When you center the control stick on a PlayStation 3 controller, it sits in something called the "dead zone." This is an area where a small movement on the control stick is ignored by the game. It prevents bumps on the controller or a slightly off-center stick from controlling the game unexpectedly. But for games where extreme precision is required, such as first-person shooters and some driving games, the dead zone can make the controller imprecise. If the dead zone on your controller is too noticeable, there are several things you can try to fix it.
Load the game you wish to play and, from the main menu, navigate to the settings screen. Look for an option that allows you to set your controller preferences. Some games let you to change the controller's sensitivity, as well as adjust the dead zone. For example, "Test Drive Unlimited 2" lets you to change the sensitivity, dead zone, damping and linearity of the controller, to suit your driving style and comfort level.
Replace the controller with a different version of the same model, to see whether the problems you are having could be caused by a worn-out controller. As with all mechanical devices, wear on the stick will slowly cause it to lose sensitivity and feeling, and the dead zone will increase. Borrow a controller from a friend or try the game on someone else's console before paying $50 or more for a new one, as it may be a problem with the game's setup, rather than the controller.
Replace the joysticks with commercially available replacements. This can be done by unscrewing the cover on the controller, taking the stick out and putting in a new one. This is a good option if one stick in particular is problematic, because that suggests it is not a game setup issue but one with the controller itself.
You also can replace the rubber mats under the joysticks, if they look worn. These tell the controller where the joystick is.
Taking apart the controller may void your warranty. If it is still under warranty, you may be able to get it replaced by Sony.