I have a third order process and I have to design a PID controller by cancelling out the two most dominant poles of the process. The process transfer function is:
To cancel out the poles the controller becomes, this is multiplied by Kc:
Now I have to cascade the controller and the process and calculate the transfer function with feedback (negative feedback), the feedback gain is 4. The problem is that I'm supposed to calculate the value of Kc using the standard second order transfer function, but that is not what I get, because of the feedback gain being 4 and not 1.