Adaptive Regulation: Reference Tracking and Disturbance Rejection PDF
Preview Adaptive Regulation: Reference Tracking and Disturbance Rejection
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 FrankAllgöwer,InstituteforSystemsTheoryandAutomaticControl, UniversitätStuttgart,Stuttgart,Germany ManfredMorari,DepartmentofElectricalandSystemsEngineering, UniversityofPennsylvania,Philadelphia,USA AdvisoryEditors P.Fleming,UniversityofSheffield,UK P.Kokotovic,UniversityofCalifornia,SantaBarbara,CA,USA A.B.Kurzhanski,MoscowStateUniversity,Moscow,Russia H.Kwakernaak,UniversityofTwente,Enschede,TheNetherlands A.Rantzer,LundInstituteofTechnology,Lund,Sweden J.N.Tsitsiklis,MIT,Cambridge,MA,USA This series reports new developments in the fields of control and information sciences—quickly, informallyandatahighlevel.Thetypeofmaterialconsidered forpublicationincludes: 1. Preliminarydraftsofmonographsandadvancedtextbooks 2. Lecturesonanewfield,orpresentinganewangleonaclassicalfield 3. Researchreports 4. Reportsofmeetings,providedtheyare (a) ofexceptionalinterestand (b) devoted to a specific topic. The timeliness of subject material is very important. Indexed by EI-Compendex, SCOPUS, Ulrich’s, MathSciNet, Current Index to Statistics, Current Mathematical Publications, Mathematical Reviews, IngentaConnect,MetaPressandSpringerlink. Moreinformationaboutthisseriesathttps://link.springer.com/bookseries/642 · 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 ©SpringerNatureSwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland 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
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