# An Introduction to Engineering Systems

### Pergamon Unified Engineering Series

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An Introduction to Engineering Systems discusses important aspects of systems engineering. It provides a background of analytical methods appropriate to hand-solution and computer solutions and shows the correlation that exists in alternate formulation. The book begins with an introduction to models and modeling of system elements. It then discusses the equilibrium formulations, signal flow graphs, and geometrical constraints of interconnected systems. After exploring aspects of system response and behavior in the time domain, the analyzes system response in the frequency domain. It also describes Z-transform methods and their application to discrete and continuous time systems. Finally, the book presents several approaches for testing the stability of linear systems. The text will provide students essential understanding of important methods of modern systems analysis.

## Table of Contents

Part I Models and Modeling

Chapter 1 Modeling of System Elements

1-1 Introduction

1-2 Model Characteristics

1-3 Model Approximations

1-4 Signals and Waveforms

1-a Electrical Elements

1-5 Introduction

1-6 The Capacitor

1-7 The Inductor

1-8 Mutual Inductance — Transformers

1-9 The Resistor

1-10 Sources

1-11 Duality

1-b Mechanical Elements

1-12 The Ideal Mass Element

1-13 The Spring

1-14 The Damper

1-15 Rigid Linkage (Mechanical Transformer)

1-16 Independent Mechanical Sources

1-17 Mechanical Elements — Rotational

1-c Fluid Elements

1-18 Liquid Systems

1-19 Liquid Resistance

1-20 Liquid Capacitance, Inductance, Sources

1-21 Gas Systems

1-d Thermal Elements

1-22 Thermal Systems

1-e N-Port Devices

1-23 Transducers

1-24 Active Networks

1-25 Modeling of Complicated Situations

1-26 Summary

Part II Interconnected Systems

Chapter 2 Interconnected Systems: Equilibrium Formulations

2-1 Interconnected Elements

2-a Kirchoff Formulation

2-2 Operational Notation

2-3 Through-Across Equilibrium Laws

2-4 Node Equilibrium Equations

2-5 Loop Equilibrium Equations

2-b State Variables and State Equations

2-6 Introduction to the State Formulation

2-7 State Equations for Linear Systems

2-8 Differential Equations in Normal Form

2-9 State Variable Transformation

2-10 Discrete and Sampled Time Systems

Chapter 3 Signal Flow Graphs

3-1 Properties of SFG

3-2 Graphing Differential Equations

3-3 Simultaneous Differential Equations

3-4 The Algebra of SFG-s

3-5 State Equations and the SFG

Chapter 4 System Geometry and Constraint Equations

4-1 Interconnected Elements

4-2 Graph of a Network

4-3 The Connection Matrix

4-4 General Form of Topological Constraints

4-5 Node Pair and Loop Variables

4-6 Branch Parameter Matrixes

4-7 Equilibrium Equations on a Node-Pair Basic

4-8 Equilibrium Equations on the Loop Basis

4-9 The Canonic LC Network

4-10 The General LC Network

4-11 The Canonic LC Network Containing R

4-12 The General RLC Network

4-13 Duality

Part III System Response a Time Domain

Chapter 5 System Response

5-a Classical Differential Equations

5-1 Features of Linear Differential Equations

5-2 General Features of Solutions of Differential Equations

5-3 The Complementary Function

5-4 The Particular Solution

5-5 Variation of Parameters

5-6 Evaluation of Integration Constants — Initial Conditions

5-7 The Series RL Circuit and its Dual

5-8 The Series RL Circuit with an Initial Current

5-9 The Series RC Circuit and its Dual

5-10 The Series RLC Circuit and its Dual

5-11 Switching of Sinusoidal Sources

5-b Numerical Methods

5-12 The Newton-Raphson Method

5-13 Numerical Solution of Differential Equations

