Design of control laws and state observers for fixed-wing uavs. simulation and experimental approach

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DesignofControlLaws andStateObserversfor Fixed-WingUAVs

SimulationandExperimental Approaches

ArturoTadeoEspinoza-Fraire FacultyofEngineering,Science,andArchitecture UniversityJuárezoftheDurangoState GómezPalacio,Durango,Mexico

AlejandroEnriqueDzulLópez

ElectricalandElectronicEngineeringDepartment TechnologicalInstituteofLaLaguna Torreón,Coahuila,Mexico

RicardoPavelParadaMorado AcademyofEngineeringinManufacturingTechnologies PolytechnicUniversityofGómezPalacio GómezPalacio,Durango,Mexico

JoséArmandoSáenzEsqueda FacultyofEngineering,Science,andArchitecture UniversityJuárezoftheDurangoState GómezPalacio,Durango,Mexico

Elsevier

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TypesetbyVTeX

3.6Uncoupledmodelofthefixed-wingUAV

4Linearcontrollers35

4.1PDandPIDcontrollers

4.2LQRcontroller

4.3LQRcontrollerwiththediscrete-timeKalmanfilter

5Nonlinearcontrollers49

6Stateobservers89

6.4Nonlinearextendedstateobserver

6.5Backsteppingobserver

6.6Simulationresultsofthecontrollawswithobservers

6.6.1PDcontrollawwithobservers

6.6.2Backsteppingcontrollawwithobservers

6.6.3RollmotionsimulationswithPDcontrollawwith observers

6.6.4YawmotionsimulationswithPDcontrollawwith observers

6.6.5AltitudemotionsimulationswithPDcontrollawwith observers

6.6.6Rollmotionsimulationswithbacksteppingcontrollawwith

6.6.7Yawmotionsimulationswithbacksteppingcontrollaw withobservers

7.3Inertialmeasurementunit(IMU)

7.9.3LQRcontroller

7.9.4LQRcontrollerwithdiscrete-timeKalmanfilter

7.9.5Backsteppingcontroller

7.10.1Luenbergerobserverappliedtoafixed-wingUAVwithPD

7.10.2SMOappliedtoafixed-wingUAVwithPDcontrollaw

7.10.3NESOappliedtoafixed-wingUAVwithPDcontrollaw

7.10.4SMOappliedtoafixed-wingUAVwithbackstepping controllaw

7.10.5NESOappliedtoafixed-wingUAVwithbackstepping

A.8.4Sequenceconvergence

A.9.5Gronwall–Bellmaninequality

D.1.2Linearquadraticregulator(LQR)

D.2.1Nestedsaturations

D.2.2Integratorbackstepping

Listoffigures

Fig.1.1

Fig.2.1 Schematicofanairfoilsection.

Fig.2.3

Fig.2.4

Fig.2.5

Fig.3.3 Movementvariablesofafixed-wingUAV.

Fig.3.4

Fig.3.5

Fig.3.6

Fig.3.7 The x -, y -,and z-axesinthebodyoftheairplane. 29

Fig.3.8 Yawangle. 32

Fig.3.9 Rollangle.

Fig.4.1 ActionofthePDcontrolleronaltitude.

Fig.4.2 ActionofthePIDcontrolleronaltitude. 37

Fig.4.3 ActionofthePDcontrolleronyaw. 38

Fig.4.4 ActionofthePIDcontrolleronyaw.

Fig.4.5 ActionofthePDcontrolleronroll.

Fig.4.6 ActionofthePIDcontrolleronroll. 39

Fig.4.7 ActionoftheLQRcontrolleronaltitude. 42

Fig.4.8 ActionoftheLQRcontrolleronyaw.

