[Mark McLeod]

Just an alternate note. This may or may not apply to your setup.
It can be untunable if the three PID loops are operating independently of one another, but are affected by one another. They can't forecast the blind-siding they get from the other loops and end up fighting the others for position.

In such an interdependent system one simple approach might be to have one of the motors act as the master (one ring to rule them all) with the others slaving themselves to it's position. Feed the master pot to the slaves as their continually changing setpoint (normalized to match the range of the slave pots and applying any relationship equation).That provides sort of a cooperative feed forward term to the slaves. I typically make the slowest mechanism the master (sometimes purposely slowing it down) and the faster mechanisms the slaves, because you can structure it so that the slaves reach equilibrium quickly and have reduced affect on the master. Overall thrashing is eliminated as the slaves make smaller incremental changes as they trail along behind the master instead of racing ahead.