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euoLt WAl ATESCHOOL MONTEREY.CALIFORNIA93943^002 Unclassified SecurityClassificationofthispage REPORT DOCUMENTATION PAGE a ReportSecurityClassificationUnclassified lb Restrictive Markings 2a Security ClassificationAuthority 3 DistributionAvailability ofReport 2b Declassification/Downgrading Schedule Approvedforpublicrelease;distributionisunlimited. 4 PerformingOrganizationReportNumber(s) 5 Monitoring Organization ReportNumber(s) 6a NameofPerformingOrganization 6bOfficeSymbol 7a NameofMonitoringOrganization NavalPostgraduateSchool (IfApplicable) 32 NavalPostgraduateSchool M6conAtdedrreesys,(ciCtyA,st9at3e,94an3d-Z5I0P0c0ode) 7MbonAtdedrreesys,(cCityA,st9at3e9,4an3d-Z5I0P0c0ode) ia NameofFunding/SponsoringOrganization 8bOfficeSymbol 9 ProcurementInstrumentIdentificationNumber (IfApplicable) 8c Address(city,state,andZIPcode) 1 SourceofFundingNumbers THEDESIGNOFANADPAroPgrTamIEVleEmenAtTNuTmbIeTrIUPrDojEectCNoON|TTasRkONoLISWoYrkSUTnitEAMccessionNo 11 Tide(IncludeSecurityClassification) 12 PersonalAuthor(s)NicholasF. RuSSO 13a TypeofReport 13b TimeCovered 14 DateofReport(year,month.day) 15 PageCount Master'sThesis From To September1992 91 16 SupplementaryNotation Theviewsexpressedinthisthesisarethoseoftheauthoranddonotreflecttheofficial policyorpositionoftheDepartmentofDefenseortheU.S.Government. 17 CosatiCodes 18 SubjectTerms(continueonreverseifnecessaryandidentifybyblocknumber) Field Group Subgroup CER,attitudecontrol,attitudehold,slewing,SpaceStation,eigenaxis,quaternion, EulerParameters,LinearQuadraticRegulator,KalmanFilter 19 Abstract(continueonreverseifnecessaryandidentifybyblocknumber ThisresearchdesignedandsimulatedanadaptiveattitudecontrolsystemfortheCrewEquipment/Retriever (CER) during autonomousattitude hold andlarge angleorslewingmaneuvers. The CER is aproposed space robot thatdeploys from the Space Station and retrieves any lost equipmentor incapacitated astronauts. The momentofinertiatensorfortheCERandacquiredtargetisnotknownapriori. Inthisresearch,themomentof inertiatensorisestimatedbyaKalmanfilterandusedtoupdatethederivedlinearquadraticregulator(LQR)and quaternionfeedbackregulator(QFR)controllaws. Computersimulationresultsshowthatduringattitudeholdthe adaptiveLQRdesignstabilizestheCERandprovidesamorefuelefficientcontrollereffort: ascomparedwitha previouslydesignednonadaptiveminimumtimecontrollerandanonadaptiveLQRdesign. Computersimulation resultsofslewingmaneuvers showthatthe adaptive QFRdesignprovides amore fuelefficientcontroller: as comparedwithanonadaptiveQFRdesign. T258508 20 Distribution/Availability ofAbstract 21 AbstractSecurityClassification |X| unclassified/unlimited | J sameasreport [J DTICusers Unclassified 22a NameofResponsibleIndividual 22b Telephone(IncludeAreacode) 22cOfficeSymbol JeffreyB.Burl (408)646-2390 EC/B1 DDFORM1473,84MAR 83APReditionmaybeuseduntilexhausted securityclassificationofthis page Allothereditionsareobsolete Unclassified Approvedforpublic release; distribution is unlimited. The Design of an Adaptive Attitude Control System by Nicholas F. Russo Lieutenant, United States Coast Guard B.S., United States Coast Guard Academy, 1985 Submittedinpartialfulfillmentofthe requirements for the degree of MASTER OF SCIENCE IN ELECTRICAL ENGINEERING fromthe NAVAL POSTGRADUATE SCHOOL September 1992 ABSTRACT This research designed and simulated an adaptive attitude control system for the Crew Equipment/Retriever (CER) during autonomous attitude hold and large angle or slewing maneuvers. The CER is a proposed space robot that deploys from the Space Station and retrieves any lost equipment or incapacitated astronauts. The moment ofinertia tensor for the CER and acquired target is not known apriori. In this research, the moment ofinertia tensor is estimated by a Kalman filter and used to update the derived linear quadratic regulator (LQR) and quaternion feedback regulator (QFR) control laws. Computer simulation results show thatduring attitudehold the adaptiveLQR design stabilizes theCER and provides a more fuel efficient controller effort: as compared with a previously designed nonadaptive minimum time controller and a nonadaptive LQR design. Computer simulation results of slewing maneuvers show that the adaptive QFR design provides a more fuel efficientcontroller: as compared with anonadaptiveQFR design. in u TABLE OF CONTENTS INTRODUCTION I. 1 A. CERS CONCEPTDESCRIPTION 1 1. CERS Origin andPurpose 1 2. CER Baseline Configuration 2 B. THESIS OBJECTIVES 5 C. THESISORGANIZATION 6 II. ATTITUDEKINEMATICS ANDDYNAMICS 7 A. ROTATIONALKINEMATICS 7 1. Direction Cosine Matrix 7 2. EulerAngles 11 3. Euler's Principal Rotation Theorem 13 4. Euler Parameters 14 5. ParameterizationDiscussion 17 B. ROTATIONALDYNAMICS 18 1. General Rigid Body 18 2. The CER 18 C. STATE VARIABLE REPRESENTATION 20 III. ATTITUDE CONTROLLAWDESIGN 23 A. DESIGNPHILOSOPHY 23 B. SPECIFICATIONS AND CONTROL DEVICES 24 C. ATTITUDE HOLD 26 1. Optimal Control Theory 26 2. Linear Quadratic Regulator 27 D. SLEWINGMANEUVERS 29 IV . . 1. EigenaxisRotations 30 2. Quaternion Feedback Regulator 30 IV. ADAPTATION LAW DESIGN 35 A. ADAPTIVECONTROLTHEORY 35 B. KALMANFILTER DESIGN 37 1. General Kalman FilterEquations 37 2. Linear Model 39 3. Nonlinear Model 41 V. RESULTS 43 A SIMULATIONPROGRAMAND IMPLEMENTATION 43 B. ATTITUDE HOLD 48 1 Comparison ofAdaptiveand Nonadaptive Control 48 2. Adaptive Control with various target scenarios 51 C. SLEWINGMANEUVERS 52 VI. CONCLUSIONS 58 A. ATTITUDE HOLD 58 B. SLEWINGMANEUVERS 58 C. FUTURERESEARCH 58 APPENDIX (MATLAB SIMULATIONPROGRAMS) 60 LIST OF REFERENCES 81 INITIALDISTRIBUTIONLIST 83 ACKNOWLEDGMENTS I would like to thank Professor John Junkins (Texas A&M) for his knowledgeable support ofthis research and invaluablepractical guidance. I give special thanks to ProfessorJeffBurl for his patience and instructive guidance as my thesis advisor. I would also like to thank Professor Roberto Cristi for his guidance in adaptive control theory, filtering techniques, and his significantrole in writing the journal article based on this research. To Lanette, Alex, and Tasha, thank you forall yourlove and support. I dedicate this thesis to you.