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(3) For the system shown below do the following: Determine / Given J = 2 kg-m2, b = 1 N-m-s, determine K and Kh for the system to have = 0.5 and a settling time of T, = 3 sec. ● R K Js+b S C

(3) For the system shown below do the following: Determine / Given J = 2 kg-m2, b = 1 N-m-s, determine K and Kh for the system to have = 0.5 and a settling time of T, = 3 sec. ● R K Js+b S C

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Problem Statement (3) For the system shown below, do the following: - Determine \(\frac{\overline{C}}{\overline{R}}\). - Given \(J = 2 \, \text{kg-m}^2\), \(b = 1 \, \text{N-m-s}\), determine \(K\) and \(K_h\) for the system to have \(\xi = 0.5\) and a settling time of \(T_s = 3 \, \text{sec}\). ### System Diagram The system diagram includes the following components: 1. **Input \(\overline{R}\)**: This is the reference input to the system. 2. **Summing Junctions**: - The first summing junction receives the input \(\overline{R}\) and feedback from the system. - The second summing junction incorporates the effect of feedback through \(K_h\). 3. **Blocks**: - **\( \frac{K}{Js+b} \)**: Represents a transfer function with parameters \(J\) (moment of inertia) and \(b\) (damping coefficient). - **\( \frac{1}{s} \)**: Represents an integrator in the control system. 4. **Feedback Path**: - The feedback to the second summing junction is through a path with a gain \(K_h\). 5. **Output \(\overline{C}\)**: The controlled output of the system. ### Notes for Analysis - \(J = 2 \, \text{kg-m}^2\) and \(b = 1 \, \text{N-m-s}\) are constants used in the transfer function calculations. - The damping ratio \(\xi = 0.5\) and the settling time \(T_s = 3 \, \text{sec}\) are desired specifications for system performance. - Analysis involves using control system techniques to find the values of \(K\) and \(K_h\) that satisfy these system requirements. This system is a classic feedback control loop with the goal of achieving specific performance criteria by adjusting the system gains.
Transcribed Image Text:### Problem Statement (3) For the system shown below, do the following: - Determine \(\frac{\overline{C}}{\overline{R}}\). - Given \(J = 2 \, \text{kg-m}^2\), \(b = 1 \, \text{N-m-s}\), determine \(K\) and \(K_h\) for the system to have \(\xi = 0.5\) and a settling time of \(T_s = 3 \, \text{sec}\). ### System Diagram The system diagram includes the following components: 1. **Input \(\overline{R}\)**: This is the reference input to the system. 2. **Summing Junctions**: - The first summing junction receives the input \(\overline{R}\) and feedback from the system. - The second summing junction incorporates the effect of feedback through \(K_h\). 3. **Blocks**: - **\( \frac{K}{Js+b} \)**: Represents a transfer function with parameters \(J\) (moment of inertia) and \(b\) (damping coefficient). - **\( \frac{1}{s} \)**: Represents an integrator in the control system. 4. **Feedback Path**: - The feedback to the second summing junction is through a path with a gain \(K_h\). 5. **Output \(\overline{C}\)**: The controlled output of the system. ### Notes for Analysis - \(J = 2 \, \text{kg-m}^2\) and \(b = 1 \, \text{N-m-s}\) are constants used in the transfer function calculations. - The damping ratio \(\xi = 0.5\) and the settling time \(T_s = 3 \, \text{sec}\) are desired specifications for system performance. - Analysis involves using control system techniques to find the values of \(K\) and \(K_h\) that satisfy these system requirements. This system is a classic feedback control loop with the goal of achieving specific performance criteria by adjusting the system gains.
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