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

1. 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)

2. 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

3. 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

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

5. 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

6. 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

7.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

8. 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

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

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