add another control's ID to generated HTML

[slow learner]

I created two server controls A and B. I have a test ASPX page containing A1
and B1. A has a property "ConnectTo" which is type B. In property page, I
change A1's "ConnectTo" to B1. I expect to see the following HTML in my test
ASPX page:

<cc1:A id="A1" style="..." runat="server" ConnectTo="B1"></cc1:A>

I can get this result if B is derived from "System.Web.UI.Control" but I
cannot if it's derived from "System.Web.UI.WebControls.WebControl". Why?

I need to take advantage of "System.Web.UI.WebControls.WebControl" so I
really need to derive from it.

slow learner