I know a lot of people, students who thought they were doing alternate but had some other hodge podge going on. Is it economy where you downstroke whenever you go to a new string? Be careful of that one. Alternate means just that: down up, regardless.
To clean up you technique I'd use a metronome but also go very slow. Go very slow and very accurately. Slowly increase your speed. And take whole notes, half notes, half note triplets, quarter notes, quarter note triplets, 8th, 8th triplets, 16th notes. This will increase your timing accuracy, which is really where 90% of the problems occur with GUiTAR players and their chops.
With the triplets I generally alter my picking to reflect the triplets feel and sound: downstroke on the downbeat of the figure. Down, up, up or down, up, down. What occurs is great rhythmic accuracy and articulation. Everything else; quarter notes, 8ths and 16th notes are alternate strokes.