Design of Control Laws and State Observers for Fixed-Wing UAVs: Simulation and Experimental Approaches

292 Pages·2022·11.325 MB·English

by  Arturo Tadeo Espinoza-Fraire, Alejandro Enrique Dzul López, Ricardo Pavel Parada Morado, José Armando Sáenz Esqueda

Design of Control Laws and State
Observers for Fixed-Wing UAVs
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Design of Control Laws
and State Observers for
Fixed-Wing UAVs
Simulation and Experimental
Approaches
Arturo Tadeo Espinoza-Fraire
Faculty of Engineering, Science, and Architecture
University Juárez of the Durango State
Gómez Palacio, Durango, Mexico
Alejandro Enrique Dzul López
Electrical and Electronic Engineering Department
Technological Institute of La Laguna
Torreón, Coahuila, Mexico
Ricardo Pavel Parada Morado
Academy of Engineering in Manufacturing Technologies
Polytechnic University of Gómez Palacio
Gómez Palacio, Durango, Mexico
José Armando Sáenz Esqueda
Faculty of Engineering, Science, and Architecture
University Juárez of the Durango State
Gómez Palacio, Durango, Mexico
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Contents
Listoffigures ix
Listoftables xvii
Preface xix
Acknowledgments xxi
Synopsis xxiii
1 Introduction 1
1.1 ClassificationofUAVs 1
1.2 Nonmilitaryapplicationsoffixed-wingUAVs 1
1.3 Controlsystemsinfixed-wingUAVs 2
1.4 Stateobserversystemsinfixed-wingUAVs 4
2 Aerodynamicprinciples 7
2.1 Theimportanceofaerodynamicprinciples 7
2.1.1 Theatmosphere 8
2.1.2 Atmosphericpressure 8
2.1.3 Standardatmosphere 8
2.1.4 Airtemperature 9
2.1.5 Airdensity 9
2.1.6 Airplanewing 10
2.1.7 Bernoullitheorem 11
2.1.8 Thecenterofpressure 11
2.2 Forcesactinginflight 12
2.2.1 Flightopposition(resistance) 13
2.2.2 Thrust 13
2.2.3 Lift 14
2.3 Axesofanairplane 14
2.3.1 Aircraftcontrolsurfaces 14
2.3.2 Thestructureofanairplane 17
2.4 Concludingremarks 18
3 Equationsofmotionofafixed-wingUAV 19
3.1 Controlsurfacesofafixed-wingMAV 19
3.2 Framecoordinatesinfixed-wingUAVs 19
3.3 Governingphysicsofafixed-wingUAV 20
3.4 Motionofarigidbody 21
3.5 Kinematicmodel 24
vi Contents
3.6 Uncoupledmodelofthefixed-wingUAV 28
3.6.1 Longitudinaldynamics 28
3.6.2 Directionalandlateraldynamics 30
3.6.3 Changeofvariables 33
3.7 Concludingremarks 33
4 Linearcontrollers 35
4.1 PDandPIDcontrollers 35
4.2 LQRcontroller 38
4.3 LQRcontrollerwiththediscrete-timeKalmanfilter 43
4.4 Concludingremarks 47
5 Nonlinearcontrollers 49
5.1 Nestedsaturationcontroller 49
5.2 Backsteppingcontroller 52
5.3 Slidingmodecontroller 54
5.4 Nestedsaturationwithslidingmode 57
5.5 Nestedsaturationwith2-SM 60
5.6 NestedsaturationwithHOSM 61
5.7 BacksteppingwithSM 63
5.8 Backsteppingwith2-SM 67
5.9 BacksteppingwithHOSM 69
5.10 MITrulebasedonthegradientmethodwithslidingmodetheory 72
5.11 Concludingremarks 88
6 Stateobservers 89
6.1 Applicationsandconceptsofstateobserversincontroltheory 89
6.2 Complementaryfilters 90
6.3 Slidingmodeobservers 91
6.3.1 Slidingsurface 91
6.3.2 Sheareffectandslidingpatch 92
6.3.3 Systemdamping 93
6.4 Nonlinearextendedstateobserver 94
6.5 Backsteppingobserver 95
6.6 Simulationresultsofthecontrollawswithobservers 104
6.6.1 PDcontrollawwithobservers 104
6.6.2 Backsteppingcontrollawwithobservers 105
6.6.3 RollmotionsimulationswithPDcontrollawwith
observers 105
6.6.4 YawmotionsimulationswithPDcontrollawwith
observers 108
6.6.5 AltitudemotionsimulationswithPDcontrollawwith
observers 108
6.6.6 Rollmotionsimulationswithbacksteppingcontrollawwith
observers 112
Contents vii
6.6.7 Yawmotionsimulationswithbacksteppingcontrollaw
withobservers 115
6.6.8 Altitudemovementsimulationswithbacksteppingcontrol
lawwithobservers 115
6.7 Concludingremarks 120
7 Testbedandexperimentalresults 121
7.1 Experimentaltestbed 121
7.2 Motorsoractuatorsinatestbed 122
7.3 Inertialmeasurementunit(IMU) 123
7.4 Telemetry 123
7.5 Optocoupler 124
7.6 Microcontrollerandaltimeter 124
7.7 MicroprocessorRabbit6000 125