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

Fig.5.8 Actionoftheslidingmodecontrolleronyaw. 57

Fig.5.9 Actionoftheslidingmodecontrolleronroll. 57

Fig.5.10 Actionofthenestedsaturationcontrollerwithslidingmodeonaltitude. 58

Fig.5.11 Actionofthenestedsaturationcontrollerwithslidingmodeonyaw. 59

Fig.5.12 Actionofthenestedsaturationcontrollerwithslidingmodeonroll. 59

Fig.5.13 Actionofthenestedsaturationcontrollerwith2-SMonaltitude. 61

Fig.5.14 Actionofthenestedsaturationcontrollerwith2-SMonyaw. 61

Fig.5.15 Actionofthenestedsaturationcontrollerwith2-SMonroll. 62

Fig.5.16 ActionofthenestedsaturationcontrollerwithHOSMonaltitude. 63

Fig.5.17 ActionofthenestedsaturationcontrollerwithHOSMonyaw. 64

Fig.5.18 ActionofthenestedsaturationcontrollerwithHOSMonroll. 64

Fig.5.19 Actionofthebacksteppingcontrollerwithslidingmodeonaltitude. 66

Fig.5.20 Actionofthebacksteppingcontrollerwithslidingmodeonyaw. 67

Fig.5.21 Actionofthebacksteppingcontrollerwithslidingmodeonroll. 67

Fig.5.22 Actionofthebacksteppingcontrollerwithsecond-orderslidingmodeon altitude. 68

Fig.5.23 Actionofthebacksteppingcontrollerwithsecond-orderslidingmodeon yaw. 69

Fig.5.24 Actionofthebacksteppingcontrollerwithsecond-orderslidingmodeon roll. 70

Fig.5.25 ActionofthebacksteppingcontrollerwithHOSMonaltitude. 71

Fig.5.26 ActionofthebacksteppingcontrollerwithHOSMonyaw. 71

Fig.5.27 ActionofthebacksteppingcontrollerwithHOSMonroll. 72

Fig.5.28 BlockdiagramoftheMRASappliedtoafixed-wingUAV. 73

Fig.5.29 AdaptivePDcontrollerresponseforaltitude(withdisturbances). 76

Fig.5.30 ControlsignaloftheadaptivePDcontrollerforaltitude(withdisturbances).

Fig.5.31 Minimizationofthecostfunctionforaltitude(withdisturbances).

Fig.5.32 Responseoftheadaptiveproportionalgaincontrollerforaltitude(with disturbances).

76

77

77

Fig.5.33 Responseoftheadaptivederivativegaincontrollerforaltitude(with disturbances). 78

Fig.5.34 ZoomofthecontrolsignaloftheadaptivePDcontrollerforaltitude(with disturbances). 78

Fig.5.35 Responseoftheslidingmanifoldcontrollerwithadaptiveproportionalgain foraltitude(withdisturbances). 79

Fig.5.36 Responseoftheslidingmanifoldcontrollerwithadaptivederivativegain foraltitude(withdisturbances). 79

Fig.5.37 AdaptivePDcontrollerresponsefortheyawangle(withdisturbances). 80

Fig.5.38 ControlsignaloftheadaptivePDcontrollerfortheyawangle(with disturbances). 80

Fig.5.39 Minimizationofthecostfunctionfortheyawangle(withdisturbances). 81

Fig.5.40 Responseoftheadaptiveproportionalgainfortheyawangle(with disturbances). 81

Fig.5.41 Responseoftheadaptivederivativegainfortheyawangle(with disturbances). 82

Fig.5.42 ZoomofthecontrolsignaloftheadaptivePDcontrollerfortheyawangle (withdisturbances). 82

Fig.5.43 Responseoftheslidingmanifoldintheadaptiveproportionalgainforthe yawangle(withdisturbances). 83

Fig.5.44 Responseoftheslidingmanifoldintheadaptivederivativegainfortheyaw angle(withdisturbances). 83

Fig.5.45 AdaptivePDcontrollerresponsefortherollangle(withdisturbances). 84

Fig.5.46 ControlsignaloftheadaptivePDcontrollerfortherollangle(with disturbances). 84

