A CE650 was vectored too close to the airport for a stabilized approach and so executed a go around. On the second approach the flaps faulted as they were extended but reset causing the aircraft to pitch up and gain altitude at which time the autopilot failed; followed by the FMS's failure. The approach was again abandoned. A normal third approach followed to a landing.

Narrative

We were given vectors for an RNAV GPS approach. Approach Control gave us a vector to the IAF which was going to require a 110 degree turn from the IAF to the IF. We had the aircraft slowed; on autopilot. Approximately 4 miles from the IAF the aircraft started to make the turn to the IF. Approach asked us if we knew our position; we said we did; and this was going to be a very difficult turn due to the vector. We broke off the approach and were given vectors for a straighter vector the IAF. After crossing the IAF to the IF we extended additional flaps; the flaps failed; the flaps extended rapidly; the aircraft pitched up with a slight altitude gain; and approach asked us if we were climbing. The FMS then failed. Broke off the approach again; and got vectors for an ILS with a circle to land approach to the same airport. After landing I called the Approach facility on the phone to discuss everything to make sure there was no misunderstanding or problems. I have flown in this area for decades and a phone call is always appreciated from both sides. They informed me there was no problem. The initial poor vector; combined with our equipment was the main factors here. After landing and powering down the electrical systems/avionics everything worked perfectly.