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Question 1. 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 t² u(t) R(s) Σ 1.5 Σ 0.2 s 10 s(s+2) C(s)

Question 1. 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 t² u(t) R(s) Σ 1.5 Σ 0.2 s 10 s(s+2) 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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### Question 1: 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 \( r(t) = 4 t^2 u(t) \) --- #### Diagram Explanation: The diagram depicts a block diagram of a feedback control system. The key elements in the diagram are as follows: 1. **Input \( R(s) \):** The input function is represented by \( R(s) \). 2. **Summing Junctions:** - The first summing junction has two inputs: the actual input \( R(s) \) (to the positive input) and the feedback signal (to the negative input). - The second summing junction receives the output of the first block (an amplifier) and the feedback signal. 3. **Blocks:** - A block with a gain of 1.5 follows the first summing junction. - After the second summing junction, the system is connected to a block with a transfer function of \( \frac{10}{s(s+2)} \). - A feedback path contains a block with a transfer function of \( 0.2s \). 4. **Output \( C(s) \):** The output function is represented by \( C(s) \). In summary, the block diagram includes a combination of summing junctions and transfer functions working together to form a feedback control system. Each block plays a specific role in the overall transfer function and system dynamics.
Transcribed Image Text:### Question 1: 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 \( r(t) = 4 t^2 u(t) \) --- #### Diagram Explanation: The diagram depicts a block diagram of a feedback control system. The key elements in the diagram are as follows: 1. **Input \( R(s) \):** The input function is represented by \( R(s) \). 2. **Summing Junctions:** - The first summing junction has two inputs: the actual input \( R(s) \) (to the positive input) and the feedback signal (to the negative input). - The second summing junction receives the output of the first block (an amplifier) and the feedback signal. 3. **Blocks:** - A block with a gain of 1.5 follows the first summing junction. - After the second summing junction, the system is connected to a block with a transfer function of \( \frac{10}{s(s+2)} \). - A feedback path contains a block with a transfer function of \( 0.2s \). 4. **Output \( C(s) \):** The output function is represented by \( C(s) \). In summary, the block diagram includes a combination of summing junctions and transfer functions working together to form a feedback control system. Each block plays a specific role in the overall transfer function and system dynamics.
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