Why I get a different response from the same system (e.g. three phase inverter with LC filter) in state space form and in transfer function (Laplace) form when using the same PI controller values ($K_p$ and $T_i$)?
First I start with differential equations for each phase $a$, $b$ and $c$ to get state space model
Than an $abc/dq$ transformation is applied (to get coupled relationship between $d$ and $q$ frame). Finally separate equations for $d$ and $q$ frame can be written and transformed to Laplace. From there I can get control scheme and calculate $K_p$ and $T_i$ to get desired overshoot and settling time.
But when I use the same $K_p$ and $T_i$ in the state space model I get extremely noisy and oscillatory response. My question is why is that? I read previous similar question “Control theory: Laplace versus state space representation” and the difference is that the transfer function neglects initial states.
Additional question: how to then calculate PI controller values when using state space form to get desired overshoot and settling time?