Fig.5.47 Minimizationofthecostfunctionfortherollangle(withdisturbances). 85

Fig.5.48 Responseoftheadaptiveproportionalgainfortherollangle(with disturbances). 85

Fig.5.49 Responseoftheadaptivederivativegainfortherollangle(with disturbances). 86

Fig.5.50 ZoomofthecontrolsignaloftheadaptivePDcontrollerfortherollangle (withdisturbances). 86

Fig.5.51 Responseoftheslidingmanifoldintheadaptiveproportionalgainforthe rollangle(withdisturbances). 87

Fig.5.52 Responseoftheslidingmanifoldintheadaptivederivativegainfortheroll angle(withdisturbances). 87

Fig.6.1 Rollangleestimationforthethreestateobservers.

106

Fig.6.2 Rollangularvelocityestimateforthethreestateobservers. 106

Fig.6.3 Rollangleestimationerrorforthethreestateobservers. 106

Fig.6.4 Rollangularvelocityestimationerrorforthethreestateobservers. 107

Fig.6.5 ExtendedstateofNESO. 107

Fig.6.6 PDcontrolsignalforrollmotion. 107

Fig.6.7 Yawangleestimationforthethreestateobservers. 108

Fig.6.8 Yawrateestimationforthethreestateobservers. 108

Fig.6.9 Yawangleestimationerrorforthethreestateobservers. 109

Fig.6.10 Yawangularrateestimationerrorforthethreestateobservers. 109

Fig.6.11 Extendedstateforyawmovement. 109

Fig.6.12 PDcontrolsignalforyawmovement. 110

Fig.6.13 Pitchangleestimationforthethreestateobservers. 110

Fig.6.14 Pitchangularvelocityestimateforthethreestateobservers. 110

Fig.6.15 Pitchangleestimationerrorforthethreestateobservers. 111

Fig.6.16 Pitchangularvelocityestimationerrorforthethreestateobservers. 111

Fig.6.17 Extendedstateforpitchingmotion. 111

Fig.6.18 SimulationofthealtitudemovementwithPDcontrolforthethree observers. 112

Fig.6.19 PDcontrolsignalforpitchmotion. 112

Fig.6.20 Rollangleestimationforthethreestateobservers. 113

Fig.6.21 Rollangularvelocityestimateforthethreestateobservers. 113

Fig.6.22 Rollangleestimationerrorforthethreestateobservers. 113

Fig.6.23 Rollangularvelocityestimationerrorforthethreestateobservers. 114

Fig.6.24 Extendedstateforrollmotion. 114

Fig.6.25 Backsteppingcontrolsignalforrollmotion. 114

Fig.6.26 Yawangleestimationforthethreestateobservers. 115

Fig.6.27 Yawrateestimationforthethreestateobservers. 115

Fig.6.28 Yawangleestimationerrorforthethreestateobservers. 116

Fig.6.29 Yawangularrateestimationerrorforthethreestateobservers. 116

Fig.6.30 Extendedstateforyawmotion.

Fig.6.31 Backsteppingcontrolsignalforyawmovement.

Fig.6.32 Pitchangleestimationforthethreestateobservers.

Fig.6.33 Pitchangularvelocityestimatesforthethreestateobservers.

Fig.6.34 Pitchangleestimationerrorforthethreestateobservers. 118

Fig.6.35 Pitchangularvelocityestimationerrorforthethreestateobservers. 118

Fig.6.36 Extendedstateforpitchingmotion. 118

Fig.6.37 Altitudemovementsimulationwithbacksteppingcontrolforthethree observers.

Fig.6.38 Backsteppingcontrolsignalforpitchmotion.

Fig.7.1 Brushlessmotor.

Fig.7.2 Exampleofservomotorusedforelevator,rudder,andaileron.

