Hello Control Theory experts,

I am currently on the topic of Internal Model Design theory. Please reference the two screenshots that I have taken - last two screenshots at the bottom. The first is from a textbook (Dorf/Bishop - Modern Control Design) and the other from an online tutorial. Both state without further elaboration as to why x(dot)r can be Arxr and 0 simultaneously. The same can be stated for the definition of r(t) = drxr(t) and r(t) = xr(t). I really did not understand this concept.

The initial definition provides the general form and defined as:

To begin the analys, it is assumed that there is zero steady-state error. Because of this, it turns into this:

Why? I don't quite understand as both references shown below did not elaborate other than make the statement as such.

Can someone please help to clarify this.

Here are my two sources:

Here are the block diagrams relating to the tutorials: