PC12 Captain reported aircraft entered a steep descent while on autopilot resulted in an ATC minimum safe altitude alert and temporary loss of aircraft control.

Narrative

While approaching ZZZ in Aircraft X on an IFR flight plan as Pilot Monitoring (PM); we were given a routine descent from 4000 ft. to 3000 ft. in IMC. As PM; I observed the PF (Pilot Flying) set the appropriate altitude/descent rate in the altitude controller with the autopilot connected. At around the altitude the aircraft should have began to capture the selected altitude; the aircraft entered a steep; un-commanded (as determined to the best of my ability in the moments afterward) descent at a moderate to fast pace; making it impossible to capture the assigned altitude safely. I was temporarily heads down in this moment when I felt an unusual sensation which caused me to quickly look up and grasp the controls. This happened at the same moment the SIC (Second in Command)/PF made a comment about a steep descent. I scanned the instruments and viewed a rapid buildup of airspeed and descent rate; with wings level. I disconnected the autopilot and held the control column with 2 hands while I commanded a reduction of power from the SIC. The audible chime was heard signifying the autopilot was successfully disengaged. It took considerable force to level the wings; requiring 2 hands. The aircraft was recovered from its unusual attitude at about 2200 ft. MSL; where I momentarily flew it wings level before deciding we should climb to a higher/safer altitude. In these moments; I queried the SIC as to what she changed on the altitude controller; and if any other changes were made that I was unaware of. She answered that she increased the descent rate from 1000 ft. from to 1500 ft. from. This was a decision that we discussed/agreed on during the descent. This decision was also made well before the aircraft would have been attempting to capture the set altitude. I verified the selections on the altitude controller and determined it was correct. My next action was the check for trim malfunction/runaway; I viewed no indications of failure. I checked the flight director control panel to see if anything was selected that should not have been. I viewed no issues. I also did not see a PUSHER CAWS. Throughout this troubleshoot phase; I maintained 2 hands on the controls while commanding for any other changes I wanted. It took considerable force to maintain wings level; and a great amount of up-trim to return to normal feel. The trim did feel like it was functioning normally; however I don't know the reason why I had to counter act so much down-trim. ATC issued us a low altitude alert and I told them that we needed a heading/altitude and that we were not ready for the approach. They assigned us with a heading/altitude and I commanded for various modes on the flight director as I hand flew back on course. I viewed no abnormal indications with the flight director; nor any unusual feelings with the controls. Flight controls were handed back to the SIC as I assisted in getting us back on the approach. Normal PF/PM duties were maintained for the rest of the flight and no further abnormalities occurred.Encourage pilots to hand fly or intervene quickly in a way that ensures safe flight when they feel confused about what the automation is doing.