Beechjet 400 Captain reported a loss of flight control while on initial approach. The Captain stated the aircraft began to pitch down then up before it was recovered for a missed approach. Flight icing was present.

Narrative

Upon passing the final approach fix on the RNAV XXL; we made the final configuration to the aircraft by selecting Flaps 30. At that time; the yoke of the airplane started to shake very badly. Right after it started to shake; the aircraft did an uncommanded pitch down. The pilot flying immediately stated to make the correction and the aircraft then went into a steep pitch up. I then assisted the pilot flying in bringing the nose to level. At that moment; the aircraft went into another uncommanded pitch down. I told the pilot flying to go around and we started a left climbing turn. I advised the tower that we were going around and that we needed an altitude above the overcast layer. I was directed to call Departure. I advised them that we had an unknown control issue and that we needed an altitude above the cloud layer. They cleared us to 7000 feet. Once above the cloud layer and a brief moment of flying; the pilot flying stated that the flight controls appeared to be operating normally. I we requested a diversion to ZZZ1 where we landed without incident.Cause: I think icing on the Horizontal Stabilizer may have been the issue.Suggestion: We conducted the flight according to all SOP's. All anti ice measures were used. There was nothing that we did to cause this incident.