System Dynamics and Response

As engineering systems become more increasingly interdisciplinary, knowledge of both mechanical and electrical systems has become an asset within the field of engineering. All engineers should have general facility with modeling of dynamic systems and determining their response and it is the objective of this book to provide a framework for that understanding. The study material is presented in four distinct parts; the mathematical modeling of dynamic systems, the mathematical solution of the differential equations and integro differential equations obtained during the modeling process, the response of dynamic systems, and an introduction to feedback control systems and their analysis. An Appendix is provided with a short introduction to MATLAB as it is frequently used within the text as a computational tool, a programming tool, and a graphical tool. SIMULINK, a MATLAB based simulation and modeling tool, is discussed in chapters where the development of models use either the transfer function approach or the state-space method.

Table of Contents:
Chapter 1 - Introduction 1.1 Dynamic Systems 1.1.2 Control Systems 1.2 Dimensions and Units 1.3 Mathematical Modeling of Dynamic Systems 1.4 System Response 1.5 Linearization of Differential Equations 1.6 Unit Impulse Function and Unit Step Function 1.6.1 Unit Impulse Function 1.6.2 Unit Step Function 1.7 Stability 1.8 MATLAB 1.9 Scope of Study 1.10 Summary 1.10.1 Chapter Highlights 1.10.2 Important Equations Problems Chapter 2 - Mechanical Systems 2.1 Inertia Elements 2.1.1 Particles 2.1.2 Rigid Bodies 2.1.3 Deformable Bodies 2.1.4 Degrees of Freedom 2.2 Springs 2.2.1 Force-Displacement Relations 2.2.2 Combinations of Springs 2.2.3 Static Deflections 2.3 Friction Elements 2.3.1 Viscous Damping 2.3.2 Coulomb Damping 2.3.3 Hysteretic Damping 2.4 Mechanical System Input 2.4.1 External Forces and Torques 2.4.2 Impulsive Forces 2.4.3 Step Forces 2.4.4 Periodic Forces 2.4.5 Motion Input 2.5 Free-Body Diagrams 2.6 Newton''s Laws 2.6.1 Particles 2.6.2 Rigid Body Motion 2.6.3 Pure Rotational Motion About a Fixed Axis of Rotation 2.6.4 Planar Motion of a Rigid Body 2.6.5 Three-Dimensional Motion of Rigid Bodies 2.6.6 D''Alembert''s Principle 2.6.6.1 Particles 2.6.6.2 Rigid Bodies Undergoing Planar Motion 2.7 Single-Degree-of Freedom Systems 2.8 Multi-Degree-of-Freedom Systems 2.9 Energy Methods 2.9.1 Principles of Work and Energy 2.9.2 Equivalent Systems 2.9.3 Energy Storage 2.9.4 Lagrange''s Equation for Multi-Degree-of-Freedom Systems 2.9.5 States and Order 2.10 Further Eamples 2.11 Summary 2.11.1 Modeling Methods 2.11.2 Chapter Highlights 2.11.3 Important Equations Problems Chapter 3 - Electrical Systems 3.1 Charge, Current, Voltage, and Power 3.2 Circuit Components 3.2.1 Resistors 3.2.2 Capacitors 3.2.3 Inductors 3.2.4 Voltage and Current Sources 3.2.5 Operational Amplifiers 3.2.6 Electric Circuits and Mechanical Systems 3.3 Kirchoff''s Laws 3.4 Circuit Reduction 3.4.1 Series and Parallel Components 3.4.2 Series Combinations 3.4.3 Parallel Combinations 3.5 Modeling of Electric Circuits 3.6 Mechanical Systems Analogies 3.6.1 Energy Principles 3.6.2 Single Loop Circuits with Voltage Sources 3.6.3 Single Loop Circuits with Current Sources 3.6.4 Multiple Loop Circuits 3.6.5 Mechanical Systems with Motion Input 3.6.6 States 3.7 Operational Amplifiers 3.8 Electromechanical Systems 3.8.1 Magnetic Fields 3.8.2 General Theory 3.8.3 DC Servomotors 3.8.4 Microelectromechanical Systems (MEMS) and Nanoelectromechanical Systems (NEMS) 3.9 Further Examples 3.10 Summary 3.10.1 Mathematical Modeling of Electrical Systems 3.10.2 Other Chapter Highlights 3.10.3 Important Equations Problems Chapter 4 - Fluid, Thermal, and Chemical Systems 4.1 Introduction 4.2 Control Volume Analysis 4.2.1 Conservation of Mass 4.2.2 Energy Equation 4.2.3 Bernoulli''s Equation 4.3 Pipe Flow 4.3.1 Losses 4.3.2 Orifices 4.3.3 Compressible Flows 4.4 Modeling of Liquid Level Systems 4.5 Pneumatic and Hydraulic Systems 4.5.1 Pneumatic Systems 4.5.2 Hydraulic Systems 4.6 Thermal Systems 4.7 Chemical and Biological Systems 4.7.1 Continuous Stirred Tank Reactors (CSTR) 4.7.2 Biological Systems 4.8 Further Examples 4.9 Summary 4.9.1 Mathematical Modeling of Transport Systems 4.9.2 Chapter Highlights 4.9.3 Important Equations Problems Chapter 5 - Laplace Transforms 5.1 Definition and Existence 5.2 Determination of Transform Pairs 5.2.1 Direct Integration 5.2.2 Use of MATLAB 5.3 Laplace