SF50 pilot reported altitude deviations related to autopilot flight control difficulties at FL310.

Narrative

Approximately 30 miles prior to ZZZ; while at level flight at 310; the plane began to climb in altitude. On the upper left of screen there was a yellow 'ele' and down arrow (elevator mist rim down). At about 150 ft. above assigned altitude I notified ATC (climb was rapid). I adjusted 'down --- up'; which temporarily helped; but then continued to climb again. Climb continues to about 400 ft. above assigned altitude. I took off autopilot and returned to FL310. Of note; the elevator trim was very difficult to turn; and upon autopilot disconnect I had to maintain significant nose down force on the stick. I have not hand flown at this altitude; so I am not sure how to compare this. I reset autopilot. The yellow elevator down indicator came back on and I manually adjusted the elevator. Deviations of up to 50 ft. occurred during these adjustments. The plane then maintained level flight under autopilot without further elevator notifications. I notified ATC that I was able to maintain level flight. Report completed about 50 nm after ZZZ.