Stability and Control of Aircraft Systems

256 Pages·2006·2.06 MB·English

by  Roy Langton

Stability and Control of
Aircraft Systems
Introduction to Classical
Feedback Control
Roy Langton

Stability and Control of Aircraft
Systems

Stability and Control of
Aircraft Systems
Introduction to Classical
Feedback Control
Roy Langton
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LibraryofCongressCataloginginPublicationData
Langton,Roy.
Stabilityandcontrolofaircraftsystems:introductiontoclassicalfeedbackcontrol/RoyLangton.
p. cm.
ISBN0-470-01891-7
1. Stabilityofairplanes. 2. Airplanes—Control. I. Title
TL574.S7L352006
629.132(cid:2)36—dc22
2006015974
BritishLibraryCataloguinginPublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
ISBN-13978-0-470-01891-0(HB)
ISBN-100-470-01891-7(HB)
Typesetin10.5/12.5ptPalatinobyIntegraSoftwareServicesPvt.Ltd,Pondicherry,India
PrintedandboundinGreatBritainbyTJInternational,Padstow,Cornwall
Thisbookisprintedonacid-freepaperresponsiblymanufacturedfromsustainableforestryinwhichat
leasttwotreesareplantedforeachoneusedforpaperproduction.
Contents
Series Preface ix
Preface xi
1 Developing the Foundation 1
1.1 Engineering Units 2
1.1.1 International System of Units (SI) 2
1.1.2 US/Imperial Units System 3
1.1.3 Comparing the SI and US/Imperial Units Systems 4
1.2 Block Diagrams 4
1.2.1 Examples of Summation (or Comparison) Devices 5
1.3 Differential Equations 11
1.3.1 Using the ‘D’ Notation 12
1.4 Spring–Mass System Example 14
1.4.1 The Standard Form of Second-order System Transfer
Function 15
1.5 Primer on Complex Numbers 18
1.5.1 The Complex Sinusoid 19
1.6 Chapter Summary 21
2 Closing the Loop 23
2.1 The Generic Closed Loop System 23
2.1.1 The Simplest Form of Closed Loop System 24
2.2 The Concept of Stability 26
vi Contents
2.3 Response Testing of Control Systems 28
2.4 The Integration Process 32
2.5 Hydraulic Servo-actuator Example 37
2.6 Calculating Frequency Response 40
2.6.1 Frequency Response of a First-order Lag 43
2.6.2 Frequency Response of a Second-order System 45
2.7 Aircraft Flight Control System Example 47
2.7.1 Control System Assumptions 48
2.7.2 Open Loop Analysis 49
2.7.3 Closed Loop Performance 53
2.8 Alternative Graphical Methods for Response Analysis 54
2.8.1 The Nyquist Diagram 54
2.8.2 Deriving Closed Loop Response from Nyquist
Diagrams 59
2.8.3 The Nichols Chart 62
2.8.4 Graphical Methods – Summary Comments and
Suggestions 66
2.9 Chapter Summary 68
3 Control System Compensation Techniques 71
3.1 Control System Requirements 71
3.2 Compensation Methods 72
3.2.1 Proportional Plus Integral Control 73
3.2.2 Proportional Plus Integral Plus Derivative Control 76
3.2.3 Lead–Lag Compensation 78
3.2.4 Lag–Lead Compensation 81
3.2.5 Feedback Compensation 84
3.3 Applications of Control Compensation 89
3.3.1 Proportional Plus Integral Example 89
3.3.2 Lead–Lag Compensation Example 97
3.3.3 Class 2 System Design Example 101
3.4 Chapter Summary 114
4 Introduction to Laplace Transforms 117
4.1 An Overview of the Application of Laplace Transforms 117
4.2 The Evolution of the Laplace Transform 118
4.2.1 Proof of the General Case 121
4.3 Applying Laplace Transforms to Linear Systems
Analysis 124
4.3.1 Partial Fractions 129
Contents vii
4.4 Laplace Transforms – Summary of Key Points 138
4.5 Root Locus 140
4.5.1 Root Locus Construction Rules 141
4.5.2 Connecting Root Locus to Conventional Linear
Analysis 146
4.6 Root Locus Example 152
4.7 Chapter Summary 155
5 Dealing with Nonlinearities 157
5.1 Definition of Nonlinearity Types 157
5.2 Continuous Nonlinearities 159
5.2.1 Engine Fuel Control System Example 161
5.3 Discontinuous Nonlinearities 167
5.3.1 Stability Analysis with Discontinuous Nonlinearities 172
5.4 The Transport Delay 176
5.5 Simulation 179
5.6 Chapter Summary 188
6 Electronic Controls 191
6.1 Analog Electronic Controls 193
6.1.1 The Operational Amplifier 194
6.1.2 Building Analog Control Algorithms 195
6.2 The Digital Computer as a Dynamic Control Element 197
6.2.1 Signal Conversion 197
6.2.2 Digital Controller Architectures 201
6.3 The Stability Impact of Digital Controls 206
6.4 Digital Control Design Example 210
6.5 Creating Digital Control Algorithms 215
6.5.1 The Integrator 215
6.5.2 The First-order Lag 216
6.5.3 The Pseudo Derivative 217
6.6 Chapter Summary 218
7 Concluding Commentary 221
7.1 An Overview of the Material 222
7.2 Graphical Tools 225
7.3 Compensation Techniques 227
7.3.1 Integral Wind-up 227
7.3.2 Avoid Using Pure Derivative Action 228
7.3.3 Mechanical Stiffness Estimates are Always High 228
viii Contents
7.4 Laplace Transforms and Root Locus Techniques 229
7.5 Nonlinearities 230
7.6 Digital Electronic Control 232
7.7 The Way Forward 233
Index 235