Fig.7.3 InertialmeasurementunitMIDGII. 123

Fig.7.4 Xbeetoobtainthevariablesfromthefixed-wingUAV. 123

Fig.7.5 Optocoupler.

Fig.7.6 Microcontroller(PropellerP8X32A).

Fig.7.7 Altimeter(MS5607). 125

Fig.7.8 MicroprocessorRabbit(RCM6000). 126

Fig.7.9 PCBcomplementaryforthemicroprocessorRabbit(RCM6000). 126

Fig.7.10 RadiocontrolFutaba(T7C). 127

Fig.7.11 Lineartransformation. 127

Fig.7.12 Embeddedsystemmountedonthefixed-wingUAV. 128

Fig.7.13 Electronicsystemblockdiagram.

Fig.7.14 Li-pobattery.

Fig.7.15 ActionofthePDcontrollerforaltitude.

Fig.7.16 ActionofthePDcontrollerforyaw.

Fig.7.17 PDcontrollerforroll.

Fig.7.18 ActionofthePIDcontrollerforaltitude.

Fig.7.19 ActionofthePIDcontrollerforyaw.

Fig.7.20 ActionofthePIDcontrollerforroll.

Fig.7.21 ActionoftheLQRcontrollerforaltitude.

130

133

133

134

Fig.7.22 ActionoftheLQRcontrollerforyaw. 135

Fig.7.23 ActionoftheLQRcontrollerforroll.

Fig.7.24 ResponseoftheLQRcontrollerwithdiscrete-timeKalmanfilterfor altitude.

Fig.7.25 ResponseoftheLQRcontrollerwithdiscrete-timeKalmanfilterforyaw.

Fig.7.26 ResponseoftheLQRcontrollerwithdiscrete-timeKalmanfilterforroll.

Fig.7.27 Responseofthebacksteppingcontrollerforaltitude.

Fig.7.28 Actionofthebacksteppingcontrolleronyaw.

Fig.7.29 Actionofthebacksteppingcontrolleronroll.

Fig.7.30 ResultsoftheexperimentapplyingtheLuenbergerobservertoafixed-wing UAVforpitchangle.

Fig.7.31 ResultsoftheexperimentapplyingtheLuenbergerobservertoafixed-wing UAVforpitchangularvelocity.

Fig.7.32 Pitchangleestimationerror.Resultsoftheexperimentapplyingthe Luenbergerobservertoafixed-wingUAV.

Fig.7.33 Pitchanglevelocityestimationerror.Resultsoftheexperimentapplying theLuenbergerobservertoafixed-wingUAV.

135

137

137

138

138

139

139

141

141

141

142

Fig.7.34 Measuredaltitude.ResultsoftheexperimentapplyingtheLuenberger observertoafixed-wingUAV.

Fig.7.35 Controlsignal.ResultsoftheexperimentapplyingtheLuenbergerobserver toafixed-wingUAV. 142

Fig.7.36 ResultsoftheexperimentapplyingtheLuenbergerobservertoafixed-wing UAVforrollangle. 143

Fig.7.37 ResultsoftheexperimentapplyingtheLuenbergerobservertoafixed-wing UAVforrollangularvelocity. 143

Fig.7.38 Rollangleestimationerror.Resultsoftheexperimentapplyingthe Luenbergerobservertoafixed-wingUAV. 143

Fig.7.39 Rollangularvelocityestimationerror.Resultsoftheexperimentapplying theLuenbergerobservertoafixed-wingUAV.

Fig.7.40 Controlsignal.ResultsoftheexperimentapplyingtheLuenbergerobserver toafixed-wingUAVforrollangle. 144

Fig.7.41 ResultsoftheexperimentapplyingtheLuenbergerobservertoafixed-wing UAVforyawangle.

144

Fig.7.42 ResultsoftheexperimentapplyingtheLuenbergerobservertoafixed-wing UAVforyawangularvelocity. 145

Fig.7.43 Yawangleestimationerror.Resultsoftheexperimentapplyingthe Luenbergerobservertoafixed-wingUAV.

