Routh Hurwitz (RH) Criterion MCQ

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Routh Hurwitz (RH) Criterion MCQ

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Questions Type Questions

Q.1. A system described by the transfer function:

G(s)=\frac{1}{s^{3}+\alpha s^{2}+Ks+3} is stable

The constraints on α and K are

  • \alpha > 0, \alpha K< 3
  • \alpha > 0, \alpha K> 3
  • \alpha < 0, \alpha K> 3
  • \alpha < 0, \alpha K< 3

Answer: \alpha > 0, \alpha K> 3

Q.2. The feedback control system in the figure below is stable

Routh Hurwitz (RH) Criterion MCQ
  • for all K≥0
  • only K≥0
  • only if 0≤ K < 1
  • only if 0 ≤ K ≤ 1  

Answer: only if 0≤ K < 1

Q.3. The characteristic polynomial of a system is q(s)=2s^{5}+s^{4}+4s^{3}+2s^{2}+2s+1. The system is

  • Stable
  • Marginally stable
  • Unstable
  • Oscillatory

Answer: Unstable

Q.4. The open-loop transfer function of a unity feedback system

G(s)=\frac{K}{s(s^{2}+s+2)(s+3)}

The range of K for which the system is stable is

  • \frac{21}{4}> K> 0
  • 13> K> 0
  • \frac{21}{4}< K< \infty
  • -6< K< \infty

Answer: \frac{21}{4}> K> 0

Q.5. For the polynomial:

P(s)=s^{5}+s^{4}+2s^{3}+2s^{2}+3s+15, the number of roots which lie in the right half of the s-plane is

  • 4
  • 2
  • 3
  • 1

Answer: 2

Q. 6. The Positive values of “K” and ‘a’ so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are

Routh Hurwitz (RH) Criterion MCQ
  • 1, 0.75
  • 2, 0.75
  • 1, 1
  • 2, 2

Answer: 2, 0.75

Q.7. A certain system has transfer function G(s)=\frac{s+8}{s^{2}+\alpha s-4}, where α is a parameter. Consider the standard negative unity feedback configuration as shown below:

Which of the following statements is true ?

  • The closed-loop system is never stable for any value of α
  • For some positive values of α, the closed-loop system is stable, but not for all positive values.
  • For all positive values of α, the closed-loop system is stable.
  • The closed-loop system is stable for all values of α, both positive and negative.

Answer: For all positive values of α, the closed-loop system is stable.

Q.8. The number of open right half plane poles of

G(s)=\frac{10}{s^{5}+2s^{4}+3s^{3}+6s^{2}+5s+3}
  • 0
  • 1
  • 2
  • 3

Answer: 2

Q.9. The open-loop transfer function of unity feedback control system is G(s)=\frac{K}{s(s+a)(s+b)}, 0< a\leq b

The system is stable is

  • 0< K< \frac{(a+b)}{ab}
  • 0< K< \frac{ab}{(a+b)}
  • 0< K< ab(a+b)
  • 0< K< \frac{a}{b}(a+b)

Answer: 0< K< ab(a+b)

Q.10. The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is

  • negative real and exponential functions of s
  • negative real, both exponential and sinusoidal function of.s.
  • both exponential and sinusoidal functions of s
  • complex, both exponential and sinusoidal functions of s.

Answer: negative real, both exponential and sinusoidal function of.s.

Q.11. The given characteristic polynomial s^{4}+s^{3}+2s^{2}+2s+3=0 has

  • zero roots in RHS of s-plane
  • one root in RHS of s-plane
  • two roots in RHS of s-plane
  • three roots in RHS of s-plane

Answer: two roots in RHS of s-plane

Q.12. The characteristic equation of a control system is given by s^{6}+2s^{5}+8s^{4}+12s^{3}+20s^{2}+16s+16=0. The number of the roots of the equation which lie in the imaginary axis of s-plane is

  • zero
  • 2
  • 4
  • 6

Answer: 4

Q.13. An open loop system has a transfer function \frac{1}{s^{3}+1.5s^{2}+s-1}. it is converted into a closed loop system by providing a negative feedback having 20(s + 1). Which one of the following is correct?

The open loop and closed loop system are, respectively

  • stable and stable
  • stable and unstable
  • unstable and stable
  • unstable and unstable

Answer: unstable and stable

Q.14. The open loop transfer function of a unity negative feedback control system is given by

G(s)=\frac{k}{(s+2)(s+4)(s^{2}+6s+25)}

Which is the value of k which causes sustained oscillations in the closed loop system?

  • 666.25
  • 790
  • 990
  • 1190

Answer: 666.25

Q.15. The unit step response of a system is 1-e^{-t}(1+t). Which is this system?

  • Unstable
  • Stable
  • Critically stable
  • Oscillatory

Answer: Stable

Q.16. The system having characteristic equation:

s^{4}+2s^{3}+3s^{2}+2s+K=0 is to be used as an oscillator. What are the values of k and the frequency of oscillation ω?

  • k = 1 and ω = 1 r/s
  • k = 1 and ω = 2 r/s
  • k = 2 and ω = 1 r/s
  • k = 2 and ω = 2 r/s

Answer: k = 2 and ω = 1 r/s

Q.17. The characteristic equation of a control system is

s^{5}+15s^{4}+85s^{3}+225s^{2}+274s+120=0

What are the number of roots of the equation which lie to the left of the line s+1=0 ?

  • 2
  • 3
  • 4
  • 5

Answer: 3

Q.18. The open loop transfer function of a unity feedback control system is given by

G(s)=Ke^{-Ts}

Where K and T are variables and are greater than zero. The stability of the closed loop system depends on

  • K only
  • Both K and T
  • T only
  • Neither K nor T

Answer: T only

Q. 19. Consider the unity feedback system with G(s)=\frac{K}{(s^{2}+2s+2)(s+2)}

The system is marginally stable. What is the radian frequency of oscillation?

  • \sqrt{2}
  • \sqrt{3}
  • \sqrt{5}
  • \sqrt{6}

Answer: \sqrt{6}

Q.20. For what positive value of K does the polynomial

s^{4}+8s^{3}+24s^{2}+32s+K

have roots with zero real parts ?

  • 10
  • 20
  • 40
  • 80

Answer: 80

Q.21. The characteristics equation of a control system is given as

s^{4}+8s^{3}+24s^{2}+32s+K=0

What is the range of values of K for this system to be stable ?

  • 0 ≤ K < 80
  • 0 ≤ K < 100
  • 0 ≤ K < 300
  • 0 ≤ K < 600

Answer: 0 ≤ K < 80

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