7.8 Li-pobattery 129
7.9 Experimentalresultsforlinearandnonlinearcontrollers 129
7.9.1 PDcontroller 129
7.9.2 PIDcontroller 131
7.9.3 LQRcontroller 134
7.9.4 LQRcontrollerwithdiscrete-timeKalmanfilter 136
7.9.5 Backsteppingcontroller 136
7.10 Experimentalresultsforlinearandnonlinearobservers 140
7.10.1 Luenbergerobserverappliedtoafixed-wingUAVwithPD
controllaw 140
7.10.2 SMOappliedtoafixed-wingUAVwithPDcontrollaw 146
7.10.3 NESOappliedtoafixed-wingUAVwithPDcontrollaw 150
7.10.4 SMOappliedtoafixed-wingUAVwithbackstepping
controllaw 154
7.10.5 NESOappliedtoafixed-wingUAVwithbackstepping
controllaw 162
7.11 Concludingremarks 170
A Mathematicalreview 171
A.1 Vectors 171
A.2 Lineartransformations 172
A.3 Euclideannorm 172
A.4 Matrices 172
A.5 Spectralnorm 175
A.6 P-norms 176
A.7 Dyadicproduct,crossproduct,andantisymmetricmatrix 177
A.8 Topologicalconcepts 179
A.8.1 Sets 179
A.8.2 Metricspaces 180
A.8.3 Linearindependence 181
viii Contents
A.8.4 Sequenceconvergence 181
A.9 Functions 181
A.9.1 Continuousfunctions 181
A.9.2 Differentiablefunctions 183
A.9.3 Meanvaluetheorem 184
A.9.4 Implicitfunctiontheorem 185
A.9.5 Gronwall–Bellmaninequality 185
A.10 Contractionmapping 186
B Kinematicsanddynamicsbackground 189
B.1 Kinematics 189
B.2 Dynamics 191
C StabilityintheLyapunovsense 193
C.1 DirectLyapunovmethod 194
D Fundamentalsoflinearandnonlinearcontrollers 197
D.1 Fundamentalsoflinearcontrollers 197
D.1.1 PIDandPDcontrollertheory 197
D.1.2 Linearquadraticregulator(LQR) 198
D.2 Fundamentalsofnonlinearcontrollers 201
D.2.1 Nestedsaturations 201
D.2.2 Integratorbackstepping 203
D.2.3 Slidingmodecontrol 204
D.2.4 Modelreferenceadaptivecontrol(MRAC) 205
E Discrete-timeKalmanfilter 207
F Linearandnonlinearcontrollers:programsfortheembedded
system 209
F.1 PDcontrollerinaltitude 209
F.2 Backsteppingcontrollerinaltitude 219
G Linearandnonlinearstateobservers:programsfortheembedded
system 231
G.1 LuenbergerobserverwithPDcontrollerinyaw 231
G.2 SMOobserverwithPDcontrollerinaltitude 241
H MATLAB® programtograph 253
I Altimeterprogram 255
Bibliography 257
Index 261
List of figures
Fig.1.1 Generalcontrolscheme. 4
Fig.1.2 BlockdiagramoftheMRASappliedtofixed-wingUAVs. 4
Fig.1.3 Generalstateobserversscheme. 5
Fig.2.1 Schematicofanairfoilsection. 10
Fig.2.2 Airflowaroundthewing. 11
Fig.2.3 Centerofpressure. 12
Fig.2.4 Pressuredisplacementlimits. 12
Fig.2.5 Forcesactinginflight. 13
Fig.2.6 Axisofanairplane. 15
Fig.2.7 Locationofflaps,slats,andspoilersonawing. 17
Fig.2.8 Genericairframe. 17
Fig.3.1 Controlsurfaces. 20
Fig.3.2 FixedcoordinateframeEandframeattachedtotheairplaneB. 20
Fig.3.3 Movementvariablesofafixed-wingUAV. 21
Fig.3.4 Momentsandaerodynamicforcesintheairplane. 24
Fig.3.5 Representationz-y-xofEulerangles. 25
Fig.3.6 Longitudinalmovement. 29
Fig.3.7 Thex-,y-,andz-axesinthebodyoftheairplane. 29
Fig.3.8 Yawangle. 32
Fig.3.9 Rollangle. 32
Fig.4.1 ActionofthePDcontrolleronaltitude. 37
Fig.4.2 ActionofthePIDcontrolleronaltitude. 37
Fig.4.3 ActionofthePDcontrolleronyaw. 38
Fig.4.4 ActionofthePIDcontrolleronyaw. 38
Fig.4.5 ActionofthePDcontrolleronroll. 39
Fig.4.6 ActionofthePIDcontrolleronroll. 39
Fig.4.7 ActionoftheLQRcontrolleronaltitude. 42
Fig.4.8 ActionoftheLQRcontrolleronyaw. 42
Fig.4.9 ActionoftheLQRcontrolleronroll. 43
Fig.4.10 ActionoftheLQRcontrollerwiththediscrete-timeKalmanfilteron
altitude. 45
Fig.4.11 ActionoftheLQRcontrollerwiththediscrete-timeKalmanfilteronyaw. 45
Fig.4.12 ActionoftheLQRcontrollerwiththediscrete-timeKalmanfilteronroll. 46
Fig.5.1 Actionofthenestedsaturationcontrolleronaltitude. 51
Fig.5.2 Actionofthenestedsaturationcontrolleronyaw. 51
Fig.5.3 Actionofthenestedsaturationcontrolleronroll. 52
Fig.5.4 Actionofthebacksteppingcontrolleronaltitude. 54
Fig.5.5 Actionofthebacksteppingcontrolleronyaw. 54
Fig.5.6 Actionofthebacksteppingcontrolleronroll. 55
Fig.5.7 Actionoftheslidingmodecontrolleronaltitude. 56