This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Relative Stability Analysis”.

1. A system with unity feedback having open loop transfer function as G(s) = K(s+1)/s3+as2+2s+1. What values of ‘K’ and ’a’ should be chosen so that the system oscillates ?

a) K =2, a =1

b) K =2, a =0.75

c) K =4, a =1

d) K =4, a =0.75

View Answer

Explanation: Solving Routh Hurwitz table whenever row of zero occurs, the roots are located symmetrically on the imaginary axis then the system response oscillates, a =1+K/2+K. If K =2 is consider then a =0.75.

2. The open loop transfer functions with unity feedback are given below for different systems.

Among these systems the unstable system is

a) G(s) =2/s+2

b) G(s) =2/s(s+2)

c) G(s) =2/(s+2)s^{^}2

d) G(s) =2(s+1)/s(s+2)

View Answer

Explanation: 1+2/s

^{^}2(s+2) =0. The coefficient of‘s’ is missing. Hence the system is unstable.

3. Determine the stability of closed loop control system whose characteristic equation is

s^{5}+s^{4}+2s^{3}+2s^{2}+11s+10=0.

a) Stable

b) Marginally stable

c) Unstable

d) None of the mentioned

View Answer

Explanation: By Routh array s =0 and s =+j. It is having a pair of conjugate root lying on imaginary axis. System is marginally stable.

4. Determine the condition for the stability of unity feedback control system whose open loop transfer function is given by

G(s) = 2e^{-st}/s(s+2)

a) T >1

b) T <0

c) T <1

d) T >0

View Answer

Explanation: G(s) =2(1-sT)/s(s+2)

By Routh array analysis, for stable system, all the elements of first column need to be positive T<1.

5.Determine the value of K such that roots of characteristic equation given below lies to the left of the line s = -1. s^{3}+10s^{2}+18s+K.

a) K>16 and K<9

b) K<16

c) 9<K<16

d) K<9

View Answer

Explanation: In Routh array analysis the first column must be positive and after solving K<16 and K>9.

6. Consider a negative feedback system where G(s) =1/(s+1) and H(s) =K/s(s+2). The closed loop system is stable for

a) K>6

b) 0<K<2

c) 8<K<14

d) 0<K<6

View Answer

Explanation: Using Routh array, for stability k<6.

7. The characteristic equation of a feedback control system is s^{3}+Ks^{2}+9s+18. When the system is marginally stable, the frequency of the sustained oscillation:

a) 1

b) 1.414

c) 1.732

d) 3

View Answer

Explanation: Solve using Routh array and for the system to be marginally stable, K = -2. Polynomial for sustained oscillation w = 3 rad/s.

8. Consider a characteristic equation, s^{4}+3s^{3}+5s^{2}+6s+k+10=0. The condition for stability is

a) K>5

b) -10<K

c) K>-4

d) -10<K<-4

View Answer

Explanation: Solve Roth array for the system stable, -10<K<4.

9. The polynomial s^{4}+Ks^{3}+s^{2}+s+1=0 the range of K for stability is _____________

a) K>5

b) -10<K

c) K>-4

d) K-1>0

View Answer

Explanation: Solving using Routh array we get K-1>0 and is always negative for K>1.

10. The characteristic equation of a system is given by3s^{4}+10s^{3}+5s^{2}+2=0. This system is:

a) Stable

b) Marginally stable

c) Unstable

d) Linear

View Answer

Explanation: There is missing coefficient so system is unstable.

**Sanfoundry Global Education & Learning Series – Control Systems.**

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