CONTROL SYSTEM – ROUTH HURWITZ CRITERION MCQs

1. A linear time-invariant system is said to be stable if it satisfies the condition:

A) For a bounded input, the output must be bounded.
B) In the absence of input, the output of the system tends to zero irrespective of the initial conditions.
C) Both A and B
D) None

2.Investigate the stability of a closed-loop system having characteristic equation given as s⁴+2s³+3s²+4s+5=0

A) Stable
B) Marginally Stable
C) Asymptotic Stable
D) Unstable

3. The number of sign changes in the first column of Routh’s array indicates:

A) The number of open-loop poles in the Right Half Plane(RHP).
B) The number of zeros of the system in the RHP.
C) The number of roots of the characteristics equation in the RHP.
D) The number of open-loop zeros in the RHP.

4. If the system having complex poles on Jw-axis(Imaginary axis)then the system will be:

A) stable
B) Marginally stable
C) unstable
D) Conditionally stable

5. The open-loop transfer function of a feedback control is given as G(s)H(s)=K/s(s+4)(s²+2s+2).Find the value of K for stability.

A) K>0
B) K>11.56
C) 0<K>11.56
D)0<K<11.56

6. When all the elements in any row of Routh’s array are zero then what would be the possibility of the location of roots of the characteristics equation in the s-plane?

A) Pair of real roots with opposite signs
B) pair of conjugate roots on the imaginary axis.
C) Complex conjugate roots forming quadrates in the s-plane.
D) All of the above

A) b0 , b1 , b2 , b3 > 0 and b1 b2 – b0 b3 < 0
B) b_{0 ,} b_{1 ,} b₂ , b₃ > 0 and b₁ b₂ – b₀ b₃ > 0
C) b_{0 ,} b_{1 ,} b₂ , b₃ > 0 and b₁ b₂ – b₀ b₃ = 0
D) b_{0  ,} b₂ > 0 and b_{3 ,} b₁ < 0

8. A system is said to be unstable for which of the following condition:

A) If any of the roots of the characteristic equation has a positive real part.
B) If there is a repeated root on the jw axis.
C) If complex poles are in the right half of the s-plane.
D) All of the above.

9. The polynomial whose coefficients are the elements of the row just above the rows of zeros in the Routh Array is called the Auxiliary equation.

A) True
B) False

10. The characteristic equation of a feedback control system is s3+ ks2 + 5s + 10 = 0.For the system to be critically stable, the value of K should be:

A) 1
B) 2
C) 3
D) 4