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1、SPRINGERADAVANCEDTEXTBOOKSINCONTROLANDSIGNALPROCESSINGRobustandAdaptiveControlwithAerospaceApplicationsTheSolutionsManualEugeneLavretsky,Ph.D.,KevinA.Wise,Ph.D.2/9/2014Thesolutionsmanualcoversalltheoreticalproblemsfromthetextbookanddiscussesseveralsimulation-orient
2、edexercises.Chapter1Exercise1.1.Detailedderivationsoftheaircraftdynamicmodescanbefoundinmanystandardflightdynamicstextbooks,suchas[1].Furtherinsightscanbeobtainedthroughapproximationsofthesemodesandtheirdynamicsusingtime-scaleseparationpropertiesoftheequationsthatg
3、overnfightdynamics[3].Thetime-scaleseparationconceptwillnowbeillustrated.Setcontrolinputstozeroandchangeorderofthestatesin(1.7)to:.Thenthelongitudinaldynamicscanbepartitionedintotwosubsystems:orequivalently,Formostaircraft,theirspeedsaremuchgreaterthantheverticalfo
4、rceandmomentsensitivityderivativesduetospeed,andso:.Alsoandso:.Theseassumptionsareatthecoreofthetime-scaleseparationprinciple:Theaircraftfastdynamics(theshort-period)isalmostindependentanddecoupledofthevehicleslowdynamics(thephugoid).With,theshort-perioddynamicsare
5、:Theshort-periodcharacteristicequationis:Comparingthistothesecondorderpolynomial,,givestheshort-periodnaturalfrequencyandthedampingratio.Foropen-loopstableaircraft,,whichallowsforfurthersimplificationofthevehicleshort-periodmodes.Approximationsforthephugoiddynamics
6、canbederivedbysettingtheshort-perioddynamicstozeroandcomputingtheremainingmodes.Thisisoftenreferredtoasthe“residualizationoffastdynamics”.Thephugoiddynamicsapproximationtakestheform,orequivalentlyExplicitderivationsforthephugoidmodenaturalfrequencyanddampingratioca
7、nbefoundin[3].Exercise1.3.SimilartoExercise1.1approach,basedonthetime-scaleseparationprinciple,canalsobeappliedtothelateral-directionaldynamics(1.29)toshowthatthedynamics(1.30)representthe“fast”motionandarecomprisedofthevehiclerollsubsidenceandthedutch-rollmodes.Th
8、eslowmode(calledthe“spiral”)hastherootattheorigin.Thereaderisreferredto[1],[2],and[3]fordetails.Chapter2Exercise2.1.SameasExample2.1.Exercise2.2.
