Adaptive Regulation: Reference Tracking and Disturbance Rejection

369 Pages·2022·14.595 MB·English

by  Vladimir Nikiforov, Dmitry Gerasimov

Lecture Notes in Control and Information Sciences 491
Vladimir Nikiforov
Dmitry Gerasimov
Adaptive
Regulation
Reference Tracking and Disturbance
Rejection
Lecture Notes in Control and Information
Sciences
Volume 491
SeriesEditors
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UniversitätStuttgart,Stuttgart,Germany
ManfredMorari,DepartmentofElectricalandSystemsEngineering,
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A.Rantzer,LundInstituteofTechnology,Lund,Sweden
J.N.Tsitsiklis,MIT,Cambridge,MA,USA
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·
Vladimir Nikiforov Dmitry Gerasimov
Adaptive Regulation
Reference Tracking and Disturbance
Rejection
VladimirNikiforov DmitryGerasimov
FacultyofControlSystemsandRobotics FacultyofControlSystemsandRobotics
ITMOUniversity ITMOUniversity
SaintPetersburg,Russia SaintPetersburg,Russia
ISSN0170-8643 ISSN1610-7411 (electronic)
LectureNotesinControlandInformationSciences
ISBN978-3-030-96090-2 ISBN978-3-030-96091-9 (eBook)
https://doi.org/10.1007/978-3-030-96091-9
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Tothememoryofmymentor,
Prof.IliyaMiroshnik
VladimirNikiforov
Tomybelovedchildren,AlexanderandEgor
DmitryGerasimov
Preface
The main topic of this book is the design of adaptive control laws for asymptotic
referencetrackingandcompletedisturbancerejectioninthepresenceofuncertain-
ties.Whiletherearealotofapproachestosuchcontrolproblems,thebookisfocused
onthoseonesthatarebasedontheadaptiveimplementationoftheinternalmodel
principle(IMP).
Therearetwofundamentalproblemsinautomaticcontrol:attenuation(rejection)
of external disturbances and tracking of reference signals. These both problems
solved simultaneously are commonly referred to as the regulation problem, while
theexternalsignals(i.e.,disturbancestoberejectedandreferencestobetracked)are
referredtoasexogenoussignalsorsimplyexosignals.
There are a lot of control techniques proposed to solve the regulation problem.
Inthecasewhenthereisnoaprioriinformationaboutexogeneoussignals,various
control techniques provide prescribed attenuation of the external disturbances and
prescribed residual tracking error only. At the same time, in many practical appli-
cations, more stringent requirement is imposed on controller and consists in zero
steady-statecontrolerror.Itcanbeenforcedifonlysomeinformationaboutexoge-
noussignalsisavailableapriori.Inparticular,thisinformationcanbeextractedfrom
anexosignalmodel.SuchconjectureisusedinthefamousIMP.
AccordingtotheIMP,theexogeneoussignalismodelledastheoutputofadynam-
ical autonomous system, called exosystem, excited by nonzero initial conditions.
Thenthedisturbanceinfluenceontheplantresponsecanbecompletelyeliminated
or the reference signal can be asymptotically tracked if the exosystem model is
suitablyreduplicatedinthefeedbackloopofthecontrolsystem.
From the practical point of view, the most important class of the exosignals is
representedbyperiodicorquasi-periodicfunctionsmodelledasbiasedsinusoidoras
asumofbiasedsinusoids.Suchexogeneoussignalsaretypicalforvarietyofpractical
applications: electromechanical drives, robotics, rotating machineries, closed-loop
systems of active suppression of noise and vibration, audio signal processing, and
soon.
ThemainquestionconcerningpracticalimplementationoftheIMPconsistsinthe
following:whatpreciseinformationabout theplantandexosystem models should
vii
viii Preface
be known a priori? Initially, the IMP was proposed more than 50 years ago for a
prioriknownlinearplantsandknownlinearexosystems,andlateritwasextendedto
differentclassesofaprioriknownnonlinearsystems.Inthiscase,theIMPresultsin
control laws (controllers) with pre-determined and fixed structure and parameters.
WewillcallthisapproachnonadaptiveimplementationoftheIMP.
ThemainshortcomingofthenonadaptiveimplementationoftheIMPliesinthe
factthatexactmodelsofbothaplanttobecontrolledandanexosystemgenerating
exosignalsmustbeknown.Inparticular,itmeansthatonemustknowexactwaveform
oftheexogeneoussignals.Thecasewhentheplantwithuncertainmodelisaffected
byaprioriuncertainexternaldisturbanceismorerealisticandhasagreaterpractical
importance.ThiscaseimpliesadaptiveimplementationoftheIMP.
During the last decades, adaptive implementation of the IMP was successfully
developedforsolutionstotheproblemsofrejection/trackingofexogenoussignals
generatedbylinearexosystemswithunknownparameters,foruncertainexogenous
signalsaffectinglinearandnonlinearplantswithunknownparameters.Recently,new
problemofadaptiveimplementationoftheIMPforsystemswithinputdelaydraws
aseriousattention.Thisisduetothefactthattimedelayisacommonphenomenon
observedinmanyreal-worldtechnicalapplications.Anumberofsolutionsofexternal
disturbances rejection in systems with input delay were proposed on the basis of
combinationofprediction-liketechniqueswithindirect(identificationbased)aswell
aswithdirectadaptation.
Bynow,thereexistsagreatvarietyofdifferentnonadaptiveaswellasadaptive
implementations of the IMP that solve many important theoretical and practical
problems. However, these solutions look unrelated and sometimes lead to similar
results.Themainpurposeofthisbookistogiveaunifiedandsystematicpresentation
