Table Of ContentStudies in Systems, Decision and Control 384
Moussa Labbadi
Yassine Boukal
Mohamed Cherkaoui
Advanced Robust
Nonlinear Control
Approaches
for Quadrotor
Unmanned Aerial
Vehicle
Roadmap to Improve Tracking-Trajectory
Performance in the Presence of External
Disturbances
Studies in Systems, Decision and Control
Volume 384
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· ·
Moussa Labbadi Yassine Boukal
Mohamed Cherkaoui
Advanced Robust Nonlinear
Control Approaches
for Quadrotor Unmanned
Aerial Vehicle
Roadmap to Improve Tracking-Trajectory
Performance in the Presence of External
Disturbances
MoussaLabbadi YassineBoukal
EngineeringforSmartandSustainable DepartmentofAeronautics,Space
SystemsResearchCenter,Mohammadia andDefense
SchoolofEngineers CapgeminiEngineering
MohammedVUniversityinRabat Toulouse,France
Rabat,Morocco
MohamedCherkaoui
EngineeringforSmartandSustainable
SystemsResearchCenter,Mohammadia
SchoolofEngineers
MohammedVUniversityinRabat
Rabat,Morocco
ISSN2198-4182 ISSN2198-4190 (electronic)
StudiesinSystems,DecisionandControl
ISBN978-3-030-81013-9 ISBN978-3-030-81014-6 (eBook)
https://doi.org/10.1007/978-3-030-81014-6
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Thisworkisdedicatedto
MybrotherMohamedLABBADI,deceasedin
theprimeofhislife.MayAllah,theAlmighty,
havehiminhisholymercy!
—MoussaLabbadi
MyfatherLarbiBOUKAL,whopassedaway
tooearly,andwhoalwayspushedand
motivatedmeinmystudies.MayGod,the
Almighty,havehiminhisholymercy!
—YassineBoukal
Preface
The present book aims to develop and design some robust nonlinear flight control
strategiesforthequadrotorUAV(QUAV)systeminthepresenceofexternaldistur-
bances,andthesystemuncertainties.Thisbookpresentsnewcontrolapproachesto
synthesizethenonlinearcontrolofthetrajectoryoftheQUAV.Despitearichlitera-
ture,theproblemhasnotyetbeenadequatelyaddressedanditisdifficulttoprovide
high-precisionflightpathfollowinginthepresenceofthesedisturbances.Thiswork
proposedrobustcontroltechniquestoachieveadequateset-pointtrackingofdifferent
complex trajectories of QUAV and unknown disturbance rejection with smoother
controlaction.Basedonslidingmodecontrol(SMC)theory,backsteppingtechnique,
fractional-ordercalculus,andadaptivelaws,trackingmethodsarepresentedforthe
QUAV.Themainmotivationsofthisbookaregivenbythefollowingpoints:
1. DesigningacontrolstrategyforQUAVtomeetcertainrequirements(precision,
minimumenergyconsumption,andsimplestructure)posesanadditionalchal-
lenge.Also,thedesignofflightcontrollersforthesemulti-rotordronespresents
threeimportantchallenges:(i)thevehicledynamicsaremulti-input,multi-output
(MIMO) and strongly nonlinear coupled; (ii) the dynamics of the quadrotor
involve various sources of uncertainties, including parametric uncertainties,
unmodeleduncertainties,andexternaldisturbances;(iii)therearemultiplestates
varyingovertimeandentrydelaysintocontrolsystems.So,thisbookproposes
robustflightcontrolschemesagainsttheseperturbations.
2. Inthepresenceofexternaldisturbances,thetrajectoryfollowingperformance
oftheQUAVmaybedegraded,anditsdynamicsystemsmayalsoleadtoinsta-
bility.ThecouplingbetweenthepositionandattitudeoftheQUAVincreasesthe
stabilityproblemwithsatisfiedperformance.Hence,disturbancesthataffected
theQUAVsystemshouldbeconsideredinthedesignoftheflightcontrollerto
enhancetheQUAVcontrolperformance.Thehigh-orderSMCisusuallyapplied
to nonlinear complex systems under disturbances. The super-twisting and its
versioncontrolsaresuccessfullyadaptedtononlinearsystems.
3. ItisgenerallyknownthattheSMCtechniqueappliedforQUAVisrobustcontrol,
butdoesnotguaranteefinitetimeconvergence.Also,thesystemuncertaintiescan
vii
viii Preface
degradethecontrolperformance.Asaresult,thenonlinearslidingmodevariables
aredesignedandparametricuncertaintiesarerejectedtoenhancedtheperfor-
manceoftheclosed-loopsystem.Inaddition,somecontrollawsaredeveloped
toguaranteetheslidingmodeoftheQUAVstatesintheinitialtime.Therefore,
thedevelopmentofhybridfinite-timecontrolandglobalSMCissignificantfor
thecontrolofQUAVsystemswithperturbations.
