- Leduce the block diagram to a single transfer function, G(s) = G3(s) R(s) G1(s) Ge(s) H(s) G2(s) C(s) R(S) G4(s) C(s)
Transfer function
A transfer function (also known as system function or network function) of a system, subsystem, or component is a mathematical function that modifies the output of a system in each possible input. They are widely used in electronics and control systems.
Convolution Integral
Among all the electrical engineering students, this topic of convolution integral is very confusing. It is a mathematical operation of two functions f and g that produce another third type of function (f * g) , and this expresses how the shape of one is modified with the help of the other one. The process of computing it and the result function is known as convolution. After one is reversed and shifted, it is defined as the integral of the product of two functions. After producing the convolution function, the integral is evaluated for all the values of shift. The convolution integral has some similar features with the cross-correlation. The continuous or discrete variables for real-valued functions differ from cross-correlation (f * g) only by either of the two f(x) or g(x) is reflected about the y-axis or not. Therefore, it is a cross-correlation of f(x) and g(-x) or f(-x) and g(x), the cross-correlation operator is the adjoint of the operator of the convolution for complex-valued piecewise functions.
![**Title:** Simplifying a Block Diagram to a Single Transfer Function
**Objective:**
Reduce the block diagram to a single transfer function, \( G(s) = \frac{C(s)}{R(s)} \).
**Diagram Explanation:**
- The diagram consists of multiple blocks and summing junctions.
- **Input:** \( R(s) \)
- **Output:** \( C(s) \)
**Key Components:**
1. **Blocks:**
- \( G_1(s) \), \( G_2(s) \), \( G_3(s) \), \( G_4(s) \), \( G_5(s) \) represent transfer function blocks.
- Each block processes the input signal according to its transfer function.
2. **Feedback Path:**
- The output \( C(s) \) is fed back into the system through blocks \( G_3(s) \), \( G_5(s) \), \( G_4(s) \), and \( H(s) \).
3. **Summing Junctions:**
- The diagram has summing junctions depicted by circles with "+" and "-" symbols indicating the addition or subtraction of signals.
- First junction combines \( R(s) \) and a feedback signal from \( H(s) \).
- Second junction combines the output of \( G_1(s) \) and the output of \( G_5(s) \).
- Third junction combines the output of \( G_2(s) \) and the output from the feedback loop through \( G_4(s) \).
**Feedback Loops:**
- The feedback loop from \( C(s) \) goes through \( G_4(s) \) before impacting the summing point near \( G_2(s) \).
- Another feedback path runs through \( H(s) \) impacting the initial summing junction.
**Task:**
The challenge is to combine these elements into a single transfer function \( G(s) \).
Understanding this diagram involves knowledge of control theory principles such as block diagram reduction techniques, parallel and series block combinations, and feedback loop analysis.
**Use Case:**
This type of analysis is crucial in designing stable and efficient control systems in engineering applications. By reducing the complexity of block diagrams, engineers can better predict system behavior and optimize performance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e11f595-a40a-4bf3-b7d2-0a0cab1f1556%2F83e35dac-49ff-469f-9d3c-e8899193aa96%2F03nnqsv_processed.jpeg&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 10 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![Introductory Circuit Analysis (13th Edition)](https://www.bartleby.com/isbn_cover_images/9780133923605/9780133923605_smallCoverImage.gif)
![Delmar's Standard Textbook Of Electricity](https://www.bartleby.com/isbn_cover_images/9781337900348/9781337900348_smallCoverImage.jpg)
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
![Introductory Circuit Analysis (13th Edition)](https://www.bartleby.com/isbn_cover_images/9780133923605/9780133923605_smallCoverImage.gif)
![Delmar's Standard Textbook Of Electricity](https://www.bartleby.com/isbn_cover_images/9781337900348/9781337900348_smallCoverImage.jpg)
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
![Fundamentals of Electric Circuits](https://www.bartleby.com/isbn_cover_images/9780078028229/9780078028229_smallCoverImage.gif)
![Electric Circuits. (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780134746968/9780134746968_smallCoverImage.gif)
![Engineering Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780078028151/9780078028151_smallCoverImage.gif)