Fig.7.44 Estimationoftheyawangularvelocity.Resultsoftheexperimentapplying theLuenbergerobservertoafixed-wingUAV.

Fig.7.45 Controlsignal.ResultsoftheexperimentapplyingtheLuenbergerobserver toafixed-wingUAVforyawangle.

Fig.7.46 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforpitch angle.

Fig.7.47 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforpitch angularvelocity.

Fig.7.48 Pitchangleestimationerror.ResultsoftheexperimentapplyingSMOtoa fixed-wingUAV.

Fig.7.49 Pitchanglevelocityestimationerror.Resultsoftheexperimentapplying SMOtoafixed-wingUAV.

Fig.7.50 Measuredaltitude.ResultsoftheexperimentapplyingSMOtoa fixed-wingUAVforpitchangle.

Fig.7.51 Controlsignal.ResultsoftheexperimentapplyingSMOtoafixed-wing UAVforpitchangle.

Fig.7.52 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforroll angle.

Fig.7.53 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforroll angularvelocity.

Fig.7.54 Rollangleestimationerror.ResultsoftheexperimentapplyingSMOtoa fixed-wingUAV.

Fig.7.55 Rollangularvelocityestimationerror.Resultsoftheexperimentapplying SMOtoafixed-wingUAV.

Fig.7.56 Controlsignal.ResultsoftheexperimentapplyingSMOtoafixed-wing UAVforrollangle.

Fig.7.57 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforyaw angle.

145

145

146

146

147

147

147

148

148

148

149

149

149

150

150

Fig.7.58 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforyaw angularvelocity. 151

Fig.7.59 Yawangleestimationerror.ResultsoftheexperimentapplyingSMOtoa fixed-wingUAV. 151

Fig.7.60 Estimationoftheyawangularvelocity.Resultsoftheexperimentapplying SMOtoafixed-wingUAV. 151

Fig.7.61 Controlsignal.ResultsoftheexperimentapplyingSMOtoafixed-wing UAVforyawangle. 152

Fig.7.62 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforpitch angle. 152

Fig.7.63 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforpitch angularvelocity. 152

Fig.7.64 Pitchangleestimationerror.ResultsoftheexperimentapplyingNESOtoa fixed-wingUAV. 153

Fig.7.65 Pitchanglevelocityestimationerror.Resultsoftheexperimentapplying NESOtoafixed-wingUAV. 153

Fig.7.66 Measuredaltitude.ResultsoftheexperimentapplyingNESOtoa fixed-wingUAVforpitchangle.

153

Fig.7.67 Controlsignal.ResultsoftheexperimentapplyingNESOtoafixed-wing UAVforpitchangle. 154

Fig.7.68 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforroll angle. 154

Fig.7.69 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforroll angularvelocity.

Fig.7.70 Rollangleestimationerror.ResultsoftheexperimentapplyingNESOtoa fixed-wingUAV.

155

155

Fig.7.71 Rollangularvelocityestimationerror.Resultsoftheexperimentapplying NESOtoafixed-wingUAV. 155

Fig.7.72 Controlsignal.ResultsoftheexperimentapplyingNESOtoafixed-wing UAVforrollangle. 156

Fig.7.73 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforyaw angle.

Fig.7.74 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforyaw angularvelocity.

156

156

Fig.7.75 Yawangleestimationerror.ResultsoftheexperimentapplyingNESOtoa fixed-wingUAV. 157

Fig.7.76 Estimationoftheyawangularvelocity.Resultsoftheexperimentapplying NESOtoafixed-wingUAV. 157

Fig.7.77 Controlsignal.ResultsoftheexperimentapplyingNESOtoafixed-wing UAVforyawangle. 157

Fig.7.78 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforpitch angle.

Fig.7.79 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforpitch angularvelocity.

