"The future ain't what it used to be."

Plausible time travel.



Hello everyone. I am a member of a game development company by the name of Elektric Orbit (we're new so you wouldn't know us) We are trying to iron out some details on our stroy which involves time travel being developed some time in the future.
Here is a low down of our beta version of the story.

The year is 2431, you play an ex military special forces soldier codenamed sut579, now recruted into a black op unit know to a select few only as 5-1.
Since the early 22nd century many organizations have been attemping to crack the puzzle that is time - more specificly, time travel. The leaders in this area at 2392 were a black budget organization calling themselves Terra (the original Greek name for Earth). After nearly 50 attemps - several ending in near disaster - they finally did it on march 13th 2431, but they were so consumed with getting out they never stopped to think what they might be letting in.
A mysterious and supremely advanced military force consisted only of about 10 soldiers and a leader emerged from the Time-Space-Tear and took the Terra complex with intentions to destroy the Terra organizations greatest asset. The TST Generator.
You are sent in to retake the complex, assassinate the leader and and secure the TST Genrator. After you complete the first 2 objectives you discover that something happened within the Terra organization that caused Earth of the future to be turned into a wasteland inhabited only by cockaraoches, a couple of hundred humans and an alien race known as the Det'Raks.
You travel back and forth through time, from 20th century to the wasteland time trying to find out wehat that something was and how to stop it.
In the end you lead a force to storm the Terra organiztion -as the tear is opened - in an attemp to shutdown and destroy the Generator and to eleminate all key personel that know the workins of the Generator. You encounter yourself who was sent to kill you (the final boss).
2 different endings, you can alter the timeline by kiling your past self (which averts the future disaster, because it was you who led to the development of the Generator in your travels through time) or you die and the cycle continues.
Aditional notes: The Det'Raks are called so because they say this just before kiling someone. At the end of the game you discover that what they are actually saying is "Punishment".
"one mistake. One mistake out of so, so many more."

NOTE that this story has changed somewhat but this was the only version i had on hand. (feel free to tell me what you think of it)
I would like you help in getting the time travel spect of it as plausibles as possible including a how the TST Generator could work.