So i've been playing guitar for about 3 years now, in bands etc.

I play mostly heavy things, like old Metallica, Lamb of God, Shadows Fall, Darkest hour etc.

Now im having alot of trouble breaking into sweeping.

We recently learnt The Decieved by Trivium, and it has a 4-5 seconds sweeping section in the solo, that i just can't quit nail up to speed. http://www.youtube.com/watch?v=_P339orfgvo

The weird thing is, if you listen to Tranquil by Darkest Hour http://www.youtube.com/watch?v=mRZt-VsN8xY, I can nail the entire song, except for a very small section of a run, even though the sweeping in Tranquil is 5 string, and The Deceived is only 3 string...

Any suggestions on a way to improve my sweeping speed, and overal sweeping skill?

I'm sorry if i missed a thread about this, but i used the search bar and nothing came up!
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As with every technique on guitar, practice the hard part until you are capable of playing it cleanly at full speed. To do this, take it down to a manageable tempo, and use a metronome. It is imperative that this tempo be slow enough to allow you to play it perfectly, with perfect technique. Slow increase the metronome to higher tempi. Do not increase the tempo until you are able to play it perfectly at the previous one. Continue doing this until you achieve the desired speed.