Im trying to extract the State-Space-Model for an cascaded Buck/Boost-Converter from an set of Transfer-functions \$ G(s)\$ (which I generated with Plecs/Matlab).
First of all I want to analyse the Buck-Modus (Sboost=0).
The State-Space-Model should look like this:
\$ \begin{align} \dot{\vec{\Delta\mathrm{x}}} = \begin{bmatrix} \dot{\Delta \mathrm{uC1}} \\[0.5em] \dot{\Delta\mathrm{iL}} \\[0.5em] \dot{\Delta\mathrm{uC2}}\\ \end{bmatrix} = \begin{bmatrix} \mathrm{A_{11}} & \mathrm{A_{12}} & \mathrm{A_{13}} \\[0.5em] \mathrm{A_{21}} & \mathrm{A_{22}} & \mathrm{A_{23}} \\[0.5em] \mathrm{A_{31}} & \mathrm{A_{32}} & \mathrm{A_{33}} \\ \end{bmatrix} \cdot \begin{bmatrix} \Delta\mathrm{uC1} \\[0.5em] \Delta\mathrm{iL} \\[0.5em] \Delta\mathrm{uC2} \\ \end{bmatrix} + \begin{bmatrix} \mathrm{B_{11}} & \mathrm{B_{12}} & \mathrm{B_{13}} \\[0.5em] \mathrm{B_{21}} & \mathrm{B_{22}} & \mathrm{B_{23}} \\[0.5em] \mathrm{B_{31}} & \mathrm{B_{32}} & \mathrm{B_{33}} \\ \end{bmatrix} \cdot \begin{bmatrix} \Delta\mathrm{Uin} \\[0.5em] \Delta\mathrm{Uac} \\[0.5em] \Delta\delta \end{bmatrix} \end{align}\$
As you can see, my Buck/Boost-Converter contains 3 State-Variables. I did an Impulse-Response Analysis in PLECS (Simulation) to obtain the Bode-Plot from the perturbation in an equilibrium Point.
After that I used \$\mathrm{tfest}()\$ in Matlab to generate \$G(s)\$ for the Bode-Plot.
I have following Transfer-Functions:
For \$\mathrm{uC1}\$: \$ \dfrac{\mathrm{uC1}}{\mathrm{Uin}}(s),\dfrac{\mathrm{uC1}}{\mathrm{Uac}}(s),\dfrac{\mathrm{uC1}}{\delta}(s) \$
For \$\mathrm{iL}\$: \$ \dfrac{\mathrm{iL}}{\mathrm{Uin}}(s),\dfrac{\mathrm{iL}}{\mathrm{Uac}}(s),\dfrac{\mathrm{iL}}{\delta}(s) \$
For \$\mathrm{uC2}\$: \$ \dfrac{\mathrm{uC2}}{\mathrm{Uin}}(s),\dfrac{\mathrm{uC2}}{\mathrm{Uac}}(s),\dfrac{\mathrm{uC1}}{\delta}(s) \$
and want to convert them into an State-Space-Model. How can I achieve that?