158

158

Fig.7.80 Pitchangleestimationerror.ResultsoftheexperimentapplyingSMOtoa fixed-wingUAV. 159

Fig.7.81 Pitchanglevelocityestimationerror.Resultsoftheexperimentapplying SMOtoafixed-wingUAV. 159

Fig.7.82 Measuredaltitude.ResultsoftheexperimentapplyingSMOtoa fixed-wingUAVforpitchangle.

159

Fig.7.83 Controlsignal.ResultsoftheexperimentapplyingSMOtoafixed-wing UAVforpitchangle. 160

Fig.7.84 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforroll angle. 160

Fig.7.85 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforroll angularvelocity. 160

Fig.7.86 Rollangleestimationerror.ResultsoftheexperimentapplyingSMOtoa fixed-wingUAV. 161

Fig.7.87 Rollangularvelocityestimationerror.Resultsoftheexperimentapplying SMOtoafixed-wingUAV. 161

Fig.7.88 Controlsignal.ResultsoftheexperimentapplyingSMOtoafixed-wing UAVforrollangle. 161

Fig.7.89 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforyaw angle. 162

Fig.7.90 ResultsoftheexperimentapplyingSMOtoafixed-wingUAVforyaw angularvelocity.

162

Fig.7.91 Yawangleestimationerror.ResultsoftheexperimentapplyingSMOtoa fixed-wingUAV. 163

Fig.7.92 Estimationoftheyawangularvelocity.Resultsoftheexperimentapplying SMOtoafixed-wingUAV.

163

Fig.7.93 Controlsignal.ResultsoftheexperimentapplyingSMOtoafixed-wing UAVforyawangle. 163

Fig.7.94 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforpitch angle. 164

Fig.7.95 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforpitch angularvelocity. 164

Fig.7.96 Pitchangleestimationerror.ResultsoftheexperimentapplyingNESOtoa fixed-wingUAV. 164

Fig.7.97 Pitchanglevelocityestimationerror.Resultsoftheexperimentapplying NESOtoafixed-wingUAV.

165

Fig.7.98 Measuredaltitude.ResultsoftheexperimentapplyingNESOtoa fixed-wingUAVforpitchangle. 165

Fig.7.99 Controlsignal.ResultsoftheexperimentapplyingNESOtoafixed-wing UAVforpitchangle.

165

Fig.7.100 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforroll angle. 166

Fig.7.101 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforroll angularvelocity.

166

Fig.7.102 Rollangleestimationerror.ResultsoftheexperimentapplyingNESOtoa fixed-wingUAV. 167

Fig.7.103 Rollangularvelocityestimationerror.Resultsoftheexperimentapplying NESOtoafixed-wingUAV.

Fig.7.104 Controlsignal.ResultsoftheexperimentapplyingNESOtoafixed-wing UAVforrollangle.

Fig.7.105 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforyaw angle.

167

167

168

Fig.7.106 ResultsoftheexperimentapplyingNESOtoafixed-wingUAVforyaw angularvelocity. 168

Fig.7.107 Yawangleestimationerror.ResultsoftheexperimentapplyingNESOtoa fixed-wingUAV. 168

Fig.7.108 Estimationoftheyawangularvelocity.Resultsoftheexperimentapplying NESOtoafixed-wingUAV. 169

Fig.7.109 Controlsignal.ResultsoftheexperimentapplyingNESOtoafixed-wing UAVforyawangle. 169

Fig.B.1 Freebodydiagram.

Fig.D.1 BlockdiagramofaPIDcontrollerinaplant.

Fig.D.2 Optimalregulatorysystem.

Fig.D.3 GeneralblockdiagramoftheMRAC.

Fig.E.1 Discrete-timeKalmanfilterblockdiagram.

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208

Listoftables

Table4.1

Table4.3 Valuesoftheparametersofthediscrete-timeKalmanfilterforthealtitude andfortheyawandrollangles.

Table4.4 GainsoftheLQRcontrollerandtheLQRcontrollerwiththediscrete-time Kalmanfilter.

Table4.5 L2 normfortheerrorsandtheactionsofthelinearcontrollers.

Table5.1

Table5.5 Gainsofthenestedsaturationcontrollerwithsecond-orderslidingmode.

Table5.6 GainsofthenestedsaturationcontrollerwithHOSM.

Table5.7 Gainsofthebacksteppingcontrollerwithslidingmode.

Table5.8

Table5.10 L2 -normoftheerrorsandcontroleffortsofthenonlinearcontrollersand thecombinationsofthenonlinearcontrollers.

Table6.1 L2 normfortheerrorsintheobserverswithdifferentcontrollaws.

Table7.1

Table7.2

Table7.3

Table7.4 Gainsofthebacksteppingcontrollerinexperiments.

Table7.5 L2 normfortheerrorsofthelinearandnonlinearcontrollersinthereal flighttest.

Table7.6 L2 normfortheerrorsoftheobserverswithdifferentcontrollaws.

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Preface

Thistextisintendedforusebyundergraduateandpostgraduatestudentsandeven researchersinterestedinUAVs.Itcanevenbeusedincoursesinaerodynamicengineeringandautomaticcontroltheory.

Weaimtoachievetwoobjectiveswiththisbook.Thefirstistheeffectivenessto useareduceduncoupledaerodynamicmodelforfixed-wingUAVstodesignlinear andnonlinearcontrollawsandstateobservers.Thesecondistopresentseveralsimulations(numericalcomputation)andexperimentalrealflighttestresultswithlinear andnonlinearcontrollawsandstateobserversdesignedfromthereduceduncoupled aerodynamicmodel,whichishelpfulforanystudentorresearcherduetothecomplexityofcarryingoutthesetestswithfixed-wingUAVsandevenprovidetheinformation necessarytocarryoutrealflighttestswithsuchunmannedvehicles.

Thisbookprovidesmorethanenoughmaterialforaone-semestercourse.The structureofthisbookisasfollows:

• Chapter 1 presentsabriefintroductiontotheclassificationofUAVsandnonmilitaryapplicationsoffixed-wingUAVsandageneraldescriptionofcontrolsystems andstateobservers.

• Chapter 2 containsaerodynamicprinciplestounderstandtheflightoffixed-wing UAVs.

• Chapter 3 isaboutobtainingtheequationsofmotionofafixed-wingUAVand containstheaerodynamicmodelusedtodesignthenonlinearandlinearcontrol lawsandstateobservers.

• Chapter 4 andChapter 5 presentthelinearandnonlinearcontrollaws,respectively. Theresultsobtainedwithseveralcomputersimulationsarepresented.

• Chapter 6 isaboutthelinearandnonlinearstateobserversandpresentstheresults obtainedwithseveralcomputersimulations.

• Chapter 7 presentstherealflighttestresultsobtainedwiththelinearandnonlinear controllawsandwiththestateobservers.

• Theappendixpresentsessentialmaterialtounderstandthematerialpresentedin thisbook.

WerecognizethesupportandhelpforthisprojectfromourfamiliesandDennis McGonagleandSaraGrecofromtheElsevierteam.

A.T.Espinoza-Fraire

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Acknowledgments

A.T.Espinoza-Fraire:TomywifeAbrilHuizarandmychildrenMarielaandMateo.

A.Dzul:TomywifeRosyandmychildrenJaimeandRegina.

R.Pavel:TomywifeAlmaLiliaandmydaughtersSophiaandMaia.

J.Sáenz:ToDr.Campa,myfatherDr.AgustínSáaenz,andmymotherMaríaConcepciónEsqueda.

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Synopsis

Currently,theapplicationofdronesorUAVspresentsawidefieldofstudyforresearcherstosolvecivilorindustryproblems.Buttoobtainsolutionsintheseareasit isnecessarytoprovideabasisforstudyingunmannedaerialsystems.

