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20 10 Let G[s] s(s+2) reference input is a unit step. (a) 0 (b) 0.5 (c) 1.0 (d) 1.5 = and Ge[s] = K = 0.1 . Find the steady-state error when the

20 10 Let G[s] s(s+2) reference input is a unit step. (a) 0 (b) 0.5 (c) 1.0 (d) 1.5 = and Ge[s] = K = 0.1 . Find the steady-state error when the

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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The image presents a block diagram associated with an exam. - The input to the system is \( R[a] \). - A summing junction (Σ) combines \( R[a] \) with feedback, resulting in an error signal \( E[a] \). - This error signal \( E[a] \) is then processed by the first block, labeled \( C_c[a] \). - The output of \( C_c[a] \) is fed into the second block \( G[a] \). - The output of the block \( G[a] \) is the final system output \( Y[a] \). - There is a feedback loop from the output \( Y[a] \) back to the summing junction, indicating a closed-loop system. This diagram typically represents a control system with feedback, where the system adjusts its behavior based on the difference between the desired and actual outputs.
Transcribed Image Text:The image presents a block diagram associated with an exam. - The input to the system is \( R[a] \). - A summing junction (Σ) combines \( R[a] \) with feedback, resulting in an error signal \( E[a] \). - This error signal \( E[a] \) is then processed by the first block, labeled \( C_c[a] \). - The output of \( C_c[a] \) is fed into the second block \( G[a] \). - The output of the block \( G[a] \) is the final system output \( Y[a] \). - There is a feedback loop from the output \( Y[a] \) back to the summing junction, indicating a closed-loop system. This diagram typically represents a control system with feedback, where the system adjusts its behavior based on the difference between the desired and actual outputs.
**Problem Statement:** Let \( G[s] = \frac{10}{s(s+2)} \) and \( G_c[s] = K = 0.1 \). Find the steady-state error when the reference input is a unit step. **Options:** (a) 0 (b) 0.5 (c) 1.0 (d) 1.5 **Explanation:** This problem involves determining the steady-state error for a given control system with a specified transfer function and a controller gain when the input is a unit step. The steady-state error can typically be calculated using the final value theorem and the properties of the given system. The transfer functions provided represent the open-loop transfer function \( G[s] \) and the controller \( G_c[s] \), and solving the problem requires understanding how these expressions determine error in steady-state conditions, particularly for a unit step input.
Transcribed Image Text:**Problem Statement:** Let \( G[s] = \frac{10}{s(s+2)} \) and \( G_c[s] = K = 0.1 \). Find the steady-state error when the reference input is a unit step. **Options:** (a) 0 (b) 0.5 (c) 1.0 (d) 1.5 **Explanation:** This problem involves determining the steady-state error for a given control system with a specified transfer function and a controller gain when the input is a unit step. The steady-state error can typically be calculated using the final value theorem and the properties of the given system. The transfer functions provided represent the open-loop transfer function \( G[s] \) and the controller \( G_c[s] \), and solving the problem requires understanding how these expressions determine error in steady-state conditions, particularly for a unit step input.
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