Fundamentals of Modeling and Analyzing Engineering Systems

by Philip D. Cha , James J. Rosenberg , Clive L. Dym

• ISBN13: 9780521594639
• ISBN10: 0521594634
• Format: Paperback
• Copyright: 2000-04-13
• Publisher: Cambridge University Press

Summary

System modeling and analysis is a standard activity in every engineering discipline. This text offers a broad-based introduction to systems engineering that incorporates material from mechanical, electrical, aerospace, and chemical engineering. The overall theme that distinguishes it from other texts is its unified treatment of disparate physical systems, emphasizing similarities in both the modeling and behavior of lumped-element systems. Every chapter includes a wide variety of examples, as well as exercise problems, drawn from real-world mechanical, electrical, hydraulic, chemical, and thermal systems. Aimed at second- and third-year undergraduates, this introductory text offers a unified entry into the multidisciplinary world of engineering. Solutions manual available.

Table of Contents

Examples	xiii
Preface	xix
Fundamental Concepts in Mathematical Modeling	1	(17)
Systems, Modeling, and Analysis	1	(2)
Abstraction	3	(1)
Physical Dimensions and Units	4	(1)
Linearity and Superposition	5	(2)
A Gentle Introduction to Differential Equations	7	(2)
Scaling in Elementary Differential Equations	9	(2)
Balance and Conservation Laws and the System Boundary Approach	11	(5)
Balance Equations	12	(1)
Conservation Laws	12	(1)
Examples	13	(3)
Summary	16	(1)
Problems	17	(1)
Lumped-Element Modeling	18	(49)
Introduction	18	(1)
One-Dimensional Translational Mechanical Systems	19	(18)
The Elements Comprising Simple Mechanical Systems	19	(1)
Translational Springs	19	(4)
Translational Dampers	23	(1)
Mass Elements in Translational Motion	24	(1)
The Ideal Force and the Ideal Displacement Inputs	25	(1)
The Interrelationship Between Forces in Different Elements in a System: Newton's Second Law	26	(2)
The Interrelationship Between Deformations of Different Elements in a System: Consistency of Displacements	28	(1)
Simplifying Models Through Combination of Elements	29	(3)
Examples	32	(5)
Summary	37	(1)
RLC Electrical Systems	37	(21)
Some Electrical Basics: Charge, Voltage, and Current	37	(1)
The Inductive, Resistive, and Capacitive Elements	38	(1)
The Ideal Inductor Element	39	(1)
The Ideal Resistor Element	39	(1)
The Ideal Capacitor Element	40	(1)
The Ideal Current and Ideal Voltage Sources	41	(1)
The Interrelationship Between Currents in Different Elements in a System	42	(2)
The Interrelationships Between the Voltage Differences Across Elements in a System	44	(1)
Simplifying Models Through Combination of Elements	45	(5)
Examples	50	(7)
Summary	57	(1)
Summary	58	(1)
Appendix 2-A: Faraday's Law	58	(1)
Appendix 2-B: Thevenin and Norton Equivalents	59	(2)
Problems	61	(6)
Generalizing Lumped-Element Modeling	67	(58)
Introduction	67	(1)
A Framework for Unifying Lumped-Element Models	67	(18)
Some Common Approaches: Virtues and Shortcomings	67	(1)
``Basic'' Linear Graph Theory	68	(5)
Relating Linear Graph Theory to Lumped-Element Models of Physical Systems	73	(1)
Manipulation of Graph Theory Rules	74	(5)
Examples	79	(5)
Summary	84	(1)
Rotational Mechanical Systems	85	(11)
The Basics of Rotational Mechanics	85	(1)
Rotational Mechanical System Elements	86	(1)
Torsional Springs	86	(1)
Torsional Damper Elements	87	(1)
The Mass Moment of Inertia Element	88	(1)
The Ideal Torque and the Ideal Angular Displacement Inputs	89	(1)
The Rules Governing Rotational Mechanical Systems	89	(3)
Examples	92	(3)
Summary	95	(1)
Hydraulic Systems	96	(9)
Basic Physics of Incompressible Fluids	96	(2)
Hydraulic System Elements	98	(1)
The Pipe Element	98	(1)
The Tank Element	99	(2)
Ideal Flow Rate and Ideal Pressure Sources	101	(1)
The Rules Governing the Hydraulic Model	101	(1)
Examples	102	(2)
Summary	104	(1)
Thermal Systems	105	(5)
Basic Concepts in Heat Transfer	105	(1)
Thermal System Elements	106	(1)
The Thermal Resistance Element	106	(1)
The Thermal Mass Element	106	(1)
Ideal Heat Transfer Rate and Ideal Temperature Inputs	107	(1)
The Rules Governing the Thermal Model	108	(1)
Examples	108	(2)
Summary	110	(1)
Drawing Analogies	110	(7)
Summary	117	(1)
Problems	117	(8)
First-Order System Models	125	(30)
Governing Equations for First-Order Systems	125	(7)
Canonical Form of First-Order Systems	132	(3)
Classification of Responses and Systems	135	(1)
Solution of Governing Equations	135	(9)
Free Response	136	(2)
Forced Response	138	(6)
Transient Response Specifications	144	(1)
Experimental Determination of τ	145	(1)
Free Response	145	(1)
Forced Response	145	(1)
Applications of Superposition in First-Order System Models	146	(5)
Summary	151	(1)
Problems	152	(3)
Second-Order Models of Systems	155	(30)
Governing Equations for Second-Order Systems	155	(8)
Canonical Form and Classification of Response	163	(3)
Solution of Governing Equations	166	(6)
Free Response	166	(4)
Forced Response	170	(2)
