In　this　paper,　the　active　damping　control　of　the　porous　metal　foam　truncated　conical　shell　with　smart　material　macro　fiber　composite　(MFC)　is　studied.　Suppose　the　shell　has　arbitrary　elastic　supported　edges,　and　is　subjected　to　the　impact　loadings.　The　elastic　supported　edges　can　be　achieved　by　virtual　spring　technique.　Adopting　the　elastic　constraint　boundary　condition,　various　classical　boundaries　can　be　easily　realized　by　varying　the　value　of　the　spring　stiffnesses.　Along　the　thickness　direction,　there　are　three　types　of　porosity　distributions　of　truncated　conical　shell　being　considered,　and　they　are　nonuniform　symmetric,　uniform　and　nonuniform　asymmetric　distribution,　respectively.　The　sensor　layer　MFC-d31　and　the　actuator　layer　MFC-d33　are　applied　in　the　vibration　control　system.　According　to　the　first　order　shear　deformation　theory　(FSDT)　and　energy　principle,　the　dynamic　equation　of　the　system　under　electrostatic-mechanical　coupling　is　derived.　Then　it　is　discretized　into　ordinary　differential　equation　by　generalized　differential　quadrature　method　(GDQM).　The　output　charge　applied　to　the　sensor　can　be　solved　by　integral　quadrature　method　(IQM).　The　convergence　and　validation　of　the　formulation　and　numerical　calculation　are　studied　by　the　comparisons　between　the　present　solutions　and　those　from　the　literatures,　ANSYS　and　COMSOL　for　the　truncate　conical　shell　with　classical　boundary　conditions,　respectively.　Suppose　the　impact　loadings　acting　on　the　porous　truncated　conical　shell　are　step　loading　and　decreasing　loading,　respectively.　The　velocity　negative　feedback　approach　is　employed　to　diminish　the　amplitude　of　the　transient　response　and　achieve　the　active　damping　control.　Then　the　effects　of　control　gain,　external　excitation,　semi-vertex　angle　and　spring　stiffness　on　the　transient　response　control　of　the　conical　shell　are　studied　in　detail.