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A system has the following transfer function: 6s2 + 2s + 26 G(s) : 2s2 + 8

A system has the following transfer function: 6s2 + 2s + 26 G(s) : 2s2 + 8

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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A system has the following transfer function: \[ G(s) = \frac{6s^2 + 2s + 26}{2s^2 + 8}. \] This is a rational transfer function where the numerator is \(6s^2 + 2s + 26\) and the denominator is \(2s^2 + 8\). These polynomials represent the dynamics of a linear time-invariant (LTI) system in the Laplace domain. The transfer function can be used to analyze the system's stability, frequency response, and other dynamic characteristics.
Transcribed Image Text:A system has the following transfer function: \[ G(s) = \frac{6s^2 + 2s + 26}{2s^2 + 8}. \] This is a rational transfer function where the numerator is \(6s^2 + 2s + 26\) and the denominator is \(2s^2 + 8\). These polynomials represent the dynamics of a linear time-invariant (LTI) system in the Laplace domain. The transfer function can be used to analyze the system's stability, frequency response, and other dynamic characteristics.
### Problem Statement Given the transfer function: \[ \frac{Y(s)}{U(s)} = \frac{2}{2s^2 + 8} \] 1. **Convert it to a state-space equation in controllable canonical form.** 2. **Determine the category of system stability when the input \( u = 0 \).** 3. **Is this system observable?** 4. **If we wish to place the eigenvalues of \( A \) to \((-2 + j, -2 - j)\), find the state-space feedback gain \( K \).** *You must give a detailed procedure.*
Transcribed Image Text:### Problem Statement Given the transfer function: \[ \frac{Y(s)}{U(s)} = \frac{2}{2s^2 + 8} \] 1. **Convert it to a state-space equation in controllable canonical form.** 2. **Determine the category of system stability when the input \( u = 0 \).** 3. **Is this system observable?** 4. **If we wish to place the eigenvalues of \( A \) to \((-2 + j, -2 - j)\), find the state-space feedback gain \( K \).** *You must give a detailed procedure.*
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