Hybrid L1 Adaptive Control: Applications of Fuzzy Modeling, Stochastic Optimization and Metaheuristics

263 Pages·2022·16.993 MB·English

by  Roshni Maiti, Kaushik Das Sharma, Gautam Sarkar

Studies in Systems, Decision and Control 422
Roshni Maiti
Kaushik Das Sharma
Gautam Sarkar
Hybrid L1
Adaptive
Control
Applications of Fuzzy Modeling,
Stochastic Optimization and
Metaheuristics
Studies in Systems, Decision and Control
Volume 422
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· ·
Roshni Maiti Kaushik Das Sharma
Gautam Sarkar
Hybrid L Adaptive Control
1
Applications of Fuzzy Modeling, Stochastic
Optimization and Metaheuristics
RoshniMaiti KaushikDasSharma
DepartmentofAppliedPhysics DepartmentofAppliedPhysics
UniversityofCalcutta UniversityofCalcutta
Kolkata,WestBengal,India Kolkata,WestBengal,India
GautamSarkar
DepartmentofAppliedPhysics
UniversityofCalcutta
Kolkata,WestBengal,India
ISSN2198-4182 ISSN2198-4190 (electronic)
StudiesinSystems,DecisionandControl
ISBN978-3-030-97101-4 ISBN978-3-030-97102-1 (eBook)
https://doi.org/10.1007/978-3-030-97102-1
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Preface
Conventional control methodologies, viz., Proportional Integral Derivative (PID)
controller,LinearQuadraticRegulator(LQR),etc.,cancontrolLinearTimeInvariant
(LTI)systems.Though,theirperformancesdegradewhennonlinearities,timevarying
uncertainties,timevaryingdisturbances,delays,etc.,presentintothesystem.Adap-
tivecontrollersarisetotackletimevaryinguncertaintiesanddisturbances.Themost
extensivelyusedadaptivecontrolscheme,viz.,ModelReferenceAdaptiveController
(MRAC)utilizeslowadaptationgaintomaintainrobustness.Hence,MRACpossess
sluggishtransientperformance.Withtheaimtoovercomesuchproblem,L adaptive
1
controllerwasintroducedtoprovidefasttransientperformancewithhighrobustness.
However,theperformanceofbasicL adaptivecontrollerdegradeswhennonlinear-
1
ities, delays, etc., are present in the system. On the other hand, nonlinearities can
be properly modelled through universal approximator fuzzy logic. Moreover, the
parametersofthecontrollerscanbechosenbyemployingdifferentstochasticopti-
mizationandmetaheuristicstechniquestoassureoptimalperformance.Anumberof
controllerdesigningschemescanbehybridizedtocontrolpracticalsystemsconsistof
nonlinearities,timevaryinguncertainties,disturbances,cross-couplings,unmodelled
dynamics,delays,etc.,simultaneously.
Thisbookdealswiththedesigningofhybridcontrolstrategiestocontrolpractical
systemscontainingtimevaryinguncertainties,disturbances,nonlinearities,unknown
parameters,unmodelleddynamics,delays,etc.,concurrently.Inthisbook,theadvan-
tagesofdifferentcontrollersarebroughttogethertoproducesuperiorcontrolperfor-
manceforthepracticalsystems.Beingawareoftheadvantagesofadaptivecontroller
totackleunknownconstant,timevaryinguncertaintiesandtimevaryingdisturbances,
anewlyinventedadaptivecontroller,namelyL adaptivecontrollerishybridizedwith
1
otherstrategies.TheparametersofL adaptivecontrollershouldbechosensensibly
1
tomaintainproperbalancebetweengoodtransientperformanceandhighrobustness.
In this book, to facilitate optimal parameter setting of the basic L adaptive
1
controller,stochasticoptimizationandmetaheuristicstechniquesarehybridizedwith
it.AvariantofHarmonySearch(HS)algorithm,viz.,LocalBestHarmonySearch
(lbestHS) algorithm, which is a metaheuristic technique, is employed to tune the
parametervaluesofL adaptivecontroller.ThismethodistermedaslbestHSbased
1
vii
viii Preface
L (lbest HS-L ) adaptive controller. At first, the parameter values of L adap-
1 1 1
tive controller are tuned utilizing lbest HS algorithm within the ranges obtained
frommathematicalcalculationofL normcondition.Then,theunknownconstant,
1
time varying uncertainties and time varying disturbances are adapted concurrently
following adaptation laws to obtain fine-tuned values. The stability of the meta-
heuristictechniquealongwiththecontrollerisguaranteedanalyticallywiththehelp
of spectral radius convergence. This method exhibits satisfactory exploration and
exploitationcapabilities.Itsresultsarecomparedwithstochasticoptimization,viz.,
PSO-basedL adaptivecontroller.
