count number of sign changes.

Question: 14 -

G(s)H(s) = K/s(s+1)(s+3)

the point of intersection of the symptotes of the root loci with the real axis is

Options:

  1. 1.33

  2. 4

  3. -4

  4. -1.33

    5. Answer:

    -1.33
    Solution not available.

Question: 15 -

For the equation, s3 − 4s2 + s + 6 = 0 the number of roots in the left half of s-plane will be

Options:

  1. 2

  2. 1

  3. 0

  4. 3

    5. Answer:

    1
    Solution:

    No. of sign changes in first column of Routh-array=2.

    According to Routh-Hurwitz criterion, the number of changes of sign in the first column gives the number of positive real part roots of the polynomial.
    So, no. of roots in RHS of s-plane=2.
    Total no. of roots=3
    Hence, no. of roots in LHS of s-plane
    =3-2=1