2- Consider the following feedback system R(s) + M 12 2s5-s4+s²+4 1 S C(s) a) Find the closed-loop transfer function G(s) = C(s)/R(s) b) Create the Routh-Hurwitz Table c) From the table indicate how many poles are in the left half-plane (LHP), how many in the right half-plane (RHP) and on the jo axis. Explain your answers. Draw conclusions about the stability of the close-loop system
2- Consider the following feedback system R(s) + M 12 2s5-s4+s²+4 1 S C(s) a) Find the closed-loop transfer function G(s) = C(s)/R(s) b) Create the Routh-Hurwitz Table c) From the table indicate how many poles are in the left half-plane (LHP), how many in the right half-plane (RHP) and on the jo axis. Explain your answers. Draw conclusions about the stability of the close-loop system
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Please do #2
![### Practice Problems for Exam 2 Chapters 5, 6 & 7
#### Problem 1:
**Task:** Use block diagram algebra to reduce the following system to a single block; find the overall transfer function \( G(s) = \frac{C(s)}{R(s)} \).
**Diagram:**
\[ \begin{array}{c}
\begin{array}{ccc} \quad \quad R(s) \quad \quad & \quad \quad \quad \quad \quad & \quad \quad C(s)\end{array}
\\
\begin{array}{ccccc}
& + & \\
& \rightarrow & \left(\sum \right) & \rightarrow & \frac{1}{5} \quad \rightarrow \quad \left(\times \right) \rightarrow \frac{2}{s+3} \rightarrow & C(s)\\
& - \quad \quad \quad \quad \uparrow & & \rightarrow 4s &\\
\rightarrow & \left( \times \right) \quad 3 & & 3 & \rightarrow \quad & \rightarrow
\end{array}
\end{array}\]
The diagram illustrates a control system with a feedback loop. The input \( R(s) \) passes through a summing junction that adds the feedback signal before going through the series of blocks representing different transfer functions.
#### Problem 2:
**Task:** Consider the following feedback system:
**Diagram:**
\[ \begin{array}{c}
R(s) \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad C(s) \\
\quad & + & \\
\quad & \rightarrow & \left(\sum \right) & \rightarrow \frac{12}{2s^5 - s^4 + s^2 + 4} \rightarrow C(s)\\
& - \quad \quad \quad 1/s & \uparrow & \\
& \rightarrow &
\end{array}\]
**Tasks for Analysis:**
- **a)** Find the closed-loop transfer function \( G(s) = \frac{C(s)}{R(s)} \).
- **b)** Create the Routh-Hurwitz Table.
- **c)** From](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe36fb7f7-6381-4add-b52b-9085dfd27844%2Ff67069c3-dc83-4106-9474-ce30606d21a7%2Flipo1mj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Practice Problems for Exam 2 Chapters 5, 6 & 7
#### Problem 1:
**Task:** Use block diagram algebra to reduce the following system to a single block; find the overall transfer function \( G(s) = \frac{C(s)}{R(s)} \).
**Diagram:**
\[ \begin{array}{c}
\begin{array}{ccc} \quad \quad R(s) \quad \quad & \quad \quad \quad \quad \quad & \quad \quad C(s)\end{array}
\\
\begin{array}{ccccc}
& + & \\
& \rightarrow & \left(\sum \right) & \rightarrow & \frac{1}{5} \quad \rightarrow \quad \left(\times \right) \rightarrow \frac{2}{s+3} \rightarrow & C(s)\\
& - \quad \quad \quad \quad \uparrow & & \rightarrow 4s &\\
\rightarrow & \left( \times \right) \quad 3 & & 3 & \rightarrow \quad & \rightarrow
\end{array}
\end{array}\]
The diagram illustrates a control system with a feedback loop. The input \( R(s) \) passes through a summing junction that adds the feedback signal before going through the series of blocks representing different transfer functions.
#### Problem 2:
**Task:** Consider the following feedback system:
**Diagram:**
\[ \begin{array}{c}
R(s) \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad C(s) \\
\quad & + & \\
\quad & \rightarrow & \left(\sum \right) & \rightarrow \frac{12}{2s^5 - s^4 + s^2 + 4} \rightarrow C(s)\\
& - \quad \quad \quad 1/s & \uparrow & \\
& \rightarrow &
\end{array}\]
**Tasks for Analysis:**
- **a)** Find the closed-loop transfer function \( G(s) = \frac{C(s)}{R(s)} \).
- **b)** Create the Routh-Hurwitz Table.
- **c)** From
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