1
Again,thisbookthrowslightontacklingnonlinearitiesalongwithuncertainties
anddisturbancesbyhybridizedfuzzylogicwithL adaptivecontroller.Inthiscase,
1
thenonlinearsystemisdesignedbycombiningfinitenumberoflinearfuzzysystems.
Fuzzy logic-based L adaptive controller is implemented for each linearized zone
1
withthesamepremisepartutilizedtodesignthesystem.Theconventionalstatefeed-
backcontrollerofthebasicL adaptivecontrollerissubstitutedwithfuzzyParallel
1
Distributed Compensation (PDC) controller which is a nonlinear state feedback
controller.TheadaptivefuzzylogicsystemsaredesignedfromthefuzzyLyapunov
function which is the combination of zone-wise Lyapunov functions. The overall
stabilityofthenonlinearsystemwiththiscontrollerisguaranteedwiththehelpof
fuzzy Lyapunov function to retain the zonal behaviour of the system. The fuzzy
PDC-L adaptivecontrollerisefficienttotacklenonlinearitiesandatthesametime
1
cancelsunknownconstant,timevaryinguncertaintiesanddisturbancesadequately.
The performances of these two controllers are compared with different control
methodologiestovalidatetheireffectiveness.Atfirst,twoclassicalcontrollers,viz.,
ProportionalIntegralDerivative(PID)controller,LinearQuadraticGaussian(LQG)
areexamined.Then,conventionaladaptivecontroller,viz.,ModelReferenceAdap-
tive Controller (MRAC) and basic L adaptive controller are tested. After those,
1
a stochastic optimization-based L adaptive controller, viz., Particle Swarm Opti-
1
mization (PSO) based L (PSO-L ) adaptive, metaheuristic HS-based L (HS-L )
1 1 1 1
adaptive and metaheuristiclbest HS-based L (lbest HS-L ) adaptive controller are
1 1
employed. Finally, fuzzy PDC-L adaptive controller is evaluated. In simulation
1
environment,twoSingle-InputSingle-Output(SISO)systems,viz.,Duffing’soscil-
latory system and nonlinear spring mass damper system are examined. Then, one
Single-InputMulti-Output(SIMO)system,viz.,4thorderinvertedpendulumwith
cart system and one Multi-Input Multi-Output (MIMO) system, viz., Twin Rotor
MIMOSystem(TRMS)areinvestigated.Inexperimentalcasestudies,speedcontrol
of an electrical actuator, angular position control of a Two Link Robot Manipu-
lator (TLRM) and temperature control of a delay dependent air heater system are
performed. The results show that, the disturbance rejection phenomenon of basic
L adaptive controller is better than the classical controllers and Model Reference
1
AdaptiveController(MRAC).Though,thetrackingperformanceofbasicL adaptive
1
controllerisnotsatisfactory.IncaseofthelbestHS-L adaptivecontroller,transient
1
as well as tracking performances improve due to the optimal parameter setting of
L adaptivecontroller.ThefuzzyPDC-L adaptivecontrollerprovidesbettersteady
1 1
statetrackingperformancebytacklingnonlinearitiesthroughfuzzylogic-basedPDC
Preface ix
controlleraswellasfasttransientperformancebyproperlyeradicatinguncertainties
anddisturbancesbymeansoffuzzylogic-basedL adaptivecontroller.
1
Therefore, the salient features of the methods presented in this book can be
summarizedasfollows.
I Designing of local best harmony search-based L (lbest HS-L ) adaptive
1 1
controller.
(a) A newly developed adaptive controller, viz., L adaptive controller is
1
hybridizedwithametaheuristiclocalneighbourhoodvariantofHSalgo-
rithm, viz., local best harmony search (lbest HS) algorithm to obtain
optimal balance between fast transient performance and high robustness
byeliminatinguncertaintiesanddisturbances.
