Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
a. Provide and expression for the transfer function G(s) = Y(s)/U(s) of the system. b. Determine the poles and zeros of this system.

a. Provide and expression for the transfer function G(s) = Y(s)/U(s) of the system. b. Determine the poles and zeros of this system.

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...
See similar textbooks
icon
Related questions
Question
**State Space Representation of a Single-Input, Single-Output (SISO) System** A single-input, single-output (SISO) system is defined by the following state equations: \[ \dot{x}(t) = Ax(t) + Bu(t) \] \[ y(t) = Cx(t) + Du(t) \] For this system, the matrices are given as: \[ A = \begin{pmatrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ -5726 & -3765 & -477 & -15 \end{pmatrix} \] \[ B = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} \] \[ C = \begin{pmatrix} 75 & 55 & 13 & 1 \end{pmatrix} \] \[ D = 0 \] **Tasks:** a. **Derive the Transfer Function \( G(s) = \frac{Y(s)}{U(s)} \) of the System** To find the transfer function, perform the following steps: 1. Compute the Laplace transform of the state equations assuming zero initial conditions. 2. Obtain \( G(s) = C(sI - A)^{-1}B + D \). b. **Determine the Poles and Zeros of the System** - **Poles**: The poles of the system are the eigenvalues of matrix \( A \) or the roots of the characteristic equation \( \det(sI - A) = 0 \). - **Zeros**: The zeros of the system are the values of \( s \) that make \( G(s) = 0 \). By solving these, you determine the dynamic characteristics of the system's response.
Transcribed Image Text:**State Space Representation of a Single-Input, Single-Output (SISO) System** A single-input, single-output (SISO) system is defined by the following state equations: \[ \dot{x}(t) = Ax(t) + Bu(t) \] \[ y(t) = Cx(t) + Du(t) \] For this system, the matrices are given as: \[ A = \begin{pmatrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ -5726 & -3765 & -477 & -15 \end{pmatrix} \] \[ B = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} \] \[ C = \begin{pmatrix} 75 & 55 & 13 & 1 \end{pmatrix} \] \[ D = 0 \] **Tasks:** a. **Derive the Transfer Function \( G(s) = \frac{Y(s)}{U(s)} \) of the System** To find the transfer function, perform the following steps: 1. Compute the Laplace transform of the state equations assuming zero initial conditions. 2. Obtain \( G(s) = C(sI - A)^{-1}B + D \). b. **Determine the Poles and Zeros of the System** - **Poles**: The poles of the system are the eigenvalues of matrix \( A \) or the roots of the characteristic equation \( \det(sI - A) = 0 \). - **Zeros**: The zeros of the system are the values of \( s \) that make \( G(s) = 0 \). By solving these, you determine the dynamic characteristics of the system's response.
Expert Solution
steps

Step by step

Solved in 2 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Nyquist Plot
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS