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Introduction to Linear Time-Invariant Dynamic Systems for Students of Engineering

This text addresses a combination of system dynamics and responses, mechanical vibrations, mechanical and electrical systems, rigid body dynamics, and feedback control. Covered are free and forced, undamped and damped responses, in both the frequency and time domain with an emphasis on linear time-invariant (LTI) systems, including time- and Laplace-solutions of the governing ordinary differential equations. First-, second-, and fourth-order systems are addressed.

Electrical Engineering Engineering

Tác giả: William L. Hallauer Jr.
Nhà xuất bản: Virginia Tech
Nguồn: LibreTexts
Giấy phép: CC BY-NC
Ngôn ngữ: EN

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Mục lục· 145 mục

01: Introduction First and Second Order Systems Analysis MATLAB Graphing
1.01: Introduction
1.02: LTI Systems and ODEs
1.03: The Mass-Damper System I - example of 1st order linear time-invariant (LTI) system and ordinary differential equation (ODE)
1.04: A Short Discussion of Engineering Models
1.05: The Mass-Damper System II - Solving the 1st order LTI ODE for time response given a pulse excitation and an IC
1.06: The Mass-Damper System III - Numerical and Graphical Evaluation of Time Response using MATLAB
1.07: Some notes regarding good engineering graphical practice with reference to Figure 1.6.1
1.08: Plausibility Checks of System Response Equations and Calculations
1.09: The Mass-Damper-Spring System - A 2nd Order LTI System and ODE
1.10: The Mass-Spring System - Solving a 2nd order LTI ODE for Time Response
1.11: Homework problems for Chapter 1
02: Complex Numbers and Arithmetic Laplace Transforms and Partial-Fraction Expansion
2.01: Review of Complex Numbers and Arithmetic
2.02: Introduction to Application of Laplace Transforms
2.03: Partial-Fraction Expansion
2.04: Additional Useful Functions and Laplace Transforms
2.05: Chapter 2 Homework
03: Mechanical Units Low-Order Mechanical Systems and Simple Transient Responses of First Order Systems
3.01: Common Mechanical Units
3.02: Calculation of Mass from Measured Weight
3.03: Reaction Wheel
3.04: Simples Transient Responses of First Order Systems First Order Time Constant and Settling Time
3.05: Aileron-Induced Rolling of an Airplane or Missile
3.06: Translational Spring and Viscous Damper (Dapshot)
3.07: More Examples of Damped Mechanical Systems
3.08: Chapter 3 Homework
04: Frequency Response of First Order Systems Transfer Functions and General Method for Derivation of Frequency Response
4.01: Definition of Frequency Response
4.02: Response of a First Order System to a Suddenly Applied Cosine
4.03: Frequency Response of the First Order Damper-Spring System
4.04: Period Frequency and Phase of Periodic Signals
4.05: Derivation of the Complex Frequency-Response Function
4.06: Trasfer Function General Definition
4.07: Frequency-Response Function from Transfer Function
4.08: Chapter 4 Homework
05: Basic Electrical Components and Circuits
5.01: Introduction
5.02: Passive Components
5.03: Op-Amps and Op-Amp Circuits
5.04: RC Band-Pass Filter
5.05: Chapter 5 Homework
06: General Time Response of First Order Systems by Application of the Convolution Integral
6.01: The Convolution Transform and Its Inverse the Convolution Integral
6.02: General Solution of the Standard Stable First Oder ODE and IC
6.03: Examples of First Order System Response
6.04: General Solution of the Standard First Order Problem
6.05: Numerical Algorithm for the General Solution of the Standard First Order Problem
6.06: Chapter 6 Homework
07: Undamped Second Order Systems
7.01: Standard Form for Undamped Second Order Systems and Natural Frequency
7.02: General Solution for Output of Undamped Second Order Systems
7.03: Simple IC Response and Step Response of Undamped Second Order Systems
7.04: Discussion of Physical Applicability of Step-Response Solutions
7.05: Dynamic Motion of a Mechanical System
7.06: Introduction to Vibrations
7.07: Chapter 7 Homework
08: Pulse Inputs Dirac Delta Function Impulse Response Initial Value Theorem Convolution Sum
8.01: Flat Pulse
8.02: Impulse-Momentum Theorem
8.03: Flat Impulse
8.04: Dirac Delta Function
