A　non-autonomous　allelopathic　phytoplankton　model　with　nonlinear　inter-inhibition　terms　and　feedback　controls　is　studied　in　this　paper.　Based　on　the　comparison　theorem　of　differential　equation,　some　sufficient　conditions　for　the　permanence　of　the　system　are　obtained.　We　study　the　extinction　of　one　of　the　species　by　using　some　suitable　Lyapunov　type　extinction　function.　Our　analyses　extend　those　of　Xie　et　al.　(Extinction　of　a　two　species　competitive　system　with　nonlinear　inter-inhibition　terms　and　one　toxin　producing　phytoplankton.　Advances　in　Difference　Equations,　2016,　2016,　258)　and　show　that　the　feedback　controls　and　toxic　substances　have　no　effect　on　the　permanence　of　the　system　but　play　a　crucial　role　on　the　extinction　of　the　system.　Some　known　results　are　extended.　©　2020　by　the　authors.