Create a continous variable force on object
The problem with solenoids is that the force is strongly dependent on plunger position.

You might get away with it given the small range of motion, but a better option is generally a 'voice coil' actuator (I use one for cutting depth control in a record lathe, significantly less annoying then a solenoid). 
200N is quite a large load, you might benefit from some mechanical advantage (A lever)?