Lovely design!
I wish I had a bit more time to go through this, but essentially you need to draw this as a three dimensional box with vanishing lines for both sides, and then cut a cylinder out of that box. This will help a lot with perspective.
I don't have any specific examples, so you may want to look up two point perspective, a quick tip there though, because they are trying to show what it is, they often have the vanishing points in the picture, which makes the perspective look really extreme;. Ideally you should be putting the vanishing points way out to the side.