### 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 DiagramBelow 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 Explanation1. **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. **

Here we need to calculate a) forward transfer functionb) system typeC) steady state error for input…

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)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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