PA-28 pilot reported engine problems during approach to destination airport. The pilot requested priority handling and continued to destination airport.

Narrative

I was flying leveled off at 1;500 ft. on a direct heading to ZZZ1 after departing ZZZ. Approximately 10 mins after departure from Runway XXR; the aircraft engine gave some indications of not running properly. I was experiencing vibrations in the floor initially followed by sporadic loss of engine RPM; engine power; and aircraft speed. I applied carburetor heat; then made a 180 turn back to ZZZ and aligned with ZZZZZ 8 in the event I would lose the engine. Shortly after turning back the engine increasingly was losing and regaining RPM and power in a surging fashion. I requested priority handling due to a rough engine on 121.5; squawked 7700 and IDENT. I then switched fuel tanks; turned on the fuel pump; manipulated the mixture; and backed it up with the loss of power checklist. I requested a climb into the class Bravo airspace for altitude and climbed to 4;000 ft. MSL with a power reduction along the climb.After reaching ZZZ at 4;000 ft. I went onto the CTAF and announced to the 2 aircraft in the pattern my situation and that I would be circling to land off the North end of ZZZ airport in the XXR left hand downwind base to final area. I was able to safely land and taxi the aircraft back to the tie down; the engine was running rough on the ground. Stating again; there were 3 actions taken to improve the engine performance. 1) Carb heat; 2) fuel pump on and 3) fuel tank switch. After all 3 of these changes occurred the engine condition improved; likely these are the potential causes of the rough engine.