3. Using Mason's Rule, find the transfer function T(s) = for the system represented in the fugre. C(s) R(s) G₁(s) G₂(s) G4(S) G7(s) R(s) G3(s) G5(s) G6(s) H₁(s) Hz(s) H₂(s) C(s)
Follow the instructions. Kindly provide a COMPLETE and CLEAR solution. Answer it ASAP because I really need it right now. Answer should be typewritten.
Provide the following:
Step 1. Solve for k
Step 2. Solve for Tk (forward path gain)
Step 3. Identify the loop gains (TL)
Step 4. Identify the nontouching loops taken two at a time TNL(2 time)
Step 5. Identify the nontouching loops taken three at a time TNL(3 time)
Step 6. Identify the nontouching loops taken four at a time TNL(4 time)
Step 7. Solve for component ∆
Step 8. Solve for component ∆k (Note: We form ∆k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function
![3.
Using
Mason's Rule, find the transfer function
C(s)
T(s) = for the system represented in the fugre.
R(s)
G₁(s)
G₂(s) G4(S)
G7(s)
R(5) O
G6(s)
G3(s) G5(s) HĮ(s)
Hz(s)
H₂(s)
C(s)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67f4a444-cc47-4acb-953a-7b0f5dde9cf2%2F4994948c-4f8d-4518-94d5-87c79fcb562d%2Faul5jqj_processed.jpeg&w=3840&q=75)
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Solved in 11 steps with 11 images
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Follow the instructions. Kindly provide a COMPLETE and CLEAR solution. Answer it ASAP because I really need it right now.
Answer should be typewritten.
Provide the following:
Step 1. Solve for k
Step 2. Solve for Tk (forward path gain)
Step 3. Identify the loop gains (TL)
Step 4. Identify the nontouching loops taken two at a time TNL(2 time)
Step 5. Identify the nontouching loops taken three at a time TNL(3 time)
Step 6. Identify the nontouching loops taken four at a time TNL(4 time)
Step 7. Solve for component ∆
Step 8. Solve for component ∆k (Note: We form ∆k by eliminating from ∆ the loop gains that touch the kth forward path)
Step 9. Substitute on the equation for transfer function
Formula:
∆ = 1- ΣTCL + ΣTNL(2 time) - ΣTNL(3 time)+ ΣTNL(4 time)+ ......
∆k = ∆ - ΣTL touch kth forward path
![1. Use Mason's rule to find the transfer function of
the signal-flow diagram shown.
R(S) O
V₁(s)
Gy(s)
V3(s)
-H₁(s)
G₂(s)
-H₂(s)
1
V4(s) V5(s)
G3(5)
-H3(s)
C(s)](https://content.bartleby.com/qna-images/question/67f4a444-cc47-4acb-953a-7b0f5dde9cf2/fff0722c-0e5f-41e2-97b4-1ce765dc6cb5/xhiklnm_thumbnail.jpeg)
Can you redo Step 7. Solve for component ∆, Step 8. Solve for component ∆k , and Step 9. Substitute on the equation for transfer function. (Transfer function is given in the photo below, kindly provide the solution how the answer to the transfer function became like that.)
Here is the formula:
∆ = 1- ΣTCL + ΣTNL(2 time) - ΣTNL(3 time)+ ΣTNL(4 time)+ ......
∆k = ∆ - ΣTL touch kth forward path
![T(s)
1(G₁G₂G4G6 G7) + 1(G₁G₂G5 G6 G7)+1(G₁G3G4G6G7)+1(G₂G₂G5G6G₁)
A
T(s)
G₁ G₂G4G6 G7 + G₁G₂G5 G6 G7 + G₁G3G4G6 G7 + G₁G3G5 G6 G7
A](https://content.bartleby.com/qna-images/question/67f4a444-cc47-4acb-953a-7b0f5dde9cf2/77ea7a08-d0d2-4829-ad95-eeb062498afe/tqxgmk_thumbnail.jpeg)
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