Chap2. Modeling in the Frequency Domain

Slides:

Advertisements

Similar presentations

Solving Differential Equations BIOE Solving Differential Equations Ex. Shock absorber with rigid massless tire Start with no input r(t)=0, assume.

Advertisements

LAPLACE TRANSFORMS.

Signal Processing in the Discrete Time Domain Microprocessor Applications (MEE4033) Sogang University Department of Mechanical Engineering.

Lecture 131 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001.

H(s) x(t)y(t) 8.b Laplace Transform: Y(s)=X(s) H(s) The Laplace transform can be used in the solution of ordinary linear differential equations. Let’s.

Chapter 4 Modelling and Analysis for Process Control

Lecture 141 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001.

Chapter 7 Laplace Transforms. Applications of Laplace Transform notes Easier than solving differential equations –Used to describe system behavior –We.

Laplace Transforms 1. Standard notation in dynamics and control (shorthand notation) 2. Converts mathematics to algebraic operations 3. Advantageous for.

Bogazici University Dept. Of ME. Laplace Transforms Very useful in the analysis and design of LTI systems. Operations of differentiation and integration.

Laplace Transform Applications of the Laplace transform

Professor Walter W. Olson Department of Mechanical, Industrial and Manufacturing Engineering University of Toledo Loop Transfer Function Real Imaginary.

Chapter 10 Differential Equations: Laplace Transform Methods

Chapter 4 Laplace Transforms.

Topic-laplace transformation Presented by Harsh PATEL

ORDINARY DIFFERENTIAL EQUATION (ODE) LAPLACE TRANSFORM.

ECEN3714 Network Analysis Lecture #9 2 February 2015 Dr. George Scheets n Read 13.8 n Problems: 13.16a, 19a,

Sistem Kontrol I Kuliah II : Transformasi Laplace Imron Rosyadi, ST 1.

Chapter 9 Laplace Transform §9.1 Definition of Laplace Transform §9.2 Properties of Laplace Transform §9.3 Convolution §9.4 Inverse Laplace Transform §9.5.

SE 207: Modeling and Simulation Introduction to Laplace Transform

MESB 374 System Modeling and Analysis Inverse Laplace Transform and I/O Model.

INTRODUCTION TO LAPLACE TRANSFORM Advanced Circuit Analysis Technique.

Laplace Transforms 1. Standard notation in dynamics and control (shorthand notation) 2. Converts mathematics to algebraic operations 3. Advantageous for.

Introduction to Laplace Transforms. Definition of the Laplace Transform  Some functions may not have Laplace transforms but we do not use them in circuit.

(e.g., deviation variables!)

Laplace Transforms 1. Standard notation in dynamics and control (shorthand notation) 2. Converts mathematics to algebraic operations 3. Advantageous for.

Mathematical Models and Block Diagrams of Systems Regulation And Control Engineering.

Ch2 Mathematical models of systems

10. Laplace TransforM Technique

Using Partial Fraction Expansion

Chapter 7 The Laplace Transform

Inverse Laplace Transforms (ILT)

Modeling Transient Response So far our analysis has been purely kinematic: The transient response has been ignored The inertia, damping, and elasticity.

Alexander-Sadiku Fundamentals of Electric Circuits

자동제어공학 2. 물리적 시스템의 전달함수 정 우 용.

University of Warwick: AMR Summer School 4 th -6 th July, 2016 Structural Identifiability Analysis Dr Mike Chappell, School of Engineering, University.

Mathematical Models of Control Systems

Lesson 11: Solving Mechanical System Dynamics Using Laplace Transforms

LAPLACE TRANSFORMS.

Lec 4. the inverse Laplace Transform

MESB374 System Modeling and Analysis Transfer Function Analysis

Laplace Transforms Chapter 3 Standard notation in dynamics and control

Chapter 6 Laplace Transform

Engineering Analysis I

Chapter 4 Transfer Function and Block Diagram Operations

EKT 119 ELECTRIC CIRCUIT II

Mathematical Models of Physical Systems

SIGMA INSTITUTE OF ENGINEERING

Mathematical Modeling of Control Systems

Finding Real Roots of Polynomial Equations

Complex Frequency and Laplace Transform

Lecture 3: Solving Diff Eqs with the Laplace Transform

Laplace Transform Properties

ME375 Handouts - Fall 2002 MESB374 Chapter8 System Modeling and Analysis Time domain Analysis Transfer Function Analysis.