4. Designadaptivelawswithfinite-timecontroloftheerrorstozerooftheQUAV
inthepresenceofdisturbancesanduncertaintiesareachallengingproblemfor
thistypesystem.Therefore,consideringthesecontrolproblemsandguaranteeing
the finite-time stability as well as specific criteria such as perturbation rejec-
tionandrobustnesstotheparametricuncertaintiesofthesystemareverysignif-
icant for the QUAV. Also, the upper bound of these perturbations is assumed
tobeknowninadvance:inreality,thislimitisunknownanddifficulttodeter-
mine. Moreover, it is a challenging problem to develop the control laws for
addressingtheseperturbationsandguaranteethefinite-timestability.Therefore,
time-varyingSMC,terminalSMC,andnonsingularterminalSMCschemeswith
adaptivelawsneedtobefurtherstudiedforQUAVsystemsinthepresenceof
externalwinddisturbancesandparametricuncertainties.
5. The design of robust nonlinear controls with the fractional-order dynamics
suchashigh-orderSMC,TSMC,nonsingularTSMC,backsteppingtechniques,
the path following of the QUAV is realized and better robustness can be
obtainedagainstparametricuncertaintiesandperturbations.Theseflightcontrol
methodsareimportantwhentheQUAVisaffectedbyunknowncomplexdistur-
bancesduringflightmissions.Thecontrolperformanceofthesefractional-order
controllersmaybebetterthanintegercontrollers.Therefore,itisimportantto
studythesecontrolschemesfortheQUAV.Thecontrolperformanceincludingthe
transientandsteadystatesofthetrackingerrorsshouldbeenhancedfortheQUAV
inthepresenceofunknowndisturbancestominimizetheconsummationerror
energy.Thestudyusesrobustnonlinearcontrollersincludingfractionaldynamics
oftheseactions.Usingthese,theaboveperformancecanbeimprovedunderthe
effectofdisturbances.
Themaincontributionsoftheresearchworkcarriedoutinthisbookareshown
asfollows:
Firstly,onthebasicoftheresultresearchonthehigh-orderSMCfortheQUAV,
a combination of the integral SMC with the super-twisting algorithm to eliminate
thereticencephenomenonispresented.Thiscontrolmethodisproposedtostabilize
theQUAVtofollowapathinthepresenceofperturbations.Vehiclestatevariables
convergetotheirdesiredvaluesinashorttimeataspecifiedtime.Inordertoincrease
therobustnessofthecontrolsystem,anewoptimizationisusedtoadjusttheproposed
controllerparameters.Inaddition,anovelmodifiedsuper-twistingiscombinedwith
thenonlinearslidingmodecontrollertoimprovethestabilizationofthisvehicleunder
time-varyingdisturbances.Usingnonlinearslidingmodevariables,fastconvergence
ofposition/attitudeoutputsisestablished.Thiscontroltechniqueofferssomeperfor-
mance such as rejection of disturbances and reduction of chattering phenomenon.
Preface ix
TheproposedcontrolmethodsutilizetheLyapunovtheorytoprovethestabilityof
thesystem.Todemonstratetheeffectivenessofthesecontrolapproaches,numerical
simulationsaregiven.
Secondly, for the path following of the QUAV under unknown disturbances, a
hybrid finite-time control technique is proposed, which combines by three control
algorithmsincludingintegralterminalslidingmodecontrolforattitudesubsystem,
adaptivebacksteppingforaltitudechannel,andbacksteppingforhorizontalposition.
Toeliminatethereachingphaseandensureslidingmodeofthestatevariablesofthe
QUAV,arobustcontrollerisdesignedwhichtackingaccounttheinitialtime.Also,the
upperboundoftheseperturbationsisaddressedusingtheproposedcontrolapproach.
Theobtainedresultsinthepresenceofdisturbancesdemonstratetherobustnessof
theproposedcontrollers.Also,theseobtainedresultsarecomparedwithnonlinear
controllers.
Thirdly,arobustapproachtocontrollingtheQUAVhasbeenproposed.Thecontrol
techniqueisdesignedonthebasisofon-lineestimatorsofthedynamicparameters.
These adaptation methods make it possible to improve the control performance of
thissystem,andtocompensatefortheparametricerrorsduetothecouplingofthe
positionwiththeorientationoftheQUAV.Thesuggestedcontrolmethodisbasedon
thebacksteppingfastterminalSMCandanewversionoftheadaptivebackstepping.
