Add an empty at the origin of the object that you want to duplicate.
(Remember to hit CtrlA and select rotate and scale, to apply transormations on the original object).
Then, add an array modifier with object offset linked to this empty.
Set the 3D cursor to the desired centre of the circle. Add another empty here. Make it the parent of the other empty. Now select only the centre empty. Rotate.
The amount of rotation is of course dependent on the number of objects, e.g. 12 objects = 30°.
If you want the single elements to "touch" as in your picture you need to either adjust the object width or the radius. The circumference of the circle is 2 * PI * radius, so the width has to be the nth (e.g. 12) part of it. (Or, if it is not about absolute exactness, it can be done visually.)
You probably want to parent the object to the centre empty.
This circle is "controllable" as you can simply change the angle by rotating the centre empty.