Compensatory Acceleration Training is simply a method of severely exhausting your fast twitch fibers, both TypeIIA and TypeIIB, as well as your slow twitch fibers, TypeI.

The concept is simple. Take a good compound movement like bench as an example. Unrack the weight and perform the first rep normally, but have a spotter count how many seconds it took you to push the bar from chest to lockout. For this example, let's say it took 1 second.

You now begin a slow descent from lockout to your chest, your spotter counting down from 5. When you hit your chest, you push up towards lockout as fast and hard as you can.

The tempo is based on multiplying the seconds to complete the eccentric portion of the lift by 5 to create the seconds you need to perform the concentric.

If the second rep took 2 seconds to get up, it needs to take you 10 seconds to take it down.

So how does this exhaust and/or benefit the TypeIIA and TypeIIB fibers?
TypeIIB fibers contract quick and produce great amounts of power (where power = work/time). Unfortunately they fatigure very quickly. Because they are high in creatine phosphate, they are able to recover somewhat quickly. These muscles will allow you to get the motion started quickly, and thus handing the load off to the TypeIIA fibers.

TypeIIA fibers act as a transition between fast and slow twitch fibers. They do not contract as powerfully as their TypeIIB counterparts, but they have a greater tolerance to fatigue.

You should be using a weight low enough that your eccentric never exceeds a time of 3 seconds. At this point you will have handed the eccentric movement over to your slow twitch fibers (TypeI), and we don't want to do that.

Instead we want the concentric motion to focus entirely on the TypeI fibers. TypeI fibers do not produce great amounts of power, but they have a great tolerance for fatigue. To this end we are able to handle 5-15 second concentric motions.

The idea behind the Compensatory Acceleration Training method isn't to be used all the time on every lift. It's just an addition to your routine that gives you a chance to truly focus on all 3 muscle fiber types.