Abstract: Duetotheindistinctphysicalmeaningsforinternalbalancingreductionandthedifficultyinextractingbalancecoordinatesfromsensorreadings,amodelreducedmethodfrombalancedspacetomodalspacewaspresentedviareverseprojectionbasedonthedynamicsmodelofflexiblespacecraft.Accordingtotheinvarianceofthetransferfunctionandtheeigenvaluesforstatespacetransformation,theeigenfrequencieswereobtainedbythezero-poletransferfunctionofbalancedreducedmodel.Thecorrespondingrelationshipbetweenthebalancedstatesandmodalcoordinateswasgivenandthereverseprojectionmatrixwasconstructed.Thefrequencyresponseandcontrollabilityandobservabilityanalysisshowsthatthestatesofreducedmodelinmodalsubspaceandthestatesoforiginalmodelarematched.Thereducedmodelwithdefinitephysicalmeaningisapplicabletosubsequentstructuralcontroldesign.

Key words: Internalbalancingreduction, Modalsubspace, Reverseprojectionmatrix, Zeropoletransferfunction, Controllabilityandobservability, Flexiblespacecraft