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# Stability - MCQ Test

## 15 Questions MCQ Test Mock Tests Electronics & Communication Engineering GATE 2020 | Stability - MCQ Test

Description
This mock test of Stability - MCQ Test for Railways helps you for every Railways entrance exam. This contains 15 Multiple Choice Questions for Railways Stability - MCQ Test (mcq) to study with solutions a complete question bank. The solved questions answers in this Stability - MCQ Test quiz give you a good mix of easy questions and tough questions. Railways students definitely take this Stability - MCQ Test exercise for a better result in the exam. You can find other Stability - MCQ Test extra questions, long questions & short questions for Railways on EduRev as well by searching above.
QUESTION: 1

### The forward-path transfer function of a ufb system is For system to be stable, the range of K is

Solution:  Routh table is as shown in fig. S.6.211  QUESTION: 2

Solution:
QUESTION: 3

### The open-loop transfer function of a ufb system is  The closed loop system will be stable if the value of K is

Solution: Routh table is as shown in fig. 200K > 0 → K > 0, 30K2 - 140K > 0 satisfy this condition.

QUESTION: 4

The closed loop transfer function for this system is Solution:

First combine the parallel loop K/s2
and 2/s giving Then apply feedback formula with and and then multiply with s2.  QUESTION: 5

The poles location for this system is shown in fig.The value of K is  Solution:

Denominator = s3 + s2 + 2s + K Routh table is as shown in fig. Row of zeros when K = 2,
s2 + 2 = 0, ⇒ s = -1, j√2, - j√2

QUESTION: 6

The forward path transfer of ufb system is The system is

Solution:
QUESTION: 7

The forward-path transfer function of a ufb system is The system is

Solution:

Closed loop transfer function Routh table is as shown in fig. S.6.2.28 2 RHP poles so unstable.

QUESTION: 8

The open loop transfer function of a system is as The range of K for stable system will be

Solution:

The characteristic equation is 1 + G(s)H(s) = 0

⇒ s(s - 0.2)(s2 + s + 0.6)+K(s + 0.1) = 0
s4 +0.8 s3 +0.4s2 +(K - 0.12)s +0.1K = 0
Routh table is as shown in fig. S.62.29 K > 0, 055 -125K > 0 ⇒ K < 0.44 -125K2 +0.63K -0066 >0
(K - 0.149)(K - 0355) < 0, 0.149 < K < 0.355

QUESTION: 9

The open-loop transfer function of a ufb control system is given by For the system to be stable the range of K is

Solution:

Characteristic equation

s(sT1 + 1)(sT2 +1) + K = 0
T1T2s3 + (T1 + T2)s2 + s + K = 0
Routh table is as shown in fig S.6.2.30   QUESTION: 10

The closed loop transfer function of a system is The number of poles in right half-plane and in left half-plane are

Solution:

Routh table is as shown in In RHP -2 poles. In LHP -3 poles

QUESTION: 11

The closed loop transfer function of a system is The number of poles in RHP and in LHP are

Solution: 3 RHP, 2 LHP poles.

QUESTION: 12

The closed loop transfer function of a system is The number of poles in LHP, in RHP, and on jω - axis are

Solution:   No sign change exist from the s4 row down to the s0 row.
Thus, the even polynomial does not have RHP poles. Therefore because of symmetry all four poles must be on jw -axis. QUESTION: 13

For the system shown in fig. the number of poles on RHP, LHP, and imaginary axis are Solution:

Closed loop transfer function  Routh table is as shown in fig. S.6.2.34   From s4 row down to s0 there is one sign change. So LHP–1 + 1= 2 pole. RHP–1 pole, jw - axis - 2 pole.

QUESTION: 14

If a system is given unbounded input then the system is:

Solution:

If the system is given with the unbounded input then nothing can be clarified for the stability of the system.

QUESTION: 15

For the open loop system of fig. location of poles on RHP, LHP, and an jω - axis are Solution:

Routh table is as shown in fig  Them is two sign change from the s4 mw down to the s° row. So two roots are on RHS. Because of symmetry rest two roots must be in LHP. From s6 to s4 there is 1 sign change so 1 on RHP and 1 on LHP.
Total LHP 3 root, RHP 3 root.