Block Diagram Reduction Technique MCQ Quiz - Objective Question with Answer for Block Diagram Reduction Technique - Download Free PDF

Last updated on Mar 21, 2025

Latest Block Diagram Reduction Technique MCQ Objective Questions

Block Diagram Reduction Technique Question 1:

What is the rule for block diagram reduction of parallelly connected blocks?

  1. The overall transfer function of all the blocks is the multiplication of the transfer function of each separate block in the connection
  2. The overall transfer function of all the blocks is the division of the transfer function of each separate block in the connection
  3. The transfer function of the whole system will be the vector sum of the transfer function of each block multiplied by two
  4. The transfer function of the whole system will be the addition of the transfer function of each block

Answer (Detailed Solution Below)

Option 4 : The transfer function of the whole system will be the addition of the transfer function of each block

Block Diagram Reduction Technique Question 1 Detailed Solution

  • When blocks are connected in parallel, the overall transfer function is obtained by adding the transfer functions of the individual blocks.
  • In a block diagram, when blocks are connected in parallel, it means that they all receive the same input and provide outputs that contribute to the overall output.
  • If you have two or more blocks connected in parallel with transfer functions G1(S),G2(s),G3(S)then overall transfer function with G(s) for the parallel configuration is given by:
    G(S)=G1(S)+G2(s)+G3(S)
  • The transfer function of the whole system will be the addition of the transfer function of each block.

Block Diagram Reduction Technique Question 2:

In the below figure, output C1 due to R1 and R2 is given by:

F1 Engineering Mrunal 13.03.2023 D17

  1. G1R1G1G3G4R21G1G2G3G4
  2. G1R1G2G3G4R21G1G2G3G4
  3. G1R1G1G3G2R21G1G2G3G4
  4. G1R1G1G2G3G4R21G1G2G3G4

Answer (Detailed Solution Below)

Option 1 : G1R1G1G3G4R21G1G2G3G4

Block Diagram Reduction Technique Question 2 Detailed Solution

Concept:

According to Mason’s gain formula, the transfer function is given by

TF=k=1nMkΔkΔ

Where, n = no of forward paths

Mk = kth forward path gain

Δk = 1 - Sum of the loop that exists after removal of the kth forward path + sum of the gain product of two non-touching loops

Δ = 1 – (sum of the loop gains) + (sum of the gain product of two non-touching loops) – (sum of the gain product of three non-touching loops)

Calculation

While calculating output C1 due to R1 and R2 , keep C2 = 0

The forward path from R1 to C1 is:

M1=G1R1

The forward path from R2 to C1 is:

M2=G1G3G4R2

Self-loop gain:

Δ=1G1G2G3G4

T(s)=G1R1G1G3G4R21G1G2G3G4

Hence, the correct answer is option 1.

Block Diagram Reduction Technique Question 3:

A two-position control system is shown below.

F1 Shubham Ravi 16.12.21 D2
The gain k of the Tacho-generator influences mainly the

  1. Peak overshoot
  2. natural frequency of oscillation
  3. phase shift of the closed loop transfer function at very low frequencies (ω → 0)
  4. phase shift of the closed loop transfer function at very high frequencies (ω → ∞)
  5. None of these

Answer (Detailed Solution Below)

Option 1 : Peak overshoot

Block Diagram Reduction Technique Question 3 Detailed Solution

Given Block Diagram:

F1 Shubham Ravi 16.12.21 D2

Given block diagram can be reduced by,

F1 Shubham Ravi 16.12.21 D3.0

Further, It can be reduced by,

F1 Shubham Ravi 16.12.21 D7

Hence,

Y(S)R(S)=1S2+S(K+1)+1 .... (1)

The standard equation of 2nd order system can be written as,

TF = ωn2S2+2ζωnS+ωn2 .... (2)

From equation (1) & (2),

ωn = ±1

2ζωn = (K + 1)

or, 2ζ = (K + 1)

or, ζ=K+12

Peak over shoot (Mp) = e(ζπ1ζ2)

We have,

F1 Shubham Ravi 16.12.21 D4

Now,

Y(S)U(S)=1S(S+1+K)

Here, ϕ=π2tan1ωK+1

At: ω → 0 ⇒ ϕ = -(π/2)

At: ω → ∞ ⇒ ϕ = -(π)

Hence, K will only affct the Peak overshoot.

