Trapdoor is closed when redstone repeater is one block below and powered.

Grass block trapdoor on one side then on the same side of the trapdoor leave one air block and then place a repeater under the air block. when the trapdoor is in the open state and a redstone signal is sent into or take away from the repeater the trapdoor will close. If a redstone signal is sent to or taken away from the repeater the trapdoor will remain closed.
Also happens when a repeater is placed right underneath, or one block over, an open trapdoor it will also close.