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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)
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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### 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
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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