Front derailleur for a three ring chainset.
 

I am about to pull out the few remaining hairs I have left in trying to adjust the front derailleur, three front eight rear, so that it will shift smoothly. I have adjusted the height, paralleled the unit to large gear. Lowered to smallest front gear - largest rear and set stop. Set cable tension. Ran the chain out to the largest crank gear and set stop but it has all kinds of hesitation in changing from small to center and back from largest to center. The bike is five months old and has about 200 miles on it. The bike shop I bought it from went out of business about a month after I bought the bike so I can not go back to them for an adjustment. The bike is a Cannondale Quick 7 so the hardware is not top drawer and I have not had experience with three ring crank sets as my previous bikes had just two. Any help or advice you can give would be very helpful. I am not trying to run the largest in front with the smallest in back and vice versa so that is not an issue.
Thanks in advance, Frankl.

https://www.parktool.com/blog/repair...eur-adjustment
https://www.parktool.com/blog/repair...eur-adjustment
Follow these procedures from the beginning without skipping any steps.
You may not be able to use every front-rear combination; there are alternatives to the cross-chained ones.

My Sirrus has the same 3 X 8 drivetrain with the Shimano Altus front derailleur...
It is fussy to set-up but once "dialed-in", even though it's an "entry level" component, it works very well!
Here's a link to the Owner's Manual that I found helpful.
The highlighted "tip" on page 11 solved my problems... (closer to 1mm vs 3mm, for my set up)
https://cimg2.ibsrv.net/gimg/bikefor...eb1a3a34fb.png
Sounds like you know what you are doing... (but it is a"frustrating" adjustment - took me 6 or 7 "tries" LOL!) Good luck!

Thank you both VERY much.
Frank.