Block Diagram Reduction Technique Question 4:

A two-position control system is shown below.

F1 Shubham Ravi 16.12.21 D2
The gain k of the Tacho-generator influences mainly the

  1. Peak overshoot
  2. natural frequency of oscillation
  3. phase shift of the closed loop transfer function at very low frequencies (ω → 0)
  4. phase shift of the closed loop transfer function at very high frequencies (ω → ∞)

Answer (Detailed Solution Below)

Option 1 : Peak overshoot

Block Diagram Reduction Technique Question 4 Detailed Solution

Given Block Diagram:

F1 Shubham Ravi 16.12.21 D2

Given block diagram can be reduced by,

F1 Shubham Ravi 16.12.21 D3.0

Further, It can be reduced by,

F1 Shubham Ravi 16.12.21 D7

Hence,

Y(S)R(S)=1S2+S(K+1)+1 .... (1)

The standard equation of 2nd order system can be written as,

TF = ωn2S2+2ζωnS+ωn2 .... (2)

From equation (1) & (2),

ωn = ±1

2ζωn = (K + 1)

or, 2ζ = (K + 1)

or, ζ=K+12

Peak over shoot (Mp) = e(ζπ1ζ2)

We have,

F1 Shubham Ravi 16.12.21 D4

Now,

Y(S)U(S)=1S(S+1+K)

Here, ϕ=π2tan1ωK+1

At: ω → 0 ⇒ ϕ = -(π/2)

At: ω → ∞ ⇒ ϕ = -(π)

Hence, K will only affct the Peak overshoot.

Block Diagram Reduction Technique Question 5:

Determine the closed loop transfer function C(s) / R(s) for the block diagram shown in Fig.

F15 Jai Prakash 18-2-2021 Swati D11

  1. C(s)R(s)=G11G1H1G1H1H2
  2. C(s)R(s)=G11+G1H1+G1H2
  3. C(s)R(s)=G11G1H1+G1H2
  4. C(s)R(s)=G11+G1H1+G1H1H2
  5. None of these

Answer (Detailed Solution Below)

Option 3 : C(s)R(s)=G11G1H1+G1H2

Block Diagram Reduction Technique Question 5 Detailed Solution

Concept:

F1 U.B Deepak 26.03.2020 D4

If the open-loop transfer function G(s) is connected in positive feedback with a feedback gain of H(s), then the transfer function of the closed-loop system is: G(s)1G(s)H(s)

If the open-loop transfer function G(s) is connected in negative feedback with a feedback gain of H(s), then the transfer function of the closed-loop system is: G(s)1+G(s)H(s)

When two systems are connected in parallel, then the overall gain of the system will be the sum of their individual gains.

When two systems are connected in cascade connection, then the overall gain of the system will be the product of their individual gains.

Calculation:

G1 and H1 are connected in positive feedback.

The equivalent for this combination is =G11G1H1

Now, this block and H2 are in negative feedback.

The equivalent transfer function is,

C(s)R(s)=G11G1H11+G1H21G1H1

=G11G1H1+G1H2

Top Block Diagram Reduction Technique MCQ Objective Questions

Consider the control system shown in figure with feed forward action for rejection of a measurable disturbance d(t). The value of k, for which the disturbance response at the output y(t) is zero mean, is

F2 U.B Madhu 26.12.19 D 47

  1. 1
  2. -1
  3. 2
  4. -2

Answer (Detailed Solution Below)

Option 4 : -2

Block Diagram Reduction Technique Question 6 Detailed Solution

Download Solution PDF

Y(s)=[50Y(s)+KD(s)]1s+2+D(s)

Y(s)[1+50s+2]=[Ks+2+1]D(s)

Y(s)=K+s+2s+52D(s)

Y(jω)=K+2+jω52+jωD(jω)

The disturbance response at the output y(t) is zero mean.

