Everything you need is in the "Binary and Analog Handling" user manual. The "Advanced" control library is not very advanced. It is basically a slightly extended PID controller, plus a couple of support modules. (Including a "stiction compensator" which IMHO is worse than useless any any but a very few circumstances)
The only "advanced" control algorithm included in the control libraries are templates for a fuzzy logic controller. The fuzzy logic templates are quite well explained and the easiest way to learn ho to use them is to try an example.
The AC800M standard libraries do not include an MPC or an APC module. I'm not aware if any ABB group has made a library like this.
However, the PIDAdvanced controller is actually pretty good. The FeedForward and Gain Scheduling features are easy to configure and there are several PID options including P, PI, PD, and PPI - which is basically a dead time predictor. There is an autotuning feature , but my personal experience is that its pretty agressive and will give you rather unstable PID tuning numbers so I dont use it.
As a side comment... While APC is a VERY useful tool for some processes, my experience has been that a well tuned PID control system will give you better performance than an averagely set up APC system 80% of the time. I have worked with at least one customers who implemented an extensive APC system costing a lot of money over several years, who then basically removed the entire system except for one or two APC loops.
I would only add to what Rob wrote above that there is an additional package for 800xA called 800xA APC. It is licenced separately and includes offline and online tools for preparing, implementing and running an APC in Your 800xA system.
For more info, please see: 2PAA111641 - 800xA APC Datasheet
or one APC manuals:
Hope it helps,