I am looking at an old exam question and I am wondering giving a certain
G(s) how can I choose the points of the zeros in a PID Controller to have a second order response for small values of K and a first order response for large values of K. So far I have found the transfer function but I am unsure how to determine the zeros. If anyone could even provide an explanation I would be very grateful!
From here I can see that if K is small I will get a second order response, and if K is large I can see where I would get the first order response.
What I do not understand is how do I find the Zeroes (a and b) for the PID to give the desired response?
Edit: I apologize, both K and k are the same I will fix that. In the question for small K the system should have a second order response to a step input and a first order response for large values of K.