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Advanced Textbooks in Control and Signal Processing SeriesEditors ProfessorMichaelJ.Grimble,ProfessorofIndustrialSystemsandDirector ProfessorMichaelA.Johnson,ProfessorofControlSystemsandDeputyDirector IndustrialControlCentre,DepartmentofElectronicandElectricalEngineering, UniversityofStrathclyde,GrahamHillsBuilding,50GeorgeStreet,GlasgowG11QE,UK Forfurthervolumes: http://www.springer.com/series/4045 Eugene Lavretsky (cid:129) Kevin A. Wise Robust and Adaptive Control with Aerospace Applications EugeneLavretsky TheBoeingCompany HuntingtonBeach,California,USA KevinA.Wise TheBoeingCompany BoeingPhantomWorks St.Louis,Missouri,USA ISBN978-1-4471-4395-6 ISBN978-1-4471-4396-3(eBook) DOI10.1007/978-1-4471-4396-3 SpringerLondonHeidelbergNewYorkDordrecht LibraryofCongressControlNumber:2012951336 #Springer-VerlagLondon2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerpts inconnectionwithreviewsorscholarlyanalysisormaterialsuppliedspecificallyforthepurposeofbeing enteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework.Duplication ofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheCopyrightLawofthe Publisher’s location, in its current version, and permission for use must always be obtained from Springer.PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter. ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Series Editors’ Foreword The topics of control engineering and signal processing continue to flourish and develop.Incommonwithgeneralscientificinvestigation,newideas,concepts,and interpretations emerge quite spontaneously, and these are then discussed, used, discarded, or subsumed into the prevailing subject paradigm. Sometimes, these innovative concepts coalesce into a new subdiscipline within the broad subject tapestryofcontrolandsignalprocessing.Thispreliminarybattlebetween oldand newusuallytakesplaceatconferences,throughtheInternetandinthejournalsof thediscipline.Afteralittlemorematurityhasbeenacquiredbythenewconcepts, thenarchivalpublicationasascientificorengineeringmonographmayoccur. Anewconceptincontrolandsignalprocessingisknowntohavearrivedwhen sufficient material has evolved for the topic to be taught as a specialized tutorial workshop or as a course to undergraduate, graduate, or industrial engineers. Advanced Textbooks in Control and Signal Processing is designed as a vehicle forthesystematic presentationofcourse materialforboth popular andinnovative topics in the discipline. It is hoped that prospective authors will welcome theopportunitytopublish astructuredandsystematicpresentation ofsomeofthe neweremergingcontrolandsignalprocessingtechnologiesinthetextbookseries. AnaimoftheAdvancedTextbooksinControlandSignalProcessingseriesisto createalibrarythatcoversallthemainsubjectstobefoundinthecontrolandsignal processing fields. It is a growing but select series of high-quality books that now covers some fundamental topics and many more advanced topics in these areas. Wearethereforeveryfortunatetohavethistextbook fromEugeneLavretskyand Kevin Wise on Robust and Adaptive Control with Aerospace Applications enter the series. In many ways, this textbook is a departure for the series since it deals with the fundamental topics of robust and adaptive control and has very strong materialfromtheaerospaceapplicationsfield.Thus,itispossibletoseeclearlyhow the stringent performance requirements of the applications motivate and are met by the control theory developments. From the aerospace control applications, the reader will appreciate the industrial context where aircraft operates across a wide rangeofflightconditions,givingrisetomanydesignpoints.Theaerospaceindustry solves this problem by using many strategically selected control design points v vi SeriesEditors’Foreword and gain schedules the resulting controllers. Another part of the design context is theneedforcontroldesignsthatareabletotrackarangeofreferencesignalswhile remainingrobusttobothparametricandnonparametricmodeluncertainties.These