Theon-linerulesarepresentedtoestimateexactlysomeunknownparameterscaused
by wind gust and other factors. To assess/emphasize the efficacy of the proposed
controlmethodsfortheQUAV,varioussimulationsundervariousscenariosinterms
of external perturbations and parametric uncertainties are performed. A compar-
isonanalysisclearlydemonstratesthattheproposedcontrolschemesoutperformthe
competition.
Fourthly, it should be noted that all research works have focused on adaptive
upper bound uncertainty estimation using terminal SMC and fast terminal SMC
techniques.Inthisview,asecondcontrolapproachisproposedusinganewadap-
tive nonsingular fast terminal SMC controller (ANFTSMC) for the QUAV under
complex perturbations. The main advantage ANFTSM control is the avoidance of
singularity,therapiditywhenstatesarefarfromtheorigin,andthehighrobustness
against system uncertainty and external disturbances. Also, this controller ensures
fastconvergence,avoidssingularities,resolvesthereticenceeffect,andoffersrobust-
ness against unknown external perturbations and uncertainties. In addition, the
upper limit of uncertainty and unknown external perturbations of the system are
coveredbytheproposedcontrolapproach.On-lineestimationoftheseupperlimits
isintroducedonlybyvelocityandpositionmeasurements.Varioussimulationsunder
differentscenariosintermsofexternalperturbationsandparametricuncertaintiesare
performedtoassess/emphasizetheeffectivenessoftheproposedcontrolmethodsfor
theQUAV.Acomparativestudyclearlyshowstheoutperformanceoftheproposed
controlschemes.
Fifthly, the aerodynamics disturbances, parametric uncertainties, and noise
measurements are considered for the design of adaptive global time-varying SMC
(RAGTVSMC) for the trajectory tracking of the QUAV under the random distur-
bances/uncertainties. The problem of initial control effort and reaching phase is
x Preface
addressedbytheproposedcontroller.Designingtime-varyingslidingmanifoldsfor
theQUAVsystemmeettheimpacttimeandgiventheconvergenceinaspecifictime
ofthestatevariablesinthepresenceofdisturbances.Inaddition,theupperboundof
theseperturbationsisaddressedbydesigningtheadaptivelawsusingonlyvelocity
andpositionofthetrackingerrors.TodemonstratetheeffetenessoftheRAGTVSMC
method,simulationsareconducted.
Sixthly,animprovedFOcontrolisproposedfortheQUAVtosolvetheproblems
inthecontrolofthisvehicleincludingdisturbances,uncertainties,andthevariations
of the drag coefficients. The FO control method uses super-twisting based on FO
integralslidingmodevariablestoimprovethetrackingperformance.Also,ageneric
switching law with FO dynamic is designed for the QUAV to address the distur-
bances.Thecorrespondingcontrollerswithfractionalcalculusensurehighprecision,
fastconvergence,andgoodrobustnessagainstperturbations.Goodscenariosunder
different situations in the flight are proposed to evaluate the efficiency of the FO
control method, and its numerical results show better performance compared with
othercontrolstrategies.
Seventhly, motivated by the advantage of the finite-time stability in the control
theoryandfractionalcalculus,aFOglobalSMCapproachisproposedforthecontrol
problemoftheuncertainQUAVundercomplexdisturbances.Thispresentedmethod
usesthespecificslidingmanifoldstoensurefasterconvergencespeedandweakening
error.TheglobalstabilizationwithaspecifictimeoftheQUAVunderdisturbancesis
guaranteedbasedonLyapunovtheory.Finally,simulationsincludedagoodcompar-
ison with robust controllers are performed to check the correctness of theoretical
analysis.
The nonlinear SMC such nonsingular fast TSMC with FO operators enhances
the tracking performance of the QUAV against random disturbances/uncertainties
and other perturbations. Also, adaptive control law is developed to augment the
robustnessoftheproposedFOcontrolmethodinthepresenceofdisturbances.The
designed control technique ensures high accuracy and fast speed for the QUAV.
UsingFOnonsingularfastterminalslidingmanifolds,afinite-timeconvergenceof
thetrackingerrorsisachieved.
The present book intends to provide the readers an excellent understanding on
howtoobtaintherobustcontrollerpathfollowingapproachesfortheQUAVsystem
inthepresenceofknownorunknownuncertainties,disturbances,andotherproblems
ofthecontrol.Thedesignedcontrolmethodsinthisbookcanbeappliedfornonlinear
systemsundercomplexdisturbancesinvariousfieldsinengineering.Thebookcan
beusedasareferencefortheacademicresearchonthecontroltheory,drones,and
terminalslidingmodecontrol,andrelatedtothisorusedinPh.D.studyofcontrol
theoryandtheirapplicationinfieldengineering.
Rabat,Morocco MoussaLabbadi
Toulouse,France YassineBoukal
Rabat,Morocco MohamedCherkaoui
May2021
