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QUESTION: 1

The output of the feedback control system must be a function of:

Solution:

QUESTION: 2

Which of the following is not the feature of modern control systems?

Solution:

For a good control system the speed of response and stability must be high and for the slow and sluggish response is not used and undesirable.

QUESTION: 3

The principles of homogeneity and superposition are applied to ______.

Solution:

Superposition theorem states that for two signals additivity and homogeneity property must be satisfied and that is applicable for the** LTI systems**.

QUESTION: 4

The sum of the gains of the feedback paths in the signal flow graph shown in fig. is

Solution:

QUESTION: 5

A control system whose step response is -0.5(1+e^{-2t}) is cascaded to another control block whose impulse response is e^{-t}. What is the transfer function of the cascaded combination?

Solution:

- Let h1(t) is the impulse response of system.

h1(t) = d/dt(-0.5(1+e^{-2}t)) h1(t) = e^{(-2t}) h2(t) = e^{(-t)} - Cascading of two system equals to the convolution of both and convolution in time domain is equals to multiplication in frequency domain.
- So by taking Laplace transform of above two

H1(s) =1/(s+2), H2(s) = 1/(s+1) - Hence the transfer function of cascaded system is

H(s) = H1(s)H2(s)

**H(s)= 1/(s+1)(s+2)**

QUESTION: 6

The overall transfer function C/R of the system shown in fig. will be:

Solution:

QUESTION: 7

Consider the signal flow graphs shown in fig. The transfer 2 is of the graph:

Solution:

There are no loop in any graph. So option (B) is correct.

QUESTION: 8

Consider the List I and List II

The correct match is

Solution:

P. P_{1} = ab, Δ = 1, L = 0 ,T = ab

Q_{1} P_{1} = a, P_{2} = 6 , Δ = 1, L = Δ_{k} = 0,T = a+b

R. P_{1} = a, L_{1} = b, Δ = 1 - b, Δ_{1} =1,

S. P_{1} = a, L_{1} = ab, Δ = 1 - ab, Δ_{1} = 1,

QUESTION: 9

For the signal flow graph shown in fig. an equivalent graph is

Solution:

QUESTION: 10

Consider the block diagram shown in figure.

For this system the signal flow graph is

Solution:

Option (A) is correct. Best method is to check the signal flow graph. In block diagram there is feedback from 4 to 1 of gain - H_{1}H_{2} . The signal flow graph of option (A) has feedback from 4 to 1 of gain - H_{1}H_{2}

QUESTION: 11

The block diagram of a system is shown in fig. The closed loop transfer function of this system is

Solution:

Consider the block diagram as SFG. There are two feedback loop -G_{1}G_{2}H_{1} and -G_{2}G_{3}H_{2} and one forward path G_{1}G_{2} G_{3} . So (D) is correct option.

QUESTION: 12

For the system shown in fig. transfer function C(s) R(s) is

Solution:

Consider the block diagram as a SFG. Two forward path G_{1}G_{2 }and G_{3 }and three loops -G_{1}G_{2} H_{2}, -G_{2}H_{1}, -G_{3} H_{2}

There are no nontouching loop. So (B) is correct.

QUESTION: 13

In the signal flow graph shown in fig. the transfer function is

Solution:

P_{1} = 5 x 3 x 2 = 30, Δ = 1 - (3x - 3) = 10

Δ_{1} = 1,

QUESTION: 14

In the signal flow graph shown in fig. the gain C/R is

Solution:

P_{1} = 2 x 3 x 4 = 24 , P_{2} = 1 x 5 x 1 = 5

L_{1} = -2, L_{2} = -3, L_{3} = -4, L_{4} = -5,

L_{1}L_{3} = 8, Δ = 1 -(-2 - 3 - 4 - 5) + 8 = 23, Δ_{1} = 1, Δ_{2} = 1 - (-3) = 4,

QUESTION: 15

The gain C(s)/R(s) of the signal flow graph shown in fig.

Solution:

QUESTION: 16

The negative feedback closed-loop system was subjected to 15V. The system has a forward gain of 2 and a feedback gain of 0.5. Determine the output voltage and the error voltage.

Solution:

Given:

G(s) = 2

H(s) = 0.5 and R(s) = 10V

Output voltage:

= (2/1 + 2 x 0.5) x 15 = 15V

Error voltage:

= (1/1 + 2 x 0.5) x 15 = 7.5V

QUESTION: 17

For the block diagram shown in fig. transfer function C(s)/R(s) is

Solution:

Four loops -G_{1}G_{4}, -G_{1}G_{2}G_{5}, -G_{1},G_{2}G_{5}G_{7} and -G_{1}G_{2}G_{3}G_{3}G_{7}.

There is no nontouching loop. So (B) is correct.

QUESTION: 18

For the block diagram shown in fig. the numerator of transfer function is

Solution:

SFG

P_{1} = G_{2}G_{5}G_{6} , P_{2} = G_{3}G_{5}G_{6}, P_{3} = G_{3}G_{6} , P_{4} = G_{4}G_{6}

If any path is deleted, there would not be any loop.

Hence Δ_{1} = Δ_{2} = Δ_{3} = Δ_{4} = 1

QUESTION: 19

For the block diagram shown in fig. the transfer function C(s)/R(s) is

Solution:

QUESTION: 20

In the signal flow graph of figure y/x equals

Solution:

Transfer function

PK = 5 x 2 x 1 = 10

Δ_{K} = 1

Δ = 1 - (-4) = 5

= 2

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