Transform Properties 5.4 Inversion of Transforms 5.4.1 Use of Tables and Properties 5.4.2 Partial Fraction Decompositions 5.4.2.1 Real Distinct Poles 5.4.2.2 Complex Poles 5.4.2.3 Repeated Poles 5.4.2.4 Brute Force Methods 5.4.3 Inversion of Transforms of Periodic Functions 5.4.4 Use of MATLAB 5.5 Laplace Transform solution of Differential Equations 5.5.1 Systems With One Dependent Variable 5.5.2 Systems of Differential Equations 5.5.3 Integro-Differential Equations 5.5.4 Use of MATLAB 5.6 Further Examples 5.7 Summary 5.7.1 Mathematical Solutions for Response of Dynamic Systems 5.7.2 Important Equations Problems Chapter 6 - Transient Analysis and Time Domain Response 6.1 Transfer Functions 6.1.1 Definition and Determination 6.1.2 Multiple Inputs and Multiple Outputs 6.1.3 System Order 6.2 Transient Response Specification 6.2.1 Free Response 6.2.2 Impulsive Response 6.2.3 Step Response 6.2.4 Ramp Response 6.2.5 Convolution Integral 6.2.6 Transient System Response Using MATLAB 6.3 Stability Analysis 6.3.1 General Theory 6.3.2 Routh''s Method 6.3.3 Relative Stability 6.3.4 An Introduction to Root-Locus Method 6.4 First-Order Systems 6.4.1 Free Response 6.4.2 Impulsive Response 6.4.3 step Response 6.4.4 Ramp Response 6.5 Second-Order Systems 6.5.1 Free Response 6.5.2 Impulsive Response 6.5.3 Step Response 6.5.4 General Transient Response 6.6 Higher-Order Systems 6.6.1 General Case 6.6.2 Multi-Degree-of-Freedom Mechanical Systems 6.6.2a Transfer Functions 6.6.2b Undamped Systems 6.7 Systems with Time Delay 6.8 Further Examples 6.9 Summary 6.9.1 Chapter Highlights 6.9.2 Important Equations Problems Chapter 7 - Frequency Response 7.1 Undamped Second-Order Systems 7.2 Sinusoidal Transfer Function 7.3 Graphical Representation of the Frequencey Response 7.3.1 Frequencey Response Curves 7.3.2 Bode Diagrams 7.3.2.1 Construction and Asymptotes 7.3.2.2 Products of Transfer Functions 7.3.2.3 Bode Diagrams for Common Transfer Functions 7.3.2.4 Bode Diagram Parameters 7.3.3 Nyquist Diagrams 7.3.4 Use of MATLAB to Develop Bode Plots and Nyquist Diagrams 7.4 First-Order Systems 7.5 Second-Order Systems 7.5.1 One-Degree-of-Freedom Mechanical System 7.5.2 Motion Input 7.5.3 Filters 7.6 Higher Order Systems 7.6.1 Dynamic Vibration Absorbers 7.6.2 Higher Order Filters 7.7 Response Due to Periodic Input 7.8 Further Examples 7.9 Summary 7.9.1 Chapter Highlights 7.9.2 Important Equations Problems Chapter 8 - Feedback Control Systems 8.1 Block Diagrams 8.1.1 Block Diagram Algebra 8.1.2 Block Diagram Modeling of Dynamic Systems 8.2 Using SIMULINK in Block Diagram Modeling 8.3 Feedback Control 8.3.1 Proportional Control 8.3.2 Integral Contral and PI Control 8.3.4 Derivative Control and PD Control 8.3.5 Proportional Plus Integral Plus Derivative Control 8.3.6 Error and Offset 8.3.7 Response Due to Unit Step Input 8.4 Feedback Control for First-Order Systems 8.5 Control of Second-Order Systems 8.6 Control System Design 8.6.1 Design Using Root-Locus Diagrams 8.6.2 Ziegler-Nichols Tuning Rules 8.7 Further Examples 8.8 Summary 8.8.1 Chapter Highlights 8.8.2 Important Equations Problems Chapter 9 - State-Space Methods 9.1 An Example in the State-Space 9.2 General State-Space Modeling 9.2.1 Basic Concepts 9.2.2 Multi Degree-of-Freedom Mechanical Systems 9.3 State-Space Solutions for Free Response 9.3.1 Laplace Transform Solution 9.3.2 Exponential Solution 9.3.3 General Description of Free Response 9.4 State-Space Analysis of Response due to Inputs 9.4.1 Laplace Transform Solution 9.4.2 Numerical Solutions 9.4.3 Use of MATLAB Program ode45.m 9.5 Relationship Between Transfer Functions and State-Space Models 9.6 MATLAB and SIMULINK modeling in the State-Space 9.6.1 MATLAB 9.6.2 SIMULINK 9.7 Nonlinear Systems and Systems with Variable Coefficients 9.8 Further Examples 9.9 Summary 9.9.1 Chapter Highlights 9.9.2 Important Equations Problems Appendix A - Complex Algebra Appendix B - Matrix Algebra B.1 Definitions B.2 Matrix Arithmetic B.3 Determinants B.4 Matrix Inverse B.5 System of Equations B.6 Cramer''s Rule B.7 Eigenvalues and Eigenvectors Appendix C - MATLAB C.1 MATLAB Basics C.2 Plotting and Annotating Graphs C.3 Programming Commands C.3.1 Input and Output C.3.2 Conditional Statements C.3.3 Looping C.3.4 User Defined Functions C.4 Symbolic Math Toolbox C.5 Control System Toolbox Appendix D - Construction of Root-Locus Diagrams D.1 Definitions D.2 Angle and Magnitude Criteria D.3 Construction Guidelines D.4 Summary of Construction Steps D.5 Examples