PREFACE 

vii  
1 INTRODUCTION TO SYSTEM DYNAMICS 1 



1  (2) 

12 Mathematical Modeling of Dynamic Systems 


3  (2) 

13 Analysis and Design of Dynamic Systems 


5  (1) 


6  (2) 
2 THE LAPLAGE TRANSFORM 

8  (45) 


8  (1) 

22 Complex Numbers, Complex Variables, and Complex Functions 


8  (6) 

23 Laplace Transformation 


14  (15) 

24 Inverse Laplace Transformation 


29  (5) 

25 Solving Linear, TimeInvariant Differential Equations 


34  (2) 

Example Problems and Solutions 


36  (13) 


49  (4) 
3 MECHANICAL SYSTEMS 

53  (53) 


53  (4) 


57  (4) 

33 Mathematical Modeling of Simple Mechanical Systems 


61  (12) 

34 Work, Energy, and Power 


73  (8) 

Example Problems and Solutions 


81  (19) 


100  (6) 
4 TRANSFERFUNCTION APPROACH TO MODELING DYNAMIC SYSTEMS 

106  (63) 


106  (3) 


109  (3) 

43 PartialFraction Expansion with MATLAB 


112  (7) 

44 TransientResponse Analysis with MATLAB 


119  (16) 

Example Problems and Solutions 


135  (27) 


162  (7) 
5 STATE SPACE APPROACH TO MODELING DYNAMIC SYSTEMS 

169  (82) 


169  (5) 

52 TransientResponse Analysis of Systems in StateSpace Form with MATLAB 


174  (7) 

53 StateSpace Modeling of Systems with No Input Derivatives 


181  (6) 

54 StateSpace Modeling of Systems with Input Derivatives 


187  (15) 

55 Transformation of Mathematical Models with MATLAB 


202  (7) 

Example Problems and Solutions 


209  (30) 


239  (12) 
6 ELECTRICAL SYSTEMS AND ELECTROMECHANICAL SYSTEMS 

251  (72) 


251  (3) 

62 Fundamentals of Electrical Circuits 


254  (7) 

63 Mathematical Modeling of Electrical Systems 


261  (9) 


270  (4) 

65 Mathematical Modeling of Electromechanical Systems 


274  (7) 

66 Mathematical Modeling of OperationalAmplifier Systems 


281  (7) 

Example Problems and Solutions 


288  (24) 


312  (11) 
7 FLUID SYSTEMS AND THERMAL SYSTEMS 

323  (60) 


323  (1) 

72 Mathematical Modeling of LiquidLevel Systems 


324  (8) 

73 Mathematical Modeling of Pneumatic Systems 


332  (5) 

74 Linearization of Nonlinear Systems 


337  (3) 

75 Mathematical Modeling of Hydraulic Systems 


340  (8) 

76 Mathematical Modeling of Thermal Systems 


348  (4) 

Example Problems and Solutions 


352  (23) 


375  (8) 
8 TIMEDOMAIN ANALYSIS OF DYNAMIC SYSTEMS 

383  (48) 


383  (1) 

82 TransientResponse Analysis of FirstOrder Systems 


384  (4) 

83 TransientResponse Analysis of SecondOrder Systems 


388  (11) 

84 TransientResponse Analysis of Higher Order Systems 


399  (1) 

85 Solution of the State Equation 


400  (9) 

Example Problems and Solutions 


409  (15) 


424  (7) 
9 FREQUENCYDOMAIN ANALYSIS OF DYNAMIC SYSTEMS 

431  (60) 


431  (1) 

92 Sinusoidal Transfer Function 


432  (6) 

93 Vibrations in Rotating Mechanical Systems 


438  (3) 


441  (6) 

95 Dynamic Vibration Absorbers 


447  (6) 

96 Free Vibrations in MultiDegreesofFreedom Systems 


453  (5) 

Example Problems and Solutions 


458  (26) 


484  (7) 
10 TIMEDOMAIN ANALYSIS AND DESIGN OF CONTROL SYSTEMS 

491  (117) 


491  (3) 

102 Block Diagrams and Their Simplification 


494  (7) 

103 Automatic Controllers 


501  (5) 

104 TransientResponse Analysis 


506  (7) 

105 TransientResponse Specifications 


513  (9) 

106 Improving TransientResponse and SteadyState Characteristics 


522  (16) 


538  (7) 


545  (17) 

109 RootLocus Plots with MATLAB 


562  (4) 

1010 Tuning Rules for PID Controllers 


566  (10) 

Example Problems and Solutions 


576  (24) 


600  (8) 
11 FREQUENCYDOMAIN ANALYSIS AND DESIGN OF CONTROL SYSTEMS 

608  (87) 


608  (1) 

112 Bode Diagram Representation of the Frequency Response 


609  (20) 

113 Plotting Bode Diagrams with MATLAB 


629  (1) 

114 Nyquist Plots and the Nyquist Stability Criterion 


630  (10) 

115 Drawing Nyquist Plots with MATLAB 


640  (3) 

116 Design of Control Systems in the Frequency Domain 


643  (25) 

Example Problems and Solutions 


668  (22) 


690  (5) 
APPENDIX A SYSTEMS OF UNITS 

695  (5) 
APPENDIX B CONVERSION TABLES 

700  (5) 
APPENDIX C VECTORMATRIX ALGEBRA 

705  (15) 
APPENDIX D INTRODUCTION TO MATLAB 

720  (37) 
REFERENCES 

757  (2) 
INDEX 

759  