Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Troubleshooting; Workload
Aircraft Equipment Problem Less Severe; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Provided Assistance; Flight Crew Landed in Emergency Condition; Flight Crew Overcame Equipment Problem; General Maintenance Action
Aircraft
ATC instructed us to cross ZZZZZ at 14;000 feet cleared for the LOC DME - E.  We started our descent and broke out of clouds at approximately 17;000 feet and visually acquired the airport.  Selected gear down to help slow down.  Then flaps 10 as we started the 'smart turn' to capture the final approach course.  Time was XA30z from MDC [Maintenance Diagnostic Computer]. This is when we got amber AP HOLDING NOSE UP and AP STAB TRIM FAIL messages.  Stab trim indicator was amber and 2.2.  SIC ran the QRH for AP STAB TRIM FAIL and AP HOLDING NOSE UP (both on same page next to each other).  We were still descending at 2;000 FPM established on LOC. Notified ATC we had flight control issue.  QRH directed disengage AP and had warning for abrupt change in control force.  Disengaged AP and had momentary pitch dip while I adjusted to control force required to hold nose up.  SIC and I quickly discussed that leveling off or attempting to climb back up would put us in a worse situation (still descending to runway). With BKN/OVC at 17-18;000 feet; thunderstorms in vicinity; and impending night plus no traffic into ZZZ continuing to land was best option. When we disconnected AP we got a PRI STAB TRIM FAIL message. We selected flaps 20 and control forces were still manageable. We requested CFR [County/City Fire and Rescue] from ATC. While my SIC was referencing the QRH; I was concentrating on keeping the descent going to get us to a flatter approach angle and not be too high as a go around might not be possible. I knew I would be close to the ridge line near ZZZZZ1 and I could see it clearly.  The 2;000 FPM descent put us closer to the terrain than I realized and we got a Terrain Caution followed by Terrain Pull Up.  I decreased the descent rate to 800 FPM; alerts went away; I could see we were past terrain now and went back to 2;000 FPM descent. Went flaps 30 to see if I could still manage the pressure. I could.  QRH had us go to Secondary Trim which worked on short final. Made a normal landing and CFR never had time to get out of their facility.  Time from first indication to landing 6 minutes.  Canceled CFR and closed IFR flight plan with ZZZ1 on taxi in. Passengers never knew and thanked us for getting into ZZZ before Sunset.Suggestions: When referencing the QRH procedures; neither of us specifically stated 'AP STAB TRIM FAIL QRH' as trained. We just said go to the QRH.  Fortunately; my SIC was spot on and had no trouble finding the correct ones. We also didn't vocalize '...COMPLETED' at end of procedure either.  Time crunch contributed to this. It would have been desirable to notify passengers in case we did have to evacuate; however; we just didn't have the time and I might have needed my SIC to help on the controls. Announcing on CTAF we had an emergency might have allowed CFR to respond quicker vs ZZZ1 ATC calling and relaying.  I'm not sure if they monitor it. We did have communication all the way to parking. Try to be more cognizant of the altitudes on the LOC DME E to be sure we cleared terrain and not let doing the visual approach override that given the waining sunlight.
CL-350 Captain reported Stabilizer Trim Failure during approach into a mountainous terrain airport.