of the adaptive implementation of the IMP applied to the problems of asymptotic
rejectionand/ortrackingofaprioriuncertainexogenoussignals.Thekeyideabehind
theapproach,developedbytheauthorsduringthelasttwodecadesandpresentedin
thisbook,isbasedonaspecialcanonicalformoftheexosystem.Thisformenables
onetodesign,inaunifiedandsystematicway,appropriateobserversofexosignals
andobtainparameterizationsoftheexternalsignalsintheformoflinearregressions
withunknownconstantparametersandmeasuredregressors.Suchparameterizations
can be obtained using a unified and systematic way for different classes of linear
and nonlinear plants, plants with measured state or output as well as for plants
withunknownparameters.Inownturn,theparameterizationsenableonetoemploy
well-knownbasicalgorithmsofadaptationandefficientlysolveadaptiveregulation
problemsfordifferentclassesofcontrolsystems.
Anotherfocusimportantforpracticalapplicationsisthetransientperformanceof
thedisturbancerejectionand/orreferencetracking.Inthecaseofadaptivecontrol,
highperformanceofthetransientsintheclosed-loopsystemmainlyimpliesthefast
tuningofthecontrolleradjustableparametersprovidedbyanadaptationalgorithm.
Thus, an important part of this book is addressed to design and employment of
adaptationalgorithmswithimprovedparametricconvergenceachievedbydynamic
ormemoryregressorextension(DREorMRE,respectively).
Preface ix
The book starts with the introductory Chap. 1, where the control problems
addressed in this book are formulated; the main challenges related to the adaptive
compensation of signal uncertainties are discussed; and the state of the art in the
fieldofadaptiveimplementationoftheIMPissurveyed.
Chapter2presentsaunifiedapproachtodesignobserversforaclassofuncertain
exosignalsconsideredinthisbook.Thisapproachisbasedontheemploymentofthe
exosystem canonical form and results in representation of the uncertain exosignal
intheformoflinearregressionwithaconstantvectorofunknownparametersanda
measuredregressor.Inownturn,thisrepresentationallowsonetoderiveasuitable
parameterizationoftheplantsaffectedbyuncertainexternaldisturbances.
In Chap. 3, based on the plant parameterizations presented in Chap. 2, we
define canonical error models and derive for them basic algorithms of adapta-
tion. Constructing such algorithms and establishing their convergence properties,
weprovidetheoreticalbackgroundthatwillbeusedinthenextchaptersfordesign
ofdifferentadaptiveand/orrobustcontrollers.
Chapter 4 presents the controllers of adaptive reference tracking and adap-
tivedisturbancerejectionforplantswithknownparameters.Theemployeddesign
methodsarebasedoncombinationsoftheexosignalobserversintroducedinChap.2
and the basic adaptation algorithms presented in Chap. 3. The designed adaptive
controllersprovidecompleterejectionoftheexternaldisturbanceand/orasymptotic
reference tracking if the exosignals are modelled by a linear exosystem of known
orderbutwithunknownparameters.
Chapter 5 extends the results of Chap. 4 to linear and nonlinear plants with
unknown parameters, while Chap. 6 presents controllers of adaptive reference
trackingandadaptivedisturbancerejectionforLTImulti-inputmulti-output(MIMO)
plantswithknownparametersandinputdelay.
Chapter 7 presents solutions of the robust adaptive regulation problems if the
exosignals contain irregular components. In this chapter, we demonstrate how
the adaptive controllers must be modified in order to provide desirable properties
of the closed-loop control systems: boundedness of all the closed-loop signals in
thepresenceoftheirregularcomponentandasymptoticachievementofthecontrol
objectivewhentheirregularcomponentvanishes.
Thebookiswritteninaself-containedfashionandcontainsappendicespresenting
somemathematicaltoolsandrelevantbackgroundconceptsusefulforunderstanding
ofthemaincontentsofthebook.Itisassumedthataperspectivereaderisfamiliar
withstandarduniversitycoursesoflinearalgebra,differentialequations,andcontrol
system theory. The book is oriented to the senior undergraduate and graduate
students in automatic control, researches, and industrial engineers interested in
implementationofmodernmethodsofadaptivecontrol.
All chapters of the book are written in close collaboration by the authors. This
bookcontainssomeresultsthatoriginallyappearedinRussian(“HikifopovB.O.,
Adaptivnoe i pobactnoe yppavlenie c kompencacie(cid:2) vozmyweni(cid:2), CPb:
Hayka,2003,ISBN5-02-025006-6.”).
x Preface
TheworkonthebookwassupportedbytheGovernmentofRussianFederation
(grant 08-08), the Ministry of Science and Higher Education of Russian Federa-
tion,project(Goszadanie)no.2019-0898andtheRussianScienceFoundationgrant
(project17-79-20341).
The book was typeset in LaTeX. Simulations are carried out in
MATLAB/Simulink environment, the figures are made in MATLAB and
CorelDRAW.
We are thankful to our colleagues I. Furtat, A. Pyrkin, A. Bobtsov,
I. Kolmanovskiy, A. Paramonov, and O. Suzdalev for their helpful discussions,
comments,andnumerousvaluablesuggestions.
WearealsogratefultoOliverJacksonforencouragingustodothisprojectwith
Springer.
Finally, we would like to testify that without encouragement and patience of
MarinaVlasovaandLiubovUrbanovichthisbookwouldnothavebeenprepared.
SaintPetersburg,Russia VladimirNikiforov
DmitryGerasimov