**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.

Answered: Image /qna-images/answer/d5ca47d8-077a-44ed-9b2c-b024945057ba.jpg

Answered: 18. ) Let G[s] = (a) Gc [s] (b) Gc [s]…

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)

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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