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Full Description
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.
Contents
Chapter 1 - Introduction1.1 Dynamic Systems1.1.2 Control Systems1.2 Dimensions and Units1.3 Mathematical Modeling of Dynamic Systems1.4 System Response1.5 Linearization of Differential Equations1.6 Unit Impulse Function and Unit Step Function1.6.1 Unit Impulse Function1.6.2 Unit Step Function1.7 Stability1.8 MATLAB1.9 Scope of Study1.10 Summary1.10.1 Chapter Highlights1.10.2 Important EquationsProblemsChapter 2 - Mechanical Systems2.1 Inertia Elements2.1.1 Particles2.1.2 Rigid Bodies2.1.3 Deformable Bodies2.1.4 Degrees of Freedom2.2 Springs2.2.1 Force-Displacement Relations2.2.2 Combinations of Springs2.2.3 Static Deflections2.3 Friction Elements2.3.1 Viscous Damping2.3.2 Coulomb Damping2.3.3 Hysteretic Damping2.4 Mechanical System Input2.4.1 External Forces and Torques2.4.2 Impulsive Forces2.4.3 Step Forces2.4.4 Periodic Forces2.4.5 Motion Input2.5 Free-Body Diagrams2.6 Newton''s Laws2.6.1 Particles2.6.2 Rigid Body Motion2.6.3 Pure Rotational Motion About a Fixed Axis of Rotation2.6.4 Planar Motion of a Rigid Body2.6.5 Three-Dimensional Motion of Rigid Bodies2.6.6 D''Alembert''s Principle2.6.6.1 Particles2.6.6.2 Rigid Bodies Undergoing Planar Motion2.7 Single-Degree-of Freedom Systems2.8 Multi-Degree-of-Freedom Systems2.9 Energy Methods2.9.1 Principles of Work and Energy2.9.2 Equivalent Systems2.9.3 Energy Storage2.9.4 Lagrange''s Equation for Multi-Degree-of-Freedom Systems2.9.5 States and Order2.10 Further Eamples2.11 Summary2.11.1 Modeling Methods2.11.2 Chapter Highlights2.11.3 Important EquationsProblemsChapter 3 - Electrical Systems3.1 Charge, Current, Voltage, and Power3.2 Circuit Components 3.2.1 Resistors3.2.2 Capacitors3.2.3 Inductors3.2.4 Voltage and Current Sources3.2.5 Operational Amplifiers3.2.6 Electric Circuits and Mechanical Systems3.3 Kirchoff''s Laws3.4 Circuit Reduction3.4.1 Series and Parallel Components3.4.2 Series Combinations3.4.3 Parallel Combinations3.5 Modeling of Electric Circuits3.6 Mechanical Systems Analogies3.6.1 Energy Principles3.6.2 Single Loop Circuits with Voltage Sources3.6.3 Single Loop Circuits with Current Sources3.6.4 Multiple Loop Circuits3.6.5 Mechanical Systems with Motion Input3.6.6 States3.7 Operational Amplifiers3.8 Electromechanical Systems3.8.1 Magnetic Fields3.8.2 General Theory3.8.3 DC Servomotors3.8.4 Microelectromechanical Systems (MEMS) and Nanoelectromechanical Systems (NEMS)3.9 Further Examples3.10 Summary3.10.1 Mathematical Modeling of Electrical Systems3.10.2 Other Chapter Highlights3.10.3 Important EquationsProblemsChapter 4 - Fluid, Thermal, and Chemical Systems4.1 Introduction4.2 Control Volume Analysis4.2.1 Conservation of Mass4.2.2 Energy Equation4.2.3 Bernoulli''s Equation4.3 Pipe Flow4.3.1 Losses4.3.2 Orifices4.3.3 Compressible Flows4.4 Modeling of Liquid Level Systems4.5 Pneumatic and Hydraulic Systems4.5.1 Pneumatic Systems4.5.2 Hydraulic Systems4.6 Thermal Systems4.7 Chemical and Biological Systems4.7.1 Continuous Stirred Tank Reactors (CSTR)4.7.2 Biological Systems4.8 Further Examples4.9 Summary4.9.1 Mathematical Modeling of Transport Systems4.9.2 Chapter Highlights4.9.3 Important Equations ProblemsChapter 5 - Laplace Transforms5.1 Definition and Existence5.2 Determination of Transform Pairs5.2.1 Direct Integration5.2.2 Use of MATLAB5.3 Laplace Transform Properties5.4 Inversion of Transforms5.4.1 Use of Tables and Properties5.4.2 Partial Fraction Decompositions5.4.2.1 Real Distinct Poles5.4.2.2 Complex Poles5.4.2.3 Repeated Poles5.4.2.4 Brute Force Methods5.4.3 Inversion of Transforms of Periodic Functions5.4.4 Use of MATLAB5.5 Laplace Transform solution of Differential Equations5.5.1 Systems With One Dependent Variable5.5.2 Systems of Differential Equations5.5.3 Integro-Differential Equations5.5.4 Use of