An Introduction to Engineering Systems

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 Convolut