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(s + 2)(s + 4) C(s) R(s) (S+3)(6s² + 4s + 5)

(s + 2)(s + 4) C(s) R(s) (S+3)(6s² + 4s + 5)

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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Find the State-Space Representation for the following transfer function:

The given transfer function in the Laplace domain is represented as: \[ \frac{C(s)}{R(s)} = \frac{(s + 2)(s + 4)}{(s + 3)(6s^2 + 4s + 5)} \] ### Explanation: - **Numerator:** \( (s + 2)(s + 4) \) - This part represents the zeros of the system, determined by setting the numerator equal to zero (\(s = -2, -4\)). - **Denominator:** \( (s + 3)(6s^2 + 4s + 5) \) - This part contains the poles of the system. One of the poles is at \(s = -3\). The quadratic term \(6s^2 + 4s + 5\) needs to be solved to find the remaining poles. ### Context: Transfer functions are critical in control systems for analyzing the input-output relationship in the Laplace domain. They provide insights into the system's stability and behavior.
Transcribed Image Text:The given transfer function in the Laplace domain is represented as: \[ \frac{C(s)}{R(s)} = \frac{(s + 2)(s + 4)}{(s + 3)(6s^2 + 4s + 5)} \] ### Explanation: - **Numerator:** \( (s + 2)(s + 4) \) - This part represents the zeros of the system, determined by setting the numerator equal to zero (\(s = -2, -4\)). - **Denominator:** \( (s + 3)(6s^2 + 4s + 5) \) - This part contains the poles of the system. One of the poles is at \(s = -3\). The quadratic term \(6s^2 + 4s + 5\) needs to be solved to find the remaining poles. ### Context: Transfer functions are critical in control systems for analyzing the input-output relationship in the Laplace domain. They provide insights into the system's stability and behavior.
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