issuesareallconsideredinPartIofthetextunderthetitleofRobustControl. Oneofthequestionsarisingfromtheapplicationofgainschedulesiswhetherit ispossibletoreducethenumberofcontrollersbeingusedandstillmeetthesystem performancerequirements.Thisisaseriouspracticalquestion,andtheauthorsfind a solution in the methods of model reference adaptive control (MRAC) that form PartIIofthetextbook:RobustAdaptiveControl.Thesechaptersfollowasequence of developments, each one dealing with some practical aspect of MRAC, and illustrated by very appropriate case study examples. The techniques of Lyapunov stabilitytheoryareimportanttoolsinthesedevelopmentsandthewholeofChap.8is devotedtothistopic.Thesetoolsarethenusedtoprovideavarietyofperformance guarantees for the adaptive control algorithms. Beginning from state feedback MRAC, the chapter sequence moves on, adding integral control, followed by inculcating robustness, and then improving the adaptation dynamics and culminating in the use of output feedback, which is the contribution of the last chapter (Chap. 14). All the chapters are supported by reference lists and sets of exercisesforthereader. Sinceitisnotoftenthatthetextbookseriescontainsavolumefromwriterswho are based in industry, it is also fitting to say something about the authors in this Foreword. Dr.EugeneLavretskyisaBoeingSeniorTechnicalFellowatBoeingResearch andTechnology,HuntingtonBeach,California,USA.Hehasbeenresponsiblefor theflightcontrolsystemsofseveraladvancedaircraftandhaspublishednumerous technical articles on control and aerospace topics. He is a senior member of the IEEE and was a recipient of the AIAA Mechanics and Control of Flight Award (2009),theIEEEControlSystemMagazineOutstandingPaperAward(2011),and the AACC Control Engineering Practice Award (2012), for his work in the aero- spacefield. Dr. Kevin A. Wise is a Boeing Senior Technical Fellow at Boeing Phantom Works, St. Louis, Missouri, USA. He has been responsible for a wide range of aerospacedevelopmentsincludingflightcontrolsystems,ejectorseatsystems,and autonomy in unmanned aerial vehicles. Dr. Wise is a fellow of the IEEE and has receivedbothIFAC(2007)andAIAA(2004)awardsforhisworkandpublications. Bothauthorshavetaughtthematerialofthistextbookingraduate-levelcoursesat USuniversities. ThisnewtextbookisanexcellentadditiontotheAdvancedTextbooksinControl andSignalProcessingseries. IndustrialControlCentre M.J.Grimble Glasgow,Scotland,U.K. M.A.Johnson May2012 Preface Afterworkingintheaerospaceindustryforclosetoaquarterofacentury,bothof us felt strongly about writing this book, with the main goal to share our lessons learned and design insights into the development and analysis of robust and adaptivecontrolsystems.Ourfocusisonthesystemsthatarepracticalyethavea formal basis for performing their design, analysis, and performance evaluations. DuringourprofessionalcareersattheBoeingCompany,wehavehadamultitudeof opportunities to design and flight test guidance, navigation, and control (GN&C) algorithms for a variety of platforms, ranging from commercial aircraft to fully autonomous experimental aerial vehicles. Over time and after numerous trade studies,we have collectedanumberofGN&C methods thathave performed well onavarietyofaircraftsystems.So,wedecidedtowritethisbookandsharewiththe readerourexperiencesandlessonslearnedinthedesign,analysis,andevaluationof control technologies, with an emphasis on flight systems. The latter is not a prerequisite for understanding the book material, as these methods and design insights apply to all control systems. Aerospace applications and examples presentedinthisbookareratheramotivationtochallengesinconstructingreliable andnumericallyefficientcontrolalgorithms. Manypartsofthisbookarebasedonundergraduateandgraduatecontrolcourses thatwehavetaughtovertheyearsattheWashingtonUniversityinSaintLouis,the University of Missouri – Rolla, the Southern Illinois University in Edwardsville MO, and at the California Institute of Technology (Caltech). As such, the book