At ω = 0, Y(j0) = 0

K+2+052+0=0

⇒ K = -2

Find the transfer function Y(s)X(s) of the system given below

F1 Eng Arbaz 3-1-24 D1 v2

  1. G11HG1+G21HG2
  2. G11+HG1+G21+HG2
  3. G1+G21+H(G1+G2)
  4. G1+G21H(G1+G2)

Answer (Detailed Solution Below)

Option 3 : G1+G21+H(G1+G2)

Block Diagram Reduction Technique Question 7 Detailed Solution

Download Solution PDF

Concept:

Mason’s gain formula is

T=C(s)R(s)=i=1NPiΔiΔ

Where,

C(s) is the output node

R(s) is the input node

T is the transfer function or gain between R(s) and C(s)

Pi is the ith forward path gain

Δ = 1−(sum of all individual loop gains) + (sum of gain products of all possible two non-touching loops) − (sum of gain products of all possible three non-touching loops) + ........

Δi is obtained from Δ by removing the loops which are touching the ith forward path.

Calculation:

Given block diagram is,

F1 Eng Arbaz 3-1-24 D1 v2

There are two forward paths,

Δ1P1 = G1, Δ2P2 = G2

There are two loops,

- G1H, - G2H

Δ = 1 - (- G1H - G2H) = 1 + H (G1 + G2)

From mason's gain formula

Y(s)X(s)=G1+G21+H(G1+G2)

 

For the block diagram shown in figure, the transfer function C(s)R(s) is equal to – 

F1 Jai 30.11.20 Pallavi D1

  1. s2+1s2
  2. s2+s+1s2
  3. 1s2+s+1
  4. s2+s+1s

Answer (Detailed Solution Below)

Option 2 : s2+s+1s2

Block Diagram Reduction Technique Question 8 Detailed Solution

Download Solution PDF

Concept:

Mason’s gain formula to find the transfer function is given by:

TF=1ΔKPkΔk

Pk = Path Gain of kth forward path

Δ = 1 – (sum of loop gains of all individual loops) + (sum of the gain product of all possible combinations of two Non-toucing loops) ….

Δk  = Value of Δ obtained by removing all the loops touching kth forward path.

Calculation:

signal flow graph of the given block diagram

5fc8a445b1d3c61ceeb2252d 16429333555761

There are three forward paths having gain

P1 = 1 / s2, P2 = 1 / s, P3 = 1

and here Δ = 1 (∵ there is no loop)

Δ1 = Δ2 = Δ3 = 1

Transfer function using masson gain formula

 TF=1ΔKPkΔk

TF=1s2+1s+1

TF=s2+s+1s2

The transfer function C/R of the system shown in the figure is

F1 U.B Madhu 20.06.20 D6

  1. G1G21+G1H1+G2G2
  2. G1H1G2H2(1+G1H1)(1+G2H2)
  3. G1G21G1G2+G1G2H1H2
  4. G1G21+G1H1+G2H2+G1G2H1H2

Answer (Detailed Solution Below)

Option 4 : G1G21+G1H1+G2H2+G1G2H1H2

Block Diagram Reduction Technique Question 9 Detailed Solution

Download Solution PDF

The transfer function of the left side block =G11+G1H1

The transfer function of the right-side block =G21+G2H2

These two blocks are in cascade connection. Therefore, the overall transfer function will multiplication of their individual transfer functions.

TF=G1G2(1+G1H1)(1+G2H2)=G1G21+G1H1+G2H2+G1G2H1H2

The block diagram of a system is illustrated in the figure shown, where X(s) is the input and Y(s) is the output. The transfer function H(s)=Y(s)X(s) is

GATE 2019 ECE (19-41) SOLUTIONS images Q32

  1. H(s)=s2+1s3+s2+s+1
  2. H(s)=s2+1s3+2s2+s+1
  3. H(s)=s+1s2+s+1
  4. H(s)=s2+12s2+1

Answer (Detailed Solution Below)

Option 2 : H(s)=s2+1s3+2s2+s+1

Block Diagram Reduction Technique Question 10 Detailed Solution

Download Solution PDF

Solving the loop:

s+1s1+(s+1s)=s2+1s2+s+1

GATE 2019 ECE (19-41) SOLUTIONS images Q32a

Solving the second loop, we get:

GATE 2019 ECE (19-41) SOLUTIONS images Q32b

1s(s2+1s2+s+1)1+s2+1s(s2+s+1)

H(s)=s2+1s3+2s2+s+1

A two-position control system is shown below.

