Routh-Hurwitz Stability Criterion - Topic wise GATE Questions on Control Systems (from 1987)

2004
1. The open loop transfer function of a unity feedback system is G(s) = K/[s(s² + s + 2)(s + 3)]. The range of K for which the system is stable is
a) 21/44 > K > 0
b) 13 > K > 0
c) 21/4 < K < ∞
d) - 6 < K < ∞

Answer:A

Solution : https://www.youtube.com/watch?v=KmUOC_i7USs

2. for the polynomial R(s) = s⁵ + s⁴ + 2s³ + 2s² + 3s + 15, the number of roots which lie in the Right Half of the S-plane is
a) 4
b) 2
c) 3
d) 1

Answer:B

Solution : https://www.youtube.com/watch?v=P_CSEbYpX0s

2006
3. 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

a) 1, 0.75
b) 2, 0.75
c) 1, 1
d) 2, 2

Answer:B

Solution : https://www.youtube.com/watch?v=VYWtxlytlC8

2008
4. The number of open right half plane poles of G(s) = 10 / (s⁵ + 2s⁴ + 3s³ + 6s² + 5s + 3) is
a) 0
b) 1
c) 2
d) 3

Answer:C

Solution : https://www.youtube.com/watch?v=Seaj7dcM1yk

2012
5. The feedback system shown below oscillates at 2 rad/sec, when

a) K = 2 and a = 0.75
b) K = 3 and a = 0.75
c) K = 4 and a = 0.5
d) K = 2 and a = 0.5

Answer:A

Solution : https://www.youtube.com/watch?v=IBPC5lyX_X4

2014
6. Consider a transfer function

with p a positive real parameter. The maximum value of p until which G_p remains stable is ______________

Answer:2

Solution : https://www.youtube.com/watch?v=2psgTIOta3M

2015
7. A plant transfer function is given as

When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is
a) K_P> K_I/2 > 0
b) 2K_I> K_P> 0
c) 2K_I< K_P
d) 2K_I> K_P

Answer:A

Solution : https://www.youtube.com/watch?v=1jJORFpuY5Y



8. The characteristic equation of an LTI system is given by F(s) = s⁵ + 2s⁴ + 3s³ + 6s² – 4s – 8 = 0. The number of roots that lie strictly in the left half S – plane is __________.

Answer:2

Solution : https://www.youtube.com/watch?v=oz77HAXHwQU