# Difference between state space and transfer function model response (in Simulink)

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

\begin{align}\frac{dx}{dt}&=Ax+Bu\\y&=Cx+Du\end{align}

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?

• Is your starting state different for the two? Is the steady state response the same? – Phonon Oct 27 '13 at 3:46
• @Phonon Starting state is the same (simulation is done in the same file). Steady state response is also "the same", only state space is extremely noisy (see tinypic.com/r/2v0mxpv/5). If I make Ti 100 times higher, I can get the same response, but the controller is than slow (and I don't get desired overshoot and settling time) – mikebuba Nov 4 '13 at 16:20