5-14 Difference Equation Approximation

5-15 Nonlinear Systems

5-16 Various Methods for Numerical Integration

5-c Machine Solutions

5-17 The Operational Amplifier

5-18 Computer Simulation of Differential Equations

5-19 Introducing Initial Conditions

5-20 Time and Magnitude Scaling of Analog Computers

5-21 Simulation Languages for the Digital Computer

5-22 Problem Oriented Languages

Chapter 6 General Time Domain Considerations

6-1 Singularity Functions

6-2 Superposition Integral

6-3 Convolution Integral

6-4 Convolution Summation

6-5 State Equations

6-6 Numerical Solution of Continuous Time Systems

6-7 Discrete Time Systems

6-8 Continuous Time Systems with Sampled Inputs

6-9 Steady-State Output to Periodic Inputs

b Frequency Domain

Chapter 7 The Laplace Transform

7-1 The Laplace Transform

7-2 Laplace Transforms of Elementary Functions

7-3 Properties of the Laplace Transform

7-4 Inverse Laplace Transform

7-5 Problem Solving by Laplace Transforms

7-6 Expansion Theorem

7-7 Linear State Equations

7-8 Initial Conditions and Initial State Vectors

Chapter 8 s-Plane: Poles and Zeros

8-1 The System Function

8-2 Impedance and Admittance Functions

8-3 System Determinants

8-4 Thes-Plane

8-5 T(s) and its Pole-Zero Constellation

8-6 Step and Impulse Response

8-7 Step and Impulse Response of a System with One External Pole

8-8 State Models from System Functions

8-9 System Function Realization using Operational Amplifiers

Chapter 9 System Response to Sinusoidal Functions

9-1 Features of Sinusoids

9-2 Steady-State System Response to Sinusoidal Excitation Functions

9-3 Power

9-4 Phasor Diagrams

9-5 Q-Value and Bandwidth

9-6 The (jω) Plane

9-7 Magnitude-Phase and Bode Plots

Chapter 10 Special Topics in Systems Analysis

10-1 Thévenin and Norton Theorems

10-2 Maximum Power Transfer Theorems

10-3 Source Transformation

10-4 Two-port Passive Networks; y-System Equations

10-5 z-System Equations

10-6 T and II Equivalent Networks

10-7 Hybrid Parameters

10-8 Cascade Parameters, abed Coefficients

10-9 Input, Output, and Transfer Impedances

10-10 Active Networks

10-11 Tellegen's Theorem

Chapter 11 General Excitation Functions

11-1 Periodic Excitation Function—Fourier Series

11-2 Effect of Symmetry - Choice of Origin

11-3 Complex Fourier Series

11-4 Properties of Fourier Series

11-5 Numerical Determination of Fourier Coefficients

11-6 The Fourier Transform and Continuous Frequency Spectrums

11-7 Properties of Fourier Transforms

11-8 Frequency Response Characteristics

11-9 The Discrete Fourier Transform

11-10 The Fast Fourier Transform

Part IV Selected Topics

Chapter 12 The Z-Transform and Discrete Time Systems

12-1 Time Sampling and the Z-Transform

12-2 The Z-Transform

12-3 Properties of the Z-Transform

12-4 Discrete Time System Function

12-5 Z-Representation of Differentiation

12-6 Difference Equations and the Z-Transform

12-7 System Description by Difference Equations in Normal Form

Chapter 13 Stability

13-1 Pole Locations and Stability

13-2 Properties of Driving Point Functions

13-3 Routh-Hurwitz Test

13-4 The Nyquist Criterion

13-5 Discrete Time Systems

13-6 Controllability and Observability of Linear Systems

13-7 Observing the State of a System

13-8 Stability in the Sense of Liapunov

13-9 The Direct Method of Liapunov

13-10 Generating Liapunov Functions

References

Appendix A Matrixes

Index

## Product details

- No. of pages: 550
- Language: English
- Copyright: © Pergamon 1972
- Published: January 1, 1972
- Imprint: Pergamon
- eBook ISBN: 9781483151731

## About the Author

### Samuel Seely

## About the Editors

### William F. Hughes

### Arthur T. Murphy

### William H. Davenport

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