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 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