(b) SatisfactoryexplorationphenomenonofthelbestHS-L adaptivecontroller
1
is proved analytically by means of increasing population variance with
iterations.
(c) StabilityofthelbestHS-L adaptivecontrollerisguaranteedthroughmath-
1
ematicalanalysisofexploitationphenomenonintermsofspectralradius
convergenceofiterativematrix.
(d) Satisfactory transient and steady state performance of this method are
guaranteed.
II DesigningoffuzzyparalleldistributedcompensationtypeL (fuzzyPDC-L )
1 1
adaptivecontroller.
(a) Fuzzy PDC strategy is augmented with L adaptive controller to tackle
1
nonlinearities,unmodelleddynamics,delays,aswellasuncertaintiesand
disturbances,presentinthesystem.
(b) Fuzzy adaptive rules are formulated to design different components of
fuzzyPDC-L adaptivecontroller,viz.,predictor,L adaptationlaws,L
1 1 1
controllaw,PDCcontrollawandlow-passfilter.
(c) The overall stability of the fuzzy PDC-L adaptive controller is assured
1
withthehelpoffuzzyLyapunovfunction.
(d) ThetransientstateandsteadystatestableperformanceofthefuzzyPDC-
L adaptivecontrollerareguaranteedanalytically.
1
III Evaluation ofthecontrol strategiesonfour simulationcasestudies andthree
experimentalcasestudies.
(a) Differenttypesofcontrollers,viz.,PID,LQG,MRAC,basicL adaptive,
1
PSO-L adaptive,HS-L adaptivearecomparedwithlbestHS-L adap-
1 1 1
tiveandfuzzyPDC-L adaptivecontrollerinsimulationcasestudies.In
1
simulation,atfirst,twoSISOsystems,viz.,chaoticDuffing’soscillatory
systemandnonlinearspringmassdampersystemareexamined.Then,a
SIMO,non-minimumphase,unstable4thorderinvertedpendulumwith
cart system is investigated. After that, a nonlinear, cross-coupled twin
rotorMIMOsystemisconsidered.
x Preface
(b) Thecontrolstrategiesareemployedefficientlyonthreeexperimentalcase
studies,viz.,speedcontrolofelectricalactuator,angularpositioncontrol
oftwolinkrobotmanipulatorandtemperaturecontrolofdelaydependent
air heater system. The performances of the lbest HS-L adaptive and
1
fuzzyPDC-L adaptivecontrolmethodologiesarecomparedwithPID,
1
LQG, MRAC, basic L adaptive, PSO-L adaptive and HS-L adaptive
1 1 1
controller.
(c) Thecontrollersareatfirsttunedforsystemswithnodisturbanceorsmall
disturbance and then subjected to the systems with large disturbance
withoutfurthertuningtoexaminetherobustnessofthecontrollers.The
results demonstrate that, the lbest HS-L adaptive controller provides
1
better tracking and disturbance rejection phenomenon than the clas-
sical controllers, MRAC, basic L adaptive controller as well as other
1
optimization-basedL adaptivecontrollers.ThefuzzyPDC-L adaptive
1 1
controllerprovidesfasttransientperformance,bettersteadystatetracking
performanceandhighrobustnessthanallothercontrolstrategiestested.
Thisbookiscomposedoftotaleightnumberofchapters.Thisbookisorganized
asfollows.
Part-I:Prologue
ProloguecontainsintroductionofthebookinChap.1.Inthischapter,thejourney
towardsmoderncontroltheoryisportrayed.Thestateoftheartofthemoderncontrol
theoriesareelaboratednextwiththreesub-sectionsdescribingstochasticoptimiza-
tionandmetaheuristicstechniques;fuzzylogicsystems;andL adaptivecontroller.
1
Then,theliteraturesofhybridL adaptivecontrollerarearticulated.Theliteratures
1
of stability analysis of the controllers, optimization techniques are provided in the
next section. The motivations of this book from the drawbacks of existing litera-
turesarediscussednext.Then,theproposalsofthebookandmaincontributionsare
discussed.Atlast,thestructureofthebookisprovidedfollowedbythesummaryof
thechapter.
Part-II:Preliminaries
In preliminary part, Chap. 2 explains the motivations of designing basic L adap-
1
tive controller. The architecture and formulation of basic L adaptive controller
1
are elaborated with its stability analysis. The controller is implemented and then