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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

Which among these is a classification of power system stability?

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, 30K^{2} - 140K > 0

satisfy this condition.

QUESTION: 4

The closed loop transfer function for this system is

Solution:

First combine the parallel loop K/s^{2}

and 2/s giving

Then apply feedback formula with and and then multiply with s^{2}.

QUESTION: 5

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

Solution:

Denominator = s^{3} + s^{2} + 2s + K Routh table is as shown in fig.

Row of zeros when K = 2,

s^{2} + 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)(s^{2} + s + 0.6)+K(s + 0.1) = 0

s^{4} +0.8 s^{3} +0.4s^{2} +(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 -125K^{2} +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(sT_{1} + 1)(sT_{2} +1) + K = 0

T_{1}T_{2}s^{3} + (T_{1} + T_{2})s^{2} + 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 s^{4} row down to the s^{0} 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 s^{4} row down to s^{0} 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 s^{4} mw down to the s° row. So two roots are on RHS. Because of symmetry rest two roots must be in LHP. From s^{6} to s^{4} there is 1 sign change so 1 on RHP and 1 on LHP.

Total LHP 3 root, RHP 3 root.

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