If G[s] = for this system? (a) 1 (b) 2 (c) 3 (d) 4 (s+2) (s+1)(s² +4s+3) and Ge[s] = K, how many root locus branches are there
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.
![If \( G[s] = \frac{(s+2)}{(s+1)(s^2+4s+3)} \) and \( G_C[s] = K \), how many root locus branches are there for this system?
(a) 1
(b) 2
(c) 3
(d) 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ecf1484-f95f-4119-9858-43c8382b92c0%2F7eeadd76-c55d-4797-aa7d-a15294aa60e0%2Fen4kpneq_processed.jpeg&w=3840&q=75)
![**Text Transcription:**
Assume the following block diagram for the entire exam.
**Block Diagram Explanation:**
The block diagram illustrates a signal processing system with the following components:
1. **Input Signal \( R[\omega] \):**
- This is the initial signal entering the system.
2. **Summation Block (\(\Sigma\)):**
- The summation block takes two inputs: the input signal \( R[\omega] \) and a feedback signal.
- It produces an error signal \( E[\omega] \) by calculating the difference between these inputs (indicated by the minus sign).
3. **Controller Block \( C_c[\omega] \):**
- This block processes the error signal \( E[\omega] \).
- It outputs a modified signal to the next block.
4. **System Block \( G[\omega] \):**
- This block receives the output from \( C_c[\omega] \).
- It further processes the signal and generates the final output \( Y[\omega] \).
5. **Output Signal \( Y[\omega] \):**
- The final output of the system is represented by \( Y[\omega] \).
6. **Feedback Loop:**
- A feedback loop connects the output \( Y[\omega] \) back to the summation block.
- This loop indicates that the output signal is used as part of the input to the summation block to generate the error signal.
The diagram represents a typical control system where feedback is used to adjust the processing of the input signal to achieve desired output characteristics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ecf1484-f95f-4119-9858-43c8382b92c0%2F7eeadd76-c55d-4797-aa7d-a15294aa60e0%2Fac2x9p_processed.jpeg&w=3840&q=75)
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