MATLAB5.6 Further Examples5.7 Summary5.7.1 Mathematical Solutions for Response of Dynamic Systems5.7.2 Important EquationsProblemsChapter 6 - Transient Analysis and Time Domain Response6.1 Transfer Functions6.1.1 Definition and Determination6.1.2 Multiple Inputs and Multiple Outputs6.1.3 System Order6.2 Transient Response Specification 6.2.1 Free Response6.2.2 Impulsive Response6.2.3 Step Response 6.2.4 Ramp Response6.2.5 Convolution Integral6.2.6 Transient System Response Using MATLAB6.3 Stability Analysis6.3.1 General Theory6.3.2 Routh''s Method6.3.3 Relative Stability6.3.4 An Introduction to Root-Locus Method6.4 First-Order Systems6.4.1 Free Response6.4.2 Impulsive Response6.4.3 step Response6.4.4 Ramp Response6.5 Second-Order Systems6.5.1 Free Response6.5.2 Impulsive Response6.5.3 Step Response6.5.4 General Transient Response6.6 Higher-Order Systems6.6.1 General Case6.6.2 Multi-Degree-of-Freedom Mechanical Systems6.6.2a Transfer Functions6.6.2b Undamped Systems6.7 Systems with Time Delay6.8 Further Examples6.9 Summary6.9.1 Chapter Highlights6.9.2 Important EquationsProblemsChapter 7 - Frequency Response7.1 Undamped Second-Order Systems7.2 Sinusoidal Transfer Function7.3 Graphical Representation of the Frequencey Response7.3.1 Frequencey Response Curves7.3.2 Bode Diagrams7.3.2.1 Construction and Asymptotes7.3.2.2 Products of Transfer Functions7.3.2.3 Bode Diagrams for Common Transfer Functions7.3.2.4 Bode Diagram Parameters7.3.3 Nyquist Diagrams7.3.4 Use of MATLAB to Develop Bode Plots and Nyquist Diagrams7.4 First-Order Systems7.5 Second-Order Systems7.5.1 One-Degree-of-Freedom Mechanical System 7.5.2 Motion Input7.5.3 Filters7.6 Higher Order Systems7.6.1 Dynamic Vibration Absorbers7.6.2 Higher Order Filters7.7 Response Due to Periodic Input7.8 Further Examples7.9 Summary7.9.1 Chapter Highlights7.9.2 Important EquationsProblemsChapter 8 - Feedback Control Systems8.1 Block Diagrams8.1.1 Block Diagram Algebra8.1.2 Block Diagram Modeling of Dynamic Systems8.2 Using SIMULINK in Block Diagram Modeling8.3 Feedback Control8.3.1 Proportional Control8.3.2 Integral Contral and PI Control8.3.4 Derivative Control and PD Control8.3.5 Proportional Plus Integral Plus Derivative Control8.3.6 Error and Offset8.3.7 Response Due to Unit Step Input8.4 Feedback Control for First-Order Systems8.5 Control of Second-Order Systems8.6 Control System Design8.6.1 Design Using Root-Locus Diagrams8.6.2 Ziegler-Nichols Tuning Rules8.7 Further Examples8.8 Summary8.8.1 Chapter Highlights8.8.2 Important EquationsProblemsChapter 9 - State-Space Methods9.1 An Example in the State-Space9.2 General State-Space Modeling9.2.1 Basic Concepts9.2.2 Multi Degree-of-Freedom Mechanical Systems9.3 State-Space Solutions for Free Response9.3.1 Laplace Transform Solution9.3.2 Exponential Solution9.3.3 General Description of Free Response9.4 State-Space Analysis of Response due to Inputs9.4.1 Laplace Transform Solution9.4.2 Numerical Solutions9.4.3 Use of MATLAB Program ode45.m9.5 Relationship Between Transfer Functions and State-Space Models9.6 MATLAB and SIMULINK modeling in the State-Space9.6.1 MATLAB9.6.2 SIMULINK9.7 Nonlinear Systems and Systems with Variable Coefficients9.8 Further Examples9.9 Summary9.9.1 Chapter Highlights9.9.2 Important EquationsProblemsAppendix A - Complex AlgebraAppendix B - Matrix AlgebraB.1 DefinitionsB.2 Matrix ArithmeticB.3 DeterminantsB.4 Matrix InverseB.5 System of EquationsB.6 Cramer''s RuleB.7 Eigenvalues and EigenvectorsAppendix C - MATLABC.1 MATLAB BasicsC.2 Plotting and Annotating GraphsC.3 Programming CommandsC.3.1 Input and OutputC.3.2 Conditional StatementsC.3.3 LoopingC.3.4 User Defined FunctionsC.4 Symbolic Math ToolboxC.5 Control System ToolboxAppendix D - Construction of Root-Locus DiagramsD.1 DefinitionsD.2 Angle and Magnitude CriteriaD.3 Construction GuidelinesD.4 Summary of Construction StepsD.5 Examples