8.05: Ideal Impulse Response of a Standard Stable First Order System
8.06: Derivation of the Initial-Value Theorem
8.07: Ideal Impulse Response of an Undamped Second Order System
8.08: Ideal Impulse Response Versus Real Response of Systems
8.09: Unit-Step-Response Function and IRF
8.10: The Convolution Integral as a Superposition of Ideal Impulse Responses
8.11: Approximate Numerical Solutions Based on the Convolution Sum
8.12: Chapter 8 Homework
09: Damped Second Order Systems
9.01: Homogenous Solutions
9.02: Standard Form ODE
9.03: General Solution for Underdamped Second Order Systems
9.04: IC Transient Response of Underdamped Second Order Systems
9.05: Calculation of Viscous Damping Ratio
9.06: Step Response of Underdamped Second Order Systems
9.07: Ideal Impulse Response of Underdamped Second Order Systems
9.08: Step-Response Specifications for Underdamped Systems
9.09: Identification of a Mass-Damper-Spring System
9.10: Deriving Response Equations for Overdamped Second Order Systems
9.11: Chapter 9 Homework
10: Second Order Systems
10.01: Frequency Response of Undamped Second Order Systems Resonance
10.02: Frequency Response of Damped Second Order Systems
10.03: Frequency Response of Mass-Damper-Spring Systems
10.04: Frequency-Response Function of an RC Band-Pass Filter
10.05: Common Frequency-Response Functions
10.06: Beating Response of Second Order Systems to Suddenly Applied Sinusoidal Excitation
10.07: Chapter 10 Homework
11: Mechanical Systems with Rigid-Body Plane Translation and Rotation
11.01: Equations of Motion for a Rigid Body in General Plane Motion
11.02: Equation of Motion for a Rigid Body in Pure Plane Rotation
11.03: Examples
11.04: Chapter 4 Homework
12: Vibration Modes of Undamped Mechanical Systems with Two Degrees of Freedom
12.01: Undamped Mass-Spring System
12.02: Undamped Two-Mass-Two-Spring System
12.03: Vibration Modes of an Undamped Typical Model of a Wing
12.04: Chapter 12 Homework
13: Laplace Block Diagrams and Feedback-Control Systems Background
13.01: Laplace Block Diagrams for an RC Band-Pass Filter
13.02: Laplace Block Diagram with Feedback Branches
13.03: Forced Response of an m-c-k System with Base Excitation
13.04: Chapter 13 Homework
14: Introduction to Feedback Control
14.01: Initial Definitions and Terminology
14.02: Definitions and Examples of Open-Loop Control Systems
14.03: Closed-Loop Control of Rotor Position (1)
14.04: Transfer Function of a Single Closed Loop
14.05: Closed-Loop Control of Rotor Position (2)
14.06: Comments Regarding Control Theory
14.07: Chapter 14 Homework
15: Input-Error Operations
15.01: Initial Definitions PID Control
15.02: Examples of P and PI Control
15.03: Derivation of the Final-Value Theorem
15.04: Example of PD Control
15.05: Chapter 15 Homework
16: Introduction to System Stability - Time-Response Criteria
16.01: General Time-Response Stability Criterion for LTI Systems
16.02: Stable and Snstable PD-Controlled-Rotor Systems
16.03: Rouths Stability Criteria
16.04: Loci of Roots for Second Order Systems
16.05: Loci of Roots for Third Order Systems
16.06: Open-Loop Transfer Functions and Loci of Roots
16.07: Chapter 16 Homework
17: Introduction to System Stability- Frequency-Response Criteria
17.01: Gain Margins Phase Margins and Bode Diagrams
17.02: Nyquist Plots
17.03: The Practical Effects of an Open-Loop Transfer-Function Pole at s 0 j0
17.04: The Nyquist Stability Criterion
17.05: Chapter 17 Homework
18: Appendix A- Table and Derivations of Laplace Transform Pairs
18.01: A.1- Table of Laplace Transform Pairs
18.02: A.2- Laplace Transform of a Ratio of Two Polynomials
18.03: A.3- Derivation of the Laplace Transform of a Definite Integral
18.04: A.4- Applications of the Laplace Transform of a Definite Integral
18.05: A.5- Derivation of the Laplace Transform of the Convolution Integral
19: Appendix B- Notes on Work Energy and Power in Mechanical Systems and Electrical Circuits
19.01: B.1- Definitions of Work and Power
19.02: B.2- Mechanical Work Energy and Power
19.03: B.3- Work Energy and Power in Electrical Circuits
19.04: B.4- Analogies Between an m-c-k Mechanical System and an LRC Electrical B-8 Circuit
19.05: B.5- Hysteresis and Dissipation of Mechanical Energy by Damping