CORRECTION: I included a minus sign in the denominator of the DC solution for the buck-boost (Despite my own "correction" in the video). The denominator should be:
DR_1+D'R_2+D'^2R_L, not -D'^2R_L.
Continuing on with small signal modelling of power converters, here we're looking at the state space model. By writing out equations for inductor current and capacitor voltages (the "states" of the system) for each switching state, we can write out matrix equations to describe the circuit. Averaging over the switching cycle, perturbing, then linearizing the perturbation allows us to generate both DC and small signal state-space models.
This canonical form enables the application of conventional state-space control methods to power converter.
0:00 - Intro
3:45 - Method
5:20 - Buck-Boost Example
10:50 - Matrix Equations
14:50 - Averaging the equations
17:20 - The canonical form
18:20 - DC Solution
20:33 - Perturbation and Linearization
24:00 - Small Signal Model
References:
Fundamentals of Power Electronics - Erickson and Maksimovic
This is a straightforