كتاب Automatic Control For Mechanical Engineers

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Automatic Control For Mechanical Engineers
M. Galal RABIE
Professor of Mechanical Engineering

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CHAPTER 1: INTRODUCTION TO AUTOMATIC CONTROL 1
1.1 INTRODUCTION 1
1.2 SYSTEM DEFINITION 1
1.3 SYSTEM CONTROL 3
1.3.1 Open Loop Control 3
1.3.2 Closed Loop (Feedback) Control 5
1.4 SYSTEM REPRESENTATION 8
1.4.1 Schematic Diagrams 8
1.4.2 Mathematical Model 8
1.4.3 Transfer Function 9
1.4.4 Block Diagram 10
1.4.5 Signal Flow Graph 10
1.4.6 State Space Representation 10
1.4.7 Bond Graph 11
1.5 SYSTEM ANALYSIS 12
1.6 EXERCISE 12
CHAPTER 2: MATHEMATICAL TOPICS 13
2.1 INTRODUCTION 13
2.2 DIFFERENTIAL EQUATIONS 13
2.3 LAPLACE TRANSFORM 17
2.3.1 Direct Laplace Transform 17
2.3.2 Inverse Laplace Transform 18
2.3.3 Properties of Laplace Transform 18
2.3.4 Partial Fraction Expansion 20
2.3.5 Solving Differential Equations Using Laplace Transform 22
2.4 COMPLEX VARIABLES 24
2.5 LAPLACE TRANSFORM TABLES 25
2.6 EXERCISE 25
CHAPTER 3: TRANSFER FUNCTIONS 29
3.1 BASIC DEFINITIONS 29
3.2 TRANSFER FUNCTION OF SOME BASIC ELEMENTS 31
3.2.1 Proportional Element 31
3.2.2 Integrating Elements 32
3.2.2.1 Ideal hydraulic cylinder 32
3.2.2.2 Valve controlled actuator 33
3.2.3 First Order Element 35
3.2.3.1 Hydraulic servo actuator 35
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3.2.3.2 Resistance-capacitance network 36
3.2.4 Second Order Element 37
3.3 EXERCISE 38
CHAPTER 4: BLOCK DIAGRAM 43
4.1 INTRODUCTION 43
4.2 CONVENTIONS FOR BLOCK DIAGRAMS 43
4.3 DEDUCING SYSTEM TRANSFER FUNCTION 44
4.4 BLOCK DIAGRAM ALGEBRA 46
4.5 EXERCISE 50
CHAPTER 5: SIGNAL FLOW GRAPH 53
5.1 INTRODUCTION 53
5.2 CONVENTIONS FOR SIGNAL FLOW GRAPHS 53
5.3 MASON'S FORMULA 56
5.4 EXERCISE 60
CHAPTER 6: TIME DOMAIN ANALYSIS 63
6.1 INTRODUCTION 63
6.2 TIME RESPONSE OF BASIC ELEMENTS 65
6.2.1 Integrating Member 65
6.2.1.1 Response to step input 65
6.2.1.2 Response to ramp input 66
6.2.1.3 Response to input impulse 66
6.2.2 First Order Element 66
6.2.2.1 Step response 66
6.2.2.2 Response to ramp input 67
6.2.2.3 Response to input impulse 68
6.2.3 Second Order Element 69
6.2.3.1 Step response of second order element 69
6.2.3.1.1 Step response of over-damped 2nd order element 70
6.2.3.1.2 Step response of critically-damped 2nd order element 71
6.2.3.1.3 Step response of under-damped 2nd order element 71
6.2.3.1.4 Step response of un-damped 2nd order element 75
6.2.3.2 Response of second order element to ramp input 76
6.2.3.3 Response of second order element input impulse 77
6.2.4 Third and Higher Order Systems 78
6.2.5 Effect of Root Location 79
6.3 TRANSIENT RESPONSE CHARACTERISTICS 81
6.4 STEP RESPONSE TESTING OF PRACTICAL SYSTEMS 83
6.4.1 Response Apparently of First Order 83
6.4.2 Response Apparently of Under Damped Second Order 84
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6.5 EXERCISE 85
CHAPTER 7: FREQUENCY RESPONSE 91
7.1 INTRODUCTION 91
7.2 CALCULATION OF THE FREQUENCY RESPONSE 93
7.3 POLAR PLOT (NYQUIST DIAGRAM) 95
7.3.1 Polar Plot for First Order Element 95
7.3.2 Polar Plot of Second Order Element 96
7.3.3 Polar Plot of Integrating Member 98
7.3.4 Polar Plot of Higher Order Elements 98
7.4 BODE DIAGRAM 99
7.4.1 Introduction 99
7.4.2 Bode Plot of Basic Elements 101
7.4.2.1 Proportional Element 101
7.4.2.2 Integrating Element 101
7.4.2.3 First order element (simple lag) 102
7.4.2.4 Simple lead element 104
7.4.2.5 Second order element 104
7.4.2.6 Quadratic lead element 106
7.5 NICHOL'S CHART 108
7.6 EXERCISE 109
CHAPTER 8: FEEDBACK SYSTEM ACCURACY AND STABILITY 113
8.1 INTRODUCTION 113
8.2 STEADY STATE ERROR 113
8.2.1 Steady State Error with Step Input 114
8.2.2 Steady State Error with Ramp Input 116
8.3 STABILITY OF FEEDBACK SYSTEMS 117
8.3.1 Routh-Hurwitz Stability Criterion 117
8.3.2 Nyquist Stability Criterion 120
8.3.2.1 Stability analysis using Nyquist plot 120
8.3.2.2 Stability analysis using Bode plot 129
8.3.2.3 Stability analysis using Nichol's chart 130
8.4 EXERCISE 131
CHAPTER 9: ROOT LOCUS ANALYSIS 137
9.1 INTRODUCTION 137
9.2 INTERPRETATION OF ROOT LOCUS 138
9.3 EXERCISE 144
CHAPTER 10: COMPENSATION OF CONTROL SYSTEMS 147
10.1 INTRODUCTION 147
M Galal RABIE, Automatic Control for Mechanical Engineers
10.2 PHASE LEAD COMPENSATOR 150
10.3 PHASE LAG COMPENSATOR 153
10.4 LAG-LEAD COMPENSATOR 155
10.5 P, PI AND PID CONTROLLERS 157
10.6 EXERCISE 162
REFERENCES 163
INDEX

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