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Question 2. Given the following feedback system, a. Find the forward transfer function b. What system type is this? c. What is the steady-state error for an input r(t) = 4 tu(t) R(S) Σ 0.5 s2+ 3s 1 S 3 s+1 Σ C(s)

Question 2. Given the following feedback system, a. Find the forward transfer function b. What system type is this? c. What is the steady-state error for an input r(t) = 4 tu(t) R(S) Σ 0.5 s2+ 3s 1 S 3 s+1 Σ C(s)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Control Systems: Feedback System Analysis #### Question 2: Given the following feedback system, **a. Find the forward transfer function** **b. What system type is this?** **c. What is the steady-state error for an input \( r(t) = 4t \cdot u(t) \) ?** #### System Diagram Below is the block diagram of the feedback system: ``` -------------- | 0.5/(s^2 + 3s) | -------------- | V -------------- | 1/s | -------------- | V --------- | + | -----> C(s) | ∑ | ---|-----------| | \ - | | --------- | | | V | -------------- | | 3/(s+1) | | -------------- | | |________| ``` 1. The input \( R(s) \) goes into a summing junction. 2. The output of the summing junction passes through a block with transfer function \( \frac{0.5}{s^2 + 3s} \). 3. This output then splits into two paths: - One path goes through a block with a transfer function \( \frac{1}{s} \). - The other path goes through a block with a transfer function \( \frac{3}{s+1} \). 4. The outputs of these two blocks are summed again with one of them being negative and the other positive, resulting in the output \( C(s) \). #### Explanation: To solve this problem, let's break it down into the required parts: **a. Find the forward transfer function** **b. Determine the system type** **c. Calculate the steady-state error for an input \( r(t) = 4t \cdot u(t) \) ** Each step will require applying control system principles, such as using the Laplace Transform and understanding system types and error constants. #### Detailed Block Diagram Explanation 1. **Summing Junction:** Adds and subtracts the incoming signals. 2. **Transfer Functions:** Defined by blocks representing ratios of output to input in the Laplace domain. 3. **
Transcribed Image Text:### Control Systems: Feedback System Analysis #### Question 2: Given the following feedback system, **a. Find the forward transfer function** **b. What system type is this?** **c. What is the steady-state error for an input \( r(t) = 4t \cdot u(t) \) ?** #### System Diagram Below is the block diagram of the feedback system: ``` -------------- | 0.5/(s^2 + 3s) | -------------- | V -------------- | 1/s | -------------- | V --------- | + | -----> C(s) | ∑ | ---|-----------| | \ - | | --------- | | | V | -------------- | | 3/(s+1) | | -------------- | | |________| ``` 1. The input \( R(s) \) goes into a summing junction. 2. The output of the summing junction passes through a block with transfer function \( \frac{0.5}{s^2 + 3s} \). 3. This output then splits into two paths: - One path goes through a block with a transfer function \( \frac{1}{s} \). - The other path goes through a block with a transfer function \( \frac{3}{s+1} \). 4. The outputs of these two blocks are summed again with one of them being negative and the other positive, resulting in the output \( C(s) \). #### Explanation: To solve this problem, let's break it down into the required parts: **a. Find the forward transfer function** **b. Determine the system type** **c. Calculate the steady-state error for an input \( r(t) = 4t \cdot u(t) \) ** Each step will require applying control system principles, such as using the Laplace Transform and understanding system types and error constants. #### Detailed Block Diagram Explanation 1. **Summing Junction:** Adds and subtracts the incoming signals. 2. **Transfer Functions:** Defined by blocks representing ratios of output to input in the Laplace domain. 3. **
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