# Relative Stability Analysis-II MCQ’s

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
s5+s4+2s3+2s2+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, s4+3s3+5s2+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. s3+10s2+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 s3+Ks2+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 s4+Ks3+s2+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 by3s4+10s3+5s2+2=0. This system is:
a) Stable
b) Marginally stable
c) Unstable
d) Linear