Autotronic is the name given to the system that automates some transmission functions, it comprises a control module under the cab RH floor and several sensors in the transmission and hydraulic system.
Autotronic disengages 4wd at around 10mph to prevent transmission wind up and excess front tyre wear, it also controls the differential lock engagement(I cant remember exactly how) It engages the 4wd to provide 4 wheel braking when the brake pedal is depressed. It monitors pto engagement and shuts off the pto if a sudden excessive shock load is encountered. It provides a facility to engage the diff lock when the linkage is lowered (useful when ploughing) and disengages it when the implement is raised out of work automaticly.
It also monitors and controls transmission range change, transmission oil pressure .. It is a fairly reliable system and usually operates quitely in the backround until a problem occurs and problems are often due to low voltage to the control module, poor earthing, loose/damaged wires and connections. Damaged and brittle wires are common on the 30xx tractors now, many being around 20 years old now
Parts , sensors are available but can be expensive . AFAIK the original type control module are no longer available but newer versions can be retro fitted.
I'm not a mechanic but operate a 3090 regularly