Control Systems-Design controller to achieve the following
Let's write in Laplace domain for the closed loop Y=2RCG/(1+CG)  (sorry for missing math typesetting)

If we write the final value of y(t)=1, we must write in Laplace domain that the limit of sY is 1 when s approaches zero.

By applying this to the first formula we get CG=1. This is not the whole truth, because CG=1 must be true as the limit when we let s to approach zero. Thus we can add anything that approaches zero or multiply with anything that approaches 1 when s approaches zero.

To make it simple let's select CG=A where A is one when s is zero.

To check the second condition we write for the closed loop Y=2RA/(1+A)

If we select A=1+2s we get Y=R(1+2s)/(1+s) whis has a pole at -1. That's ok.

the controller: C = (1+2s)/G = s(1+s)(1+2s)/10

I wrote that something can be added to CG if that something is zero when s=0. A short calculation shows that it does not add new possiblities to simplify

One should note that altough C seems to compensate G's poles, that's not true in practice because in practical circuits the poles and zeros are not exact. This can kill the solution depending on the given declarations.