DA 900 First Officer reported the aircraft's number 3 engine malfunctioned and the flight crew performed an air turnback. While Maintenance first believed the problem to have been caused by a faulty fuel control computer; the problem was actually caused by a loose cannon plug.

Narrative

This flight was considered a training flight; myself as the instructor in the right seat to help two pilots that just come out of training; and this was their first time operating this specific airplane. I had flown this aircraft for another company so I was keenly aware of its operational considerations.We flew from ZZZ1 to ZZZ to do landings. We did four takeoffs and four landings and then headed back to ZZZ1 when out at 2300 ft.; the number three engine started to surge. I turned off the DEEC (Digital Electronic Engine Control) fuel control computer to manual mode and had control over the engine. Not sure of the malfunction; we [notified ATC] and landed back at ZZZ; yet still had the number 3 engine in idle mode.The company that owned the aircraft had a Maintenance Director. By his evaluation; we all agreed to started the number three engine again with the fuel control computer in the automatic position. It worked good so we flew the airplane back to ZZZ1. While in route; the number three engine fuel controller failed again; and we had to remain in the manual mode.Maintenance on the ground; evaluating the engine; and it was a loose cannon plug that caused the intermittent malfunction.