F1 Shubham Ravi 16.12.21 D2
The gain k of the Tacho-generator influences mainly the

  1. Peak overshoot
  2. natural frequency of oscillation
  3. phase shift of the closed loop transfer function at very low frequencies (ω → 0)
  4. phase shift of the closed loop transfer function at very high frequencies (ω → ∞)

Answer (Detailed Solution Below)

Option 1 : Peak overshoot

Block Diagram Reduction Technique Question 11 Detailed Solution

Download Solution PDF

Given Block Diagram:

F1 Shubham Ravi 16.12.21 D2

Given block diagram can be reduced by,

F1 Shubham Ravi 16.12.21 D3.0

Further, It can be reduced by,

F1 Shubham Ravi 16.12.21 D7

Hence,

Y(S)R(S)=1S2+S(K+1)+1 .... (1)

The standard equation of 2nd order system can be written as,

TF = ωn2S2+2ζωnS+ωn2 .... (2)

From equation (1) & (2),

ωn = ±1

2ζωn = (K + 1)

or, 2ζ = (K + 1)

or, ζ=K+12

Peak over shoot (Mp) = e(ζπ1ζ2)

We have,

F1 Shubham Ravi 16.12.21 D4

Now,

Y(S)U(S)=1S(S+1+K)

Here, ϕ=π2tan1ωK+1

At: ω → 0 ⇒ ϕ = -(π/2)

At: ω → ∞ ⇒ ϕ = -(π)

Hence, K will only affct the Peak overshoot.

In the below figure, output C1 due to R1 and R2 is given by:

F1 Engineering Mrunal 13.03.2023 D17

  1. G1R1G1G3G4R21G1G2G3G4
  2. G1R1G2G3G4R21G1G2G3G4
  3. G1R1G1G3G2R21G1G2G3G4
  4. G1R1G1G2G3G4R21G1G2G3G4

Answer (Detailed Solution Below)

Option 1 : G1R1G1G3G4R21G1G2G3G4

Block Diagram Reduction Technique Question 12 Detailed Solution

Download Solution PDF

Concept:

According to Mason’s gain formula, the transfer function is given by

TF=k=1nMkΔkΔ

Where, n = no of forward paths

Mk = kth forward path gain

Δk = 1 - Sum of the loop that exists after removal of the kth forward path + sum of the gain product of two non-touching loops

Δ = 1 – (sum of the loop gains) + (sum of the gain product of two non-touching loops) – (sum of the gain product of three non-touching loops)

Calculation

While calculating output C1 due to R1 and R2 , keep C2 = 0

The forward path from R1 to C1 is:

M1=G1R1

The forward path from R2 to C1 is:

M2=G1G3G4R2

Self-loop gain:

Δ=1G1G2G3G4

T(s)=G1R1G1G3G4R21G1G2G3G4

Hence, the correct answer is option 1.

Transfer function C(s)R(s) of the system shown in the figure here is:

F1 Uday.B 14-12-20 Savita D15

  1. GaGbHa(1+GaGbHb)
  2. GaGb1+GaGbHaHb
  3. GaGbHbHa(1+GaGbHb)
  4. GaHbHa(1+GaGbHb)

Answer (Detailed Solution Below)

Option 4 : GaHbHa(1+GaGbHb)

Block Diagram Reduction Technique Question 13 Detailed Solution

Download Solution PDF

Concept:

F1 U.B Deepak 26.03.2020 D4

If the open-loop transfer function G(s) is connected in positive feedback with a feedback gain of H(s), then the transfer function of the closed-loop system is: G(s)1G(s)H(s)

If the open-loop transfer function G(s) is connected in negative feedback with a feedback gain of H(s), then the transfer function of the closed-loop system is: G(s)1+G(s)H(s)

When two systems are connected in parallel, then the overall gain of the system will be the sum of their individual gains.

