That's the power valve servo motor. Its what makes the PVs move. The power valves essentially change the exhaust porting for different engine speeds, which gives you more power. Problem on the early models (pre-02) is that the power valves tended to come loose and fall........sometimes into a cylinder causing major damage. The fact that your engine is running says that hasn't happened yet, but they may have fallen and not be working. Many times they just come off and drop, and cause no damage, but do result in power loss.
I think the top speed on the GP800 was around 56-57 when new. Keep in mind that the powervalves may only be part of your problem. I seriously doubt that a problem with the powervalve system could account for all your problem.........maybe 5 mph, loss but not much more unless a loose valve has also damaged the piston. You likely have other problems.......dirty carbs, worn out piston/cylinders, etc., may also be factors.
If it hasn't been done already you need to add clips to the power valves, or replace the power valves with ones with clips, and ensure that the servo motor and cable etc., are all working. Do a search on powervalves and you will come up with 1000s of posts. It is a very common problem on the early models.
Here is a guide on a 1200 for upgrading the valves:
Shop SBT - power valve
More reading:
WaveEater Products
WaveEater Products
Copied from another post:
PV service is not that bad. Here are the basic steps...
Remove the four bolts holding the PV covers.
Remove the servo cables from the pully.
Remove the center conection bar.
Remove the small allen screw that connects the PV arm to the shaft.
Remove the shaft out the rear and front of the cylinder. There is a small clip on the end of the shaft.
Remove the larger allen screw that holds the PV guide into the cylinder.
Pull the PV out of the cylinder. It will take a bit of force to pull the guide out.
Clean everything well and reassemble with locktite on the screws.
Purchase a set of new PV links from SBT or a set of WeedEater Clips to prevent the PV pin from falling out and droping the valve in the cylinder.
Also sounds like you may need a new servo motor. Check the electrical connections 1st. Very common to see loose/broken wires to the servo motor, broken cable, etc..