Signal Flow Graph and Block Diagram MCQ Quiz in తెలుగు - Objective Question with Answer for Signal Flow Graph and Block Diagram - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

There are two forward paths in the given SFG.

P₁ = G₁ G₂ G₃ G₄

P₂ = G₁ G₅ G₈ G₄

There are five individual loops, given as

L₁ = G₁ G₂ G₉

L₂ = G₃ G₄ G₁₀

L₃ = G₁ G₅ G₈ G₄ G₁₀ G₉

L₄ = G₅ G₆

L₅ = G₇

There are three possible combinations of two non-touching loops,

L₁ and L₅, i.e. L₁₅ = G₁ G₂ G₉ G₇

L₂ and L₄, i.e. L₂₄ = G₃ G₄ G₁₀ G₅ G₆

L₂ and L₅, i.e. L₂₅ = G₃ G₄ G₁₀ G₇

After removing the branch having gain G₆ i.e. putting G₆ = 0,

Loop L₄ is removed so, the total number of loops reduced by 1 and remains four loops.

The Loop pair of two non-touching loops L₂₄ is also removed, so pairs of two non-touching loops are reduced by 1 and remains two pairs.

Mistake Points

Forward path. A path from an input node to an output node that does not re-visit any node.

G₁ G₅ G₆ G₂ G₃ G₄ is not a forward path as a node is visited twice. 

P₁ = -2

∆₁ = 1

∆₂ = 1

For DC gain, put s = 0

Concept:

A signal flow graph is a graphical representation of the relationships between the variables of a set of linear algebraic equations.

Manson's gain formula:

• Where Pk is the forward path transmittance of kth in the path from a specified input is known to an output node. In arresting Pk no node should be encountered more than once.
• Δ is called the signal flow graph determinant.
• Δ = 1 – (sum of all individual loop transmittances) + (sum of loop transmittance products of all possible pair of non-touching loops) – (sum of loop transmittance products of all possible triplets of non-touching loops) + (……) – (……)
• Δ k is the factor associated with the concerned path and involves all closed loop in the graph which are isolated from the forward path under consideration.
• The path factor Δk for the kth path is equal to the value of the grab determinant of its signal flow graph which exists after erasing the Kth path from the graph.

Explanation:

There are two forward paths, G₁ and G₂

∴ P_k = G₁ + G₂

Δ_k = 1 

There are two loop, G₁H₁ and G₂H₁

∴ Δ = 1 - G1H1 - G2H1

By using mason’s gain formula, the transfer will be 

Concept:

Mason’s Gain Formula

• It is a technique used for finding the transfer function of a control system. A formula that determines the transfer function of a linear system by making use of the signal flow graph is known as Mason’s Gain Formula.
• It shows its significance in determining the relationship between input and output.

Suppose there are ‘N’ forward paths in a signal flow graph. The gain between the input and the output nodes of a signal flow graph is nothing but the transfer function of the system. It can be calculated by using Mason’s gain formula.

Mason’s gain formula is

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.

Calculations:

The forward paths are as follows:

P₁ = 5

P₂ = 2 × 3 × 4 = 24

The loops are as follows:

L₁ = -2, L₂ = -3, L₃ = -4, L₄ = -5

The two non-touching loops are:

L₁L₃ = 8

There is no three non-touching loops

By Mason’s gain formula:-

Number of forward paths = 2

Number of loops = 1

Δ₁ = 1

The transfer function is,

It represents an integrator with a gain of 0.5.

Forward path = 8

Loops = +8, 4

Δ = 1 – (8 + 4) = -11

Transfer function 

Let us first draw the SFG.

At every summing and take-off point or pick-off point, we will consider nodes.

The SFG along with the loops marked can be drawn as follows:

Loops:

Two non-touching loops are:

The correct answer is 2.

Concept:

Mason’s Gain Formula

• It is a technique used for finding the transfer function of a control system. A formula that determines the transfer function of a linear system by making use of the signal flow graph is known as Mason’s Gain Formula.
• It shows its significance in determining the relationship between input and output.
• Suppose there are ‘N’ forward paths in a signal flow graph. The gain between the input and the output nodes of a signal flow graph is nothing but the transfer function of the system. It can be calculated by using Mason’s gain formula.

Mason’s gain formula is

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:

No of forward paths = 1

Forward Path Gain (P₁) = 10 × 1 = 10

No of individual loops = 1

The gain of the individual loops = 0.5

No of two non-touching loop gains = 0

∴ Δ = 1 – (0.5) = 0.5, Δ₁ = 1

The transfer function for given signal flow graph is given as

Concept:

Mason’s gain formula is

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,

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

Concept:

• From the above signal flow diagram, the circle represents the nodes.
• Arrows represent the path in the signal flow.

Additional Information

Forward path: Path from the input node to the output node.

Here 5,3,2 is a forward path.

Feedback loops: A closed path originates at one node and terminates at the same node. So that no node should be touched twice.

Here 3, - 3 is feedback loops.

Non-touching loops: Loops with no common node.

Here 

Touching loops: Loops with at least one touching loop.

Here  

Confusion Points Here, the pointer means asterisk (*), not the full stop point.