I had a transfer function
and I found the state space representation of the above using MATLAB.
Using $place(A,B,[poles])$, I found a gain matrix K that corresponds to the poles.
My question is that when I tried to do this using an equivalent alternate state space representation of the transfer function (e.g. using the controllable canonical form), I got a different gain matrix K.
Why is this the case? Since the system's transfer function is one and the same, shouldn't the K matrix be the same? Does this mean that there are multiple K matrices that when multiplied with the states, would give us a desired closed loop characteristic?
Would this then be an advantage over classical control, where here we can use different kinds of controllers with different gains, whereas in classical control we can only have 1 gain value that can get us to the desired closed loop pole characteristic?