Hostile Action Displacement System

The Hostile Action Displacement System, also known as HADS (TV: ) or simply the displacement system, (COMIC: ) was one of the defence mechanisms of the Doctor's TARDIS. When the outer shell of the vessel came under attack, the unit dematerialised the TARDIS and rematerialised it a short distance away after the attacker had gone, in a safer locale. (TV: The Krotons) However, another function of this was a "dispersal system" instead of its usual "displacement system", which would allow for the TARDIS to appear to actually be blown apart, but in fact remaining intact in various pieces with the shield still functional in its original position. (TV: The Witch's Familiar)

The HADS had to be manually set, and the Doctor often forgot to do so. (PROSE: The Krotons) It could also be turned back on automatically by the TARDIS' regeneration. (TV: Wild Blue Yonder)

History
When testing the ship after his exile on Earth had ended, the Third Doctor briefly lost the TARDIS when the HADS was triggered by a hailstorm, the Doctor noting to Jo Grant in embarrassment after they rediscovered the ship that the setting for the HADS was slightly too high. (PROSE: The Suns of Caresh)

While stuck on Earth and attempting to avoid meeting himself, the Fifth Doctor engaged the HADS to move the TARDIS. (AUDIO: The Mutant Phase)

The Fifth Doctor had General Tillington fire lasers at the partially-materialised TARDIS in order to trigger the HADS as part of his plan to defeat the Daleks. (AUDIO: Renaissance of the Daleks)

was able to capture the Doctor's TARDIS in a tractor beam because the Sixth Doctor had neglected to set the HADS. (PROSE: Time and the Rani)

The system triggered when the TARDIS was struck by cannon fire in 1854, which displaced the outer plasmic shell. (AUDIO: The Angel of Scutari)

Ace activated the HADS on instructions from the Seventh Doctor, moving the TARDIS from Haiti's Presidential Palace to the university. (PROSE: White Darkness)

The HADS activated itself when two Zygons tried to steal the TARDIS. (PROSE: The Bodysnatchers)

The HADS activated again when temporal corrosion on the SS Batavia threatened the TARDIS, sending Charley Pollard from 1 January 2008 to 15 January 1942. It was triggered again when temporal corrosion spreading through a Cyber-ship in 500002 came near the TARDIS, inadvertently stranding Charley there in the process. (AUDIO: The Girl Who Never Was)

After a particularly violent crash landing, the TARDIS used the HADS to move itself through time as well as space, appearing several days later. (PROSE: Dead of Winter)

The Tenth Doctor tried to activate the HADS after Finn Dargo had hacked Emergency Program One and attempted to arrest the TARDIS' occupants. The move allowed the TARDIS to materialise in an unexpected place in Dargo's ship, giving Majenta Pryce a slight advantage over Dargo's Intersol team. (COMIC: The Crimson Hand)

While fiddling with various settings, the Eleventh Doctor re-enabled the HADS in time for it to activate and leave the Doctor and Clara Oswald in a sinking submarine near the North Pole in 1983. It reappeared a short while later, but at the South Pole instead of the North Pole. (TV: Cold War) This event would later be referenced by Clara when the Twelfth Doctor assured her that the TARDIS would "turn up somewhere" after the space shuttle it had materialised in fell into a canyon. (TV: Kill the Moon)

When the Daleks attempted to destroy the TARDIS, (TV: The Magician's Apprentice) the HADS activated making it look like it had been destroyed, but the Twelfth Doctor later rematerialised the TARDIS using his sonic sunglasses, summoning pieces of it from all around the room; this action was called the "Hostile Action Dispersal System". (TV: The Witch's Familiar)

The Fourteenth Doctor reasoned that the displacement system was responsible for taking the TARDIS out of the collapsing 66-scape and into the main concourse of the Dalek Dome. (COMIC: )

At some point, the Doctor deactivated the HADS because it had once gotten him stuck in orbit for three years and the Doctor reasoned that he would never be able to land with it on. (TV: Wild Blue Yonder)

After Donna Noble spilt coffee on the TARDIS console of the Fourteenth Doctor, (TV: The Star Beast) the badly damaged TARDIS landed them on a spaceship at the edge of the universe. The Doctor triggered the TARDIS' regeneration with his sonic screwdriver, but this reactivated the HADS as well. Due to the danger of the Not-Things, the TARDIS took off on its own. As the ship self-destructed, the TARDIS returned, able to tell that the Not-Thing Doctor wouldn't be able to stop the self-destruct in time, thus ending the hostile action. When the TARDIS first crashed and when it returned, it played "Wild Blue Yonder" which the Doctor noted was a war song. (TV: Wild Blue Yonder)

Behind the scenes
According to the Make Your Own Adventure with Doctor Who novel, Search for the Doctor, Drax's TARDIS was shown to have a HADS, which was manually triggered when the vessel came under fire. As the Make Your Own Adventure series has multiple outcomes and no mechanism of determining the "right" outcome, this Wiki does not consider the novel a valid source.

Likewise, the webcast Stealing Series 9 Scripts is not considered a valid source by this Wiki, but features another use of the HADS: this time, it is one of the many defence systems placed by Steven Moffat on his underground "secret writing lair" below 221B Baker Street.