Chapter 15 Introduction to the Laplace Transform

Islamic University of Gaza Faculty of Engineering

Modeling in the Frequency Domain

Mechatronics Engineering

Chapter 3 Example 2: system at rest (s.s.)

Fundamentals of Electric Circuits Chapter 15

4. Closed-Loop Responses Using the Laplace Transform Method

EKT 119 ELECTRIC CIRCUIT II

Solution of ODEs by Laplace Transforms

Example 1: Find the magnitude and phase angle of

Chapter 4. Time Response I may not have gone where I intended to go, but I think I have ended up where I needed to be. Pusan National University Intelligent.

Chapter 2. Mathematical Foundation

Mathematical Models of Control Systems

Laplace Transforms Important analytical method for solving linear ordinary differential equations. - Application to nonlinear ODEs? Must linearize first.

Laplace Transforms Important analytical method for solving linear ordinary differential equations. - Application to nonlinear ODEs? Must linearize first.

Loop Transfer Function

Presentation transcript:

Chap2. Modeling in the Frequency Domain Automatic Control Chap2. Modeling in the Frequency Domain Kim, Do Wan HANBAT NATIONAL UNIVERSITY

Outline Laplace transform Electrical network Mechanical system

Why do we study Laplace transform

Why do we study Laplace transform Differential Equation

Why do we study Laplace transform Transfer Function Differential Equation Solution

Why do we study Laplace transform Transfer Function Differential Equation Algebraic Equation Solution

Why do we study Laplace transform Transfer Function Time-domain Frequency-domain Differential Equation Algebraic Equation Solution

Why do we study Laplace transform Transfer Function Arrangement Differential Equation Algebraic Equation Solution

Partial Fraction Expansion Laplace transform Why do we study Laplace transform Transfer Function Arrangement Differential Equation Algebraic Equation Algebraic manipulation Solution Partial Fraction Expansion

Partial Fraction Expansion Laplace transform Why do we study Laplace transform Transfer Function Arrangement Differential Equation Algebraic Equation Algebraic manipulation Solution Partial Fraction Expansion Look-up table

Inverse definition (Inverse Laplace transform)

Laplace transform Example 2.1: Solution:

Laplace transform theorems Laplace transform table

Laplace transform Example 2.1: Solution:

Example 2.2: Find the inverse Laplace transform of Solution:

Partial-fraction Expansion Laplace transform Partial-fraction Expansion To find the inverse Laplace transform of a complicated function with Case 1: Roots of the denominator of are real and distinct. Example: where hence

Laplace transform

Case 2: Roots of the denominator of are real and repeated. Laplace transform Case 2: Roots of the denominator of are real and repeated. Example:

Case 3: Roots of the denominator of are complex or imaginary Laplace transform Case 3: Roots of the denominator of are complex or imaginary Example:

Laplace transform

Skill- Assessment Exercise 2. 1 Skill- Assessment Exercise 2. 2 Laplace transform Skill- Assessment Exercise 2. 1 Skill- Assessment Exercise 2. 2

Transfer function Definition Pole, Zero Block diagram Laplace transform Transfer function Definition Pole, Zero Block diagram

Laplace transform Evaluation Pole, Zero

Skill-Assessment Exercise 2.3 Skill-Assessment Exercise 2.4 Laplace transform Example 2.5 Skill-Assessment Exercise 2.3 Skill-Assessment Exercise 2.4 Skill-Assessment Exercise 2.5 Example 2.3 (Solution)

Impedance Relationships Electrical Network Impedance Relationships

Example: Transfer function relating the input voltage to the current Electrical Network Example: Transfer function relating the input voltage to the current Kirfchhoff's voltage law: LT Transfer function

Electrical Network Examples 2.6, 2.10

Mechanical system Translational System

Mechanical system Example 2.16

Governing Principle: sum of all forces are zero. Now, Mechanical system Governing Principle: sum of all forces are zero. Now, So, the differential equation is

Homework Problems 1, 2, 7, 8, 16, 22 Read Chap. 3.2 carefully!