A common problem guitarists encounter with right hand technique is picking "in between" two strings. Playing a downstroke on a lower string followed by an upstroke on a higher string is easy enough but when you reverse the picking direction it becomes more difficult. Here is an example using open strings.
Once you are comfortable with the previous exercise, try the following 16th note patterns which make use of "inside" picking. Make sure you start with a downstroke and use strict alternate picking throughout. Once again, use a metronome and take them slowly at first.