Transient Response Specifications	172	(4)
Experimental Determination of ζ	176	(2)
Using Free Response to Determine ζ	176	(2)
Using Step Response to Determine ζ	178	(1)
Summary	178	(1)
Problems	178	(7)
Laplace Transform	185	(31)
Definition of the Laplace Transform	186	(2)
Properties of the Laplace Transform	188	(6)
Superposition	188	(1)
Shift in t or Time Delay	188	(1)
Shift in s	189	(1)
Time Derivatives	189	(1)
Time Integral	190	(1)
Final Value Theorem	191	(3)
The Inverse Laplace Transform	194	(6)
Response of First-Order Systems Using the Laplace Transforms	200	(4)
Solution of RC Free Response	201	(1)
Solution of RC Step Response	202	(1)
Solution of RC Sinusoidal Response	203	(1)
Response of Second-Order Systems Using the Laplace Transform	204	(5)
Free Response	204	(4)
Forced Unit Step Response	208	(1)
Summary	209	(1)
Appendix 6-A: Complex Arithmetic	209	(2)
Problems	211	(5)
Frequency Response of Linear, Time-Invariant Systems	216	(72)
Transfer Functions and the Sinusoidal Steady State	217	(7)
Steady-State Sinusoidal Response of First-Order Systems	217	(1)
The Transfer Function and Its Relation to the Governing Equation	218	(3)
The Relationship Between T(jω) and Sinusoidal Steady-State Response	221	(3)
Mathematical Features of the Transfer Function	224	(1)
Poles and Zeros	224	(1)
First- and Second-Order Factors and Delay Factors	224	(1)
Bode Plots	225	(13)
The General Frequency Response Function and Its Factors	226	(1)
Gain Factor: k	227	(1)
Integral and Derivative Factors: 1/jωτ and jωτ	228	(3)
First-Order Factor: 1 + jωτ	231	(3)
Quadratic Factor: 1 - (ω/ωn)2 + j2ζ(&omega/ωn)	234	(3)
Delay Factor: e-jωto	237	(1)
Frequency Response of First-Order and Second-Order Systems	238	(29)
First-Order Low-Pass Frequency Response Function	239	(1)
First-Order High-Pass Frequency Response Function	239	(1)
Second-Order Low-Pass Frequency Response Function	240	(4)
Second-Order High-Pass Frequency Response Function	244	(2)
Second-Order Band-Pass Frequency Response Function	246	(2)
Resonance	248	(2)
Transfer Functions for Systems with Delay	250	(1)
Examples	251	(16)
Impedance	267	(11)
Passing the Transform Through the Node and Loop Rule Summations	268	(1)
Impedance in Electrical and Mechanical Systems	269	(3)
Application of Impedance Techniques	272	(6)
Summary	278	(1)
Summary	278	(1)
Problems	279	(9)
State Space Formulations of Systems Problems	288	(38)
Examples of State Variables and State Equations	288	(5)
Matrix Formulation	293	(2)
Free Response and the Eigenvalue Problem	295	(3)
Stability	298	(1)
Graphical Solution	298	(1)
Forced Response and Response to a Step Input	299	(1)
Examples of State Space Formulations and Solutions	300	(17)
Phase Plane and Stability Considerations	317	(2)
Summary	319	(1)
Appendix 8-A: A Short Introduction to Matrix Manipulation	320	(3)
Problems	323	(3)
Relating the Time Domain, Frequency Domain, and State Space	326	(33)
Introduction	326	(1)
The Pole-Zero Plot	326	(5)
Relating the Pole-Zero Plot to the Transfer Function, the Governing Equation, and the State Matrix Eigenvalues	327	(1)
Relating Pole Locations to System Parameters	328	(1)
Examples	329	(2)
Relating Frequency Response to Pole Location	331	(11)
The Relationship Between the |T(s)| Surface and the Frequency Response Function	331	(3)
Higher-Order Systems and Dominant Poles	334	(1)
Examples	335	(7)
Transient Response, Poles, and Frequency Response	342	(12)
The Relationship Between the Mathematical Form of the Free Response, Pole Location, and System Parameters	342	(3)
The Effect of Nondominant Poles on Transient Behavior	345	(3)
Examples	348	(6)
State Space Trajectories, Poles, and Transient Response	354	(2)
Summary	356	(1)
Problems	356	(3)
Feedback Systems	359	(98)
Systems with Feedback	359	(6)
What Is Feedback?	359	(1)
Some Examples of Systems with Feedback	360	(5)
Representing Systems and Subsystems Using Transfer Functions	365	(7)
Representing Inputs, Outputs, and System Behavior in the s-Domain	365	(4)
Subsystem Interaction and Loading	369	(3)
Block Diagrams	372	(11)
Block Diagram Elements and Structure	372	(2)
Simplifying Block Diagrams	374	(4)
Examples	378	(5)
Properties of Feedback Systems	383	(5)
Effect of Feedback on Overall Gain	383	(1)
Effect of Feedback on Parameter Sensitivity	383	(1)
Effect of Feedback on External Disturbance or Noise	384	(2)
Effect of Feedback on Stability	386	(2)
Relative Stability and the Phase and Gain Margins	388	(11)
Relative Stability	388	(1)
Phase Margin and Gain Margin	388	(11)
Design of Controllers	399	(40)
Feedback Control Systems: General Configuration and Terminology	399	(8)
Proportional Control	407	(13)
Derivative Control and PD Control	420	(7)
Integral Control and PI Control	427	(8)
PID Control	435	(4)
Summary	439	(1)
Appendix 10-A: Feedback Circuits Based on Operational Amplifiers	440	(5)
Noninverting Amplifier	440	(2)
Inverting Amplifier	442	(3)
Appendix 10-B: DC Servomotors and Tachometers	445	(6)
DC Servomotors	445	(5)
Tachometers	450	(1)
Problems	451	(6)
Index	457