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QUESTION: 1

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

Solution:

QUESTION: 2

In the signal flow graph shown in fig. the sum of loop gain of non-touching loops is

Solution:

There cannot be common subscript because subscript refers to node number. If subscript is common, that means that node is in both loop.

QUESTION: 3

The principles of homogeneity and super position 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 transfer function of the system shown in fig. is

Solution:

**The correct option is Option C.**

**L1 = - G _{1}H_{1} P1 = G_{1}G_{2}**

**L2 = G _{2}H_{2} Δ1 = 1 - 0 = 1**

** Δ = 1 + G _{1}H_{1} - G_{1}H_{1}**

**T.f = G _{1}G_{2} (1) / 1 + G_{1}H_{1} - G_{2}H_{2}**

** = G _{1}G_{2} / 1 + G_{1}H_{1} - G_{2}H_{2}**

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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