materialisquitesuitableforseniorundergraduateandgraduatestudents,aswellas forpracticingengineersandresearchscientists,whohavehadanexposuretobasic principlesincontrolsanddynamics,suchasanundergraduatelevelcontrolcourse, covering classical methods (root locus, Bode diagrams, and Nyquist plots). Inaddition,weassumethatthereaderhasabasicunderstandingoflinearalgebra, ordinary differential equations, and is familiar with using state space methods for analysisandnumericalmodelingofdynamicalsystems.Thesearetheprerequisites. Motivated and driven by aerospace applications, this book focuses on systems whosedynamicsarecontinuous.Extensionsofthesemethodologiestodiscreteand vii viii Preface hybrid systems are possible and can be found elsewhere in the vast literature devotedtocontrolofdynamicalsystems. Overall,thisbookisself-containedwhilecoveringtheoreticaldevelopmentand practicalapplicationsofformalmethodsinrobustandoptimallinearcontrol,robust stabilityanalysis,Lyapunovstabilitytheory,andmodelreferenceadaptivecontrol (MRAC).Throughoutthisbook,wepresentdetailedsimulationexamplesandcase studies to illustrate key design steps and the benefits of applying robust and adaptive control methodologies to transport aircraft and experimental aerial platforms. Therearetwomajorpartsinthisbook.PartIpresentsrobustcontroldesignand analysis methods for linear time-invariant systems. Part II focuses on MRAC methodsforsystemswithnonlinearanduncertaindynamics. Readers will benefit from the two-part distinct structure of this book. Such an arrangementenablesaseamlesstransitionfromtheclassicallinearcontrolconcepts tothestateoftheartinadaptivesystemswhileillustratingeachdesignwithrealistic aerospace applications. Also, the two-part book organization allows us to present self-containedmaterial,coveringlinearandrobustadaptivecontroltechniquesfor dynamical systems that operate in the presence of uncertainties. Toward that end, weconsistentlygivestructureddescriptionsofbothclassicalandadvancedcontrol techniques, key design procedures and guidelines, worked examples, and Matlab simulations.Eachpartendswithasetofeducationalandchallengingexercisesthat aredirectlyrelatedtothematerialpresented.Allthesefeaturesconstitutethebook’s educationalvalue. PartIbeginswithanintroductiontochallengesincontroldesign,analysis,and simulationofaerial vehicles. Generalaviationbackgroundand current trends that leadtotheneedformoreadvancedcontrolarediscussed.Alsopresentedisabrief survey of control-theoretic methods for existing and future aerial vehicles. The theoreticalportionofPartIstartswiththeintroductionofrobustandoptimallinear control methods for linear systems. Command tracking using linear quadratic regulators(LQR)withintegralactionispresented.Thispartalsocoverstwooutput feedbackdesignmethods,suchasprojectivecontrolandlinearquadraticGaussian controlwithLoopTransferRecovery(LQG/LTR).Thesealgorithmsareemployed todevelopbaselinecontrolarchitecturesforlinearsystemswithknowndynamics. PartIIbeginswithself-containedmaterialonthedesignandanalysisofadaptive statefeedbackcontrollersforlinearandnonlinearuncertaindynamicalsystemsin continuous-time domain. An overview of Lyapunov stability theory is given, followed by theoretical fundamentals for MRAC systems. Next, approximation propertiesofartificialneuralnetworksandtheirapplicationstothedesignofdirect adaptivesystemsareintroduced,andseveralapproximation-basedMRACmethods are discussed. The part proceeds withthe development of state feedback adaptive augmentation architectures for robust baseline linear controllers, followed by extensionsandmodificationstoachievetransientperformanceinadaptivesystems, aswellastoaccommodateoutputfeedbackconstraints.Inthispart,wealsopresent adaptiveaugmentationdesignmethodstocombinerobustbaselinecontrollerswith adaptivefeedback. Preface ix Throughout this book, we discuss motivations to the design, analysis, and implementation of robust and adaptive controllers, with the aim to addressing realistic challenges that often arise in the flight control of aerial vehicles and othersystems.