Thisbookprovidesthebasisforstudyingfixed-wingUAVs,includingabrief introductionintostate-of-the-artfixed-wingUAVs.Inaddition,thedevelopmentof mathematicalmodelsthatdescribethesevehiclesisincluded.

Thecontrollersandstateobserversdiscussedinthisbookarelinearandnonlinear. Theresultsofseveralexperiments(realflighttests)andsimulationswiththelinear andnonlinearcontrollersandstateobserversarepresented.Theembeddedsystemis givenandtheelectroniccomponentsaredescribed.

Theappendixcontainsamathematicalreviewnecessarytounderstandthelinear andnonlineartheoryusedinthecontrollawsandthestateobserversinthisbook.The appendixalsocontainstheprogramcodesofsomelinearandnonlinearcontrollers andobserversusedinthisbook,anditevenincludesthenecessaryprogramcodesto readthesensorsusedintheembeddedsystem.TheMATLAB® codefortheground stationtoreadthedatafromthefixed-wingunmannedaerialsystemduringflighttests isadded.

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1 Introduction

Thischapterpresentsabriefgeneraloverviewofsomeclassifications,applications, andcontrolsystemsrealizedtoconductresearchanddevelopapplicationsinthefield offixed-wingunmannedaerialvehicles(UAVs).

1.1ClassificationofUAVs

UAVscangenerallybeclassifiedintofixed-wingaircraftandmultirotors.Bothtypes ofairvehiclespossessuniquecharacteristicsthatchallengetheirperformanceasautonomoussystems.Inthisbook,onlyUAVsofthefixed-wingclassareconsidered.

Theterm“smallUAV”referstoaclassoffixed-wingUAVswithawingspanbetween5and10feet.SmallUAVsareusuallyfueledandrequirearunwayfortake-off andlanding;insomecases,acatapultisusedfortake-off.

ThetermminiUAV(MAV)referstoaclassofUAVswithawingspansmallerthan 5feet.Smallairvehiclesaretypicallydesignedtoflyfrom10to12hoursandmay loadapproximately10to50pounds[9].Usually,thesevehiclesrunonbatteries,are launch-handed,andmaynothavelandinggear,sotheydonotrequirearunwayfor take-offorlanding.

MAVsaredesignedtoflyfrom20minutestoafewhours;payloadsrangefrom ouncestoseveralpounds.Consequently,thesmallpayloadseverelyrestrictstheload ofsensorsandmicrocontrollersthatcanbeplacedontoMAVs[9].Theserestrictions poseexcitingchallengesforthedesignofautonomoussystems.

1.2Nonmilitaryapplicationsoffixed-wingUAVs

Nowadays,thereexistmanyapplicationsofUAVs.Forexample,applicationsofthe fixed-wingUAVinagricultureincludethedetectionofinsects,weeds,diseases,crop characteristics,biomass,andbackgroundsoilproperties.

Marineapplicationsincludefollowingspecieslikewhalesanddolphinsinorderto analyzetheirmovementanddisplacementsacrosstheocean.

OtherapplicationsofUAVsincluderesearchofairquality.Thisisachievedby equippingtheUAVwithsensorstomeasureairpollution.Somesensorsusedinpollutionanalysisdetectcarbondioxide,ozone,andblacksmokeparticles.

Fixed-wingUAVshavealreadybeenappliedtocartography,whereitisnecessary tointerpret,analyze,andrepresentgraphicallyallorpartofaspecificarea,whichis appliedtomappingtasks.

OtherinterestingapplicationsofthistypeofUAVsareincivilengineeringand architecture,wheretheyareusedtoobtainthetopographyofsometerrainandconDesignofControlLawsandStateObserversforFixed-WingUAVs. https://doi.org/10.1016/B978-0-32-395405-1.00010-8 Copyright©2023ElsevierInc.Allrightsreserved.