This　paper　studies　the　nonlinear　vibrations　and　control　of　the　piezoelectric　functionally　graded　graphene-reinforced　laminated　composite　cantilever　rectangular　(PFG-GRLCCR)　variable　cross-section　plate　with　the　NPPF　controller　under　the　simultaneous　resonant　cases.　The　nonlinear　dynamic　governing　equations　of　motion　for　the　PFG-GRLCCR　variable　cross-section　plate　are　obtained　by　using　the　extended　Halpin-Tsai　mode,　linear　constitutive　equations　of　the　piezoelectric　materials,　classical　laminated　plate　theory,　von　Karman　large　deformation　theory,　and　Hamilton　principle.　Considering　Galerkin　method,　the　nonlinear　ordinary　differential　governing　equations　are　obtained.　The　nonlinear　positive　position　feedback　(NPPF)　controllers　are　designed　according　to　the　similarity　principle.　The　multiple　scale　method　is　used　to　investigate　the　nonlinear　vibration　characteristics　of　the　stable　motion　for　the　PFG-GRLCCR　variable　cross-section　plate　with　the　NPPF　controllers.　The　amplitude-frequency　response　curves,　force-amplitude　response　curves,　time　histories,　phase　portraits,　and　bifurcation　diagrams　are　given　to　investigate　the　nonlinear　dynamic　characteristics　of　the　PFG-GRLCCR　variable　cross-section　plate　with　the　NPPF　controller.　The　results　demonstrate　that　the　NPPF　controller　can　suppress　the　nonlinear　vibrations　of　the　structure　well,　and　the　effectiveness　of　the　controllers　is　best　when　the　NPPF　controller　has　a　similar　nonlinear　characteristic　with　the　structure.　The　complex　nonlinear　vibration　characteristics　appear　for　the　PFG-GRLCCR　variable　cross-section　plate　with　the　NPPF　controller.　©　2024　Elsevier　Ltd