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Using root-locus techniques, design the lead compensator

Using root-locus techniques, design the lead compensator

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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**Questions** 1. Using root-locus techniques, design the lead compensator (find \(a\), \(b\), and \(K\) of \(D(s)\)) so that the system is stable and the dominant poles of the closed-loop transfer function are at \(s = -10 \pm 12j\). The design is not unique. 2. What is the steady-state error to a unit-step reference input using your design? 3. Estimate the dynamics using your design (\(t_r\), \(t_s\), \(M_p\)). --- **Diagram Explanation** The block diagram shows a control system with a feedback loop. It consists of the following components: - **Input (R):** The reference input to the system. - **Summing Junction (\(\Sigma\)):** This block adds the input signal \(R\) and the feedback signal (subtracted), providing the error signal to the next block. - **Lead Compensator (D(s)):** The mathematical representation given by \(D(s) = K \frac{s+b}{s+a}\). This block processes the error signal to adjust the control response. - **Plant Transfer Function:** Represented by the block \(\frac{1}{s^2 + 2s + 101}\). This block models the system's dynamics. - **Output (Y):** The output signal of the system. - **Feedback Loop:** The output \(Y\) is fed back to the summing junction for comparison with the input \(R\). **Figure 1 - Questions 1, 2, 3, and 4**
Transcribed Image Text:**Questions** 1. Using root-locus techniques, design the lead compensator (find \(a\), \(b\), and \(K\) of \(D(s)\)) so that the system is stable and the dominant poles of the closed-loop transfer function are at \(s = -10 \pm 12j\). The design is not unique. 2. What is the steady-state error to a unit-step reference input using your design? 3. Estimate the dynamics using your design (\(t_r\), \(t_s\), \(M_p\)). --- **Diagram Explanation** The block diagram shows a control system with a feedback loop. It consists of the following components: - **Input (R):** The reference input to the system. - **Summing Junction (\(\Sigma\)):** This block adds the input signal \(R\) and the feedback signal (subtracted), providing the error signal to the next block. - **Lead Compensator (D(s)):** The mathematical representation given by \(D(s) = K \frac{s+b}{s+a}\). This block processes the error signal to adjust the control response. - **Plant Transfer Function:** Represented by the block \(\frac{1}{s^2 + 2s + 101}\). This block models the system's dynamics. - **Output (Y):** The output signal of the system. - **Feedback Loop:** The output \(Y\) is fed back to the summing junction for comparison with the input \(R\). **Figure 1 - Questions 1, 2, 3, and 4**
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