18. ) Let G[s] = (a) Gc [s] (b) Gc [s] = (c) Ge[s] = 0.167(S-1) S 0.75 (s+1) S 0.5 (s+1) S (S-1) (s+1)(s+2) (d) No such controller exists. . Select a controller to stabilize the closed-loop system.
18. ) Let G[s] = (a) Gc [s] (b) Gc [s] = (c) Ge[s] = 0.167(S-1) S 0.75 (s+1) S 0.5 (s+1) S (S-1) (s+1)(s+2) (d) No such controller exists. . Select a controller to stabilize the closed-loop system.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![**Problem 18: Control System Stabilization**
Given the transfer function for the open-loop system:
\[ G[s] = \frac{(s-1)}{(s+1)(s+2)} \]
Select a controller to stabilize the closed-loop system.
Options for controllers:
(a) \[ G_C[s] = \frac{0.167(s-1)}{s} \]
(b) \[ G_C[s] = \frac{0.75(s+1)}{s} \]
(c) \[ G_C[s] = \frac{0.5(s+1)}{s} \]
(d) No such controller exists.
Choose the appropriate controller among the given options to achieve stability in the closed-loop system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ecf1484-f95f-4119-9858-43c8382b92c0%2Fd5ca47d8-077a-44ed-9b2c-b024945057ba%2Fh8kqy6s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 18: Control System Stabilization**
Given the transfer function for the open-loop system:
\[ G[s] = \frac{(s-1)}{(s+1)(s+2)} \]
Select a controller to stabilize the closed-loop system.
Options for controllers:
(a) \[ G_C[s] = \frac{0.167(s-1)}{s} \]
(b) \[ G_C[s] = \frac{0.75(s+1)}{s} \]
(c) \[ G_C[s] = \frac{0.5(s+1)}{s} \]
(d) No such controller exists.
Choose the appropriate controller among the given options to achieve stability in the closed-loop system.
![Assume the following block diagram for the entire exam.
The diagram is a block diagram illustrating a control system or signal processing system. Here's a detailed explanation:
1. **Input Signal (R[ω])**: The diagram begins with an input signal denoted as R[ω], which enters a summation node.
2. **Summation Node (Σ)**: The summation node sums the input signal R[ω] with a feedback signal (denoted by the line looping back to the summation point). The result of this summation is an error signal E[ω].
3. **Error Signal (E[ω])**: The error signal E[ω] is then fed into a controller block labeled Gc[ω].
4. **Controller Block (Gc[ω])**: The controller processes the error signal to produce a controlled output.
5. **Controlled Output**: The output from the controller block then goes to another block labeled G[ω].
6. **Block G[ω]**: This block represents a system or plant that processes the input from the controller block to generate the final output signal Y[ω].
7. **Output Signal (Y[ω])**: The final output of the system is Y[ω]. This output is also fed back into the summation node as part of the feedback loop.
**Explanation of Diagram Components:**
- **Feedback Loop**: The path from Y[ω] back to the summation node represents a feedback mechanism, which is essential for adjusting the output in relation to the input.
- **Blocks and Signals**: Each block represents a system function or operation applied to signals that help control or modify the response of the system.
This diagram illustrates the interactions between different components in a closed-loop control system, crucial for tasks requiring precise output regulation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ecf1484-f95f-4119-9858-43c8382b92c0%2Fd5ca47d8-077a-44ed-9b2c-b024945057ba%2Fclaiqyr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Assume the following block diagram for the entire exam.
The diagram is a block diagram illustrating a control system or signal processing system. Here's a detailed explanation:
1. **Input Signal (R[ω])**: The diagram begins with an input signal denoted as R[ω], which enters a summation node.
2. **Summation Node (Σ)**: The summation node sums the input signal R[ω] with a feedback signal (denoted by the line looping back to the summation point). The result of this summation is an error signal E[ω].
3. **Error Signal (E[ω])**: The error signal E[ω] is then fed into a controller block labeled Gc[ω].
4. **Controller Block (Gc[ω])**: The controller processes the error signal to produce a controlled output.
5. **Controlled Output**: The output from the controller block then goes to another block labeled G[ω].
6. **Block G[ω]**: This block represents a system or plant that processes the input from the controller block to generate the final output signal Y[ω].
7. **Output Signal (Y[ω])**: The final output of the system is Y[ω]. This output is also fed back into the summation node as part of the feedback loop.
**Explanation of Diagram Components:**
- **Feedback Loop**: The path from Y[ω] back to the summation node represents a feedback mechanism, which is essential for adjusting the output in relation to the input.
- **Blocks and Signals**: Each block represents a system function or operation applied to signals that help control or modify the response of the system.
This diagram illustrates the interactions between different components in a closed-loop control system, crucial for tasks requiring precise output regulation.
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