Pilot reported engine roughness and lack of Engine Throttle response on descent. The Engine continued to show a lack of response to Throttle movement so the Pilot continued the approach and landed. The aircraft was turned over to maintenance for action.

Narrative

I was doing a normal; other than being solo; practice area flight. The run up was great; the takeoff was fine; everything else was perfectly normal. It is when I begin my preparation to come back to the airport; descending and reducing the throttle. It is when I first noticed that when I brought the RPMs down to roughly 3;700-4;000 RPM; to begin a gradual descent; is when I first noticed that it would run rough at a lower RPM. And when I reference 'roughness' in the engine it means that the engine; and subsequently the plane; began to shake vigorously. It was quickly fixed by a twist of the throttle to add some power. The rest of the pattern was a normal pattern; except that I was higher than normal because of a 737 on the parallel. When I was about a half mile away from the runway threshold; the engine began to run rough again; but this time it was more than the previous and was not fixed with a simple light twist of the throttle that would bring the RPMs up a couple hundred. I then began to manipulate the throttle and it was just stuck at 3;700 RPM; even with near full throttle it didn't do anything. I then brought it back to near idle and it was dancing all over the place. I saw a quick burst of an increase in RPM; then it decreased. I thought it was going to continue to decrease.I then switched fuel tanks and pushed the carb. heat in the see if anything was going to fix then problem; it didn't. With this terror and trouble I was having; I contacted Tower and advised them of my situation. After 10-15 seconds after the last contact with Tower; the RPMs began to act more normal and responsive to the inputs I was giving it. For the flare and touchdown; I put the throttle back into the idle 'position' and landed. Although when vacating the runway; my RPMs dropped way below the normal idle power to 1;700 RPM and it was running with a light roughness. I then; after I was clear of the runway; I tried to see if twisting the throttle clockwise to see if adding power would fix the situation; and this time it did. I think the cause of this incident was the dual carburetor system de-syncronizing or something to do with the pulley system that controls the throttle and the valve that opens and closes the fuel air mixture. Being a student solo in the cockpit and something like this occurring; I think that the decisions made might not have benefited the situation and just took some time that I could have been focusing on something else; put on a solution that was probable in my mind at the moment. I think something that would be done to prevent this from occurring would be not going to full idle when coming into land because that is when I think it is most messed up.