An Introduction to Engineering Systems

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.

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 DualityPart 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 (j¿) 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