Chaotic　response　is　a　robust　effect　in　natural　systems,　and　it　is　usually　unfavorable　for　applications　owing　to　uncertainty.　In　this　paper,　we　propose　several　control　strategies　to　stabilize　the　chaotic　rhythm　of　a　fractional　piecewise-smooth　oscillator.　First,　the　Melnikov　analysis　is　applied　to　the　system,　and　the　critical　condition　for　the　occurrence　of　homoclinic　chaos　is　scrupulously　established.　Then,　by　applying　appropriate　control　mechanisms,　including　delayed　feedback　control　and　periodic　excitations,　to　the　system,　we　can　eliminate　the　zeros　in　the　original　Melnikov　function,　which　serve　as　sufficient　criteria　for　chaos　suppression.　Numerical　simulations　further　demonstrate　the　accuracy　of　the　theoretical　results　and　the　validity　of　the　control　schemes.　Finally,　the　effects　of　parameter　variations　on　the　efficiency　of　control　strategies　are　investigated.　Note　that　we　use　the　complex　Simpson　formula　to　calculate　the　complicated　Melnikov　functions　presented　in　this　paper.　The　current　work　may　open　a　new　innovative　path　to　detect　and　control　the　chaotic　dynamics　of　fractional　non-smooth　models.