The potential performance of a control loop is limited by the apparent or real dead time in the loop. You are up against a stone wall if you try to get better performance out of a loop, than the dead time will allow, by tuning alone. If you need better performance, reduce the dead time, reduce the disturbance, use feed forward or do something else, but tuning can do only so much. There are sophisticated approaches to reducing the problem, but these are not for the novice.
For more information you may refer to a booklet "Controller Tuning and Control Loop Performance, a Primer, Second Edition" which is available in the US at the cash discounted price of $17 if paid with a check or money order.
If you want more information on this booklet, visit
David W. St. Clair Straight-Line Control Co.