Smooth Aster?

It's a bit late in the season to start trying to repair my lack of knowledge about the various types of asters, but I came across this poor little thing still blooming out in my field, and just had to try to identify it.

The blossom is pale lilac, with a yellow central disk.



The leaves clasp the stem, and their edges are smooth or almost imperceptibly toothed.



I think it's a Smooth Aster. They normally grow as high as four feet, but this particularly one has been run over by a brush mower a couple of times during the summer.

I've previously identified two other varieties of lilac-colored asters. Not sure if I'm right about any of these.