When two systems are connected in cascade connection, then the overall gain of the system will be the product of their individual gains.

Calculation:

The transfer function of the right part of the given block diagram is GaGb1+GaGbHb

Both are connected in cascade connection, therefore the overall transfer function is

=GaHbHa(1+GaGbHb)

The overall transfer function C(s)/R(s) of the system shown in the figure below is

F13 Uday 14-12-2020 Swati D1

  1. G1G21G2H1+G1G2H1
  2. G1G21+G1H1G1G2H2
  3. G1G21+G2H1+G1G2H2
  4. G1G2G2H1G1H1G2

Answer (Detailed Solution Below)

Option 3 : G1G21+G2H1+G1G2H2

Block Diagram Reduction Technique Question 14 Detailed Solution

Download Solution PDF

Concept:

F1 U.B Deepak 26.03.2020 D4

If the open-loop transfer function G(s) is connected in positive feedback with a feedback gain of H(s), then the transfer function of the closed-loop system is: G(s)1G(s)H(s)

If the open-loop transfer function G(s) is connected in negative feedback with a feedback gain of H(s), then the transfer function of the closed-loop system is: G(s)1+G(s)H(s)

When two systems are connected in parallel, then the overall gain of the system will be the sum of their individual gains.

When two systems are connected in cascade connection, then the overall gain of the system will be the product of their individual gains.

Calculation:

G2 and H1 are connected in a feedback loop.

The simplified expression for this block is G21+G2H1

Now, the block diagram can be simplified as shown below.

F13 Uday 14-12-2020 Swati D2

Now, the overall transfer function is

C(s)R(s)=G1G21+G2H11+G1G2H21+G2H1

=G1G21+G2H1+G1G2H2

By performing cascading and / or summing / differencing operations using transfer function blocks G1 (s) and G2 (s), one CANNOT realize a transfer function of the form

  1. G1(s)G2(s)
  2. G1(s)G2(s)
  3. G1(s)(1G1(s)+G2(s))
  4. G1(s)(1G1(s)G2(s))

Answer (Detailed Solution Below)

Option 2 : G1(s)G2(s)

Block Diagram Reduction Technique Question 15 Detailed Solution

Download Solution PDF

G1(s)G2(s) can be realized directly by cascading the systems.

G1(s)(1G1(s)+G2(s))=1+G1(s)G2(s) can be realised by providing a unity feed forward path around the cascaded arrangement.

G1(s)(1G1(s)G2(s))=1G1(s)G2(s)  can be realised by providing a unity feed forward path around the cascaded arrangement and multiplying -1 to the cascaded arrangement of G1(s)G2(s).

Thus, only G1(s)G2(s) cannot be realised using the above systems.

Additional Information

Block diagram reduction rules:

Rule 1: Moving the branch point ahead of the block:

F1 Uday Madhu 18.08.20 D15

Rule 2: Moving the branch point before the block:

F1 Uday Madhu 18.08.20 D16

Rule 3: Moving the summing point ahead of the block

F1 Uday Madhu 18.08.20 D11

Rule 4: Moving the summing point before the block

F1 Uday Madhu 18.08.20 D13

Rule 5: Interchanging the summing points

F1 Uday Madhu 18.08.20 D10

Application:

Given Block diagram

Equivalent block diagram

F1 Uday.S 23-12-20 Savita D13

F1 Uday.S 23-12-20 Savita D11

F1 Uday.S 23-12-20 Savita D14

F1 Uday.S 28-12-20 Savita D1

F1 Uday.S 23-12-20 Savita D15

F1 Uday.S 23-12-20 Savita D9

F1 Uday.S 23-12-20 Savita D16

F1 Uday.S 23-12-20 Savita D10

Get Free Access Now
Hot Links: lotus teen patti teen patti real cash withdrawal teen patti apk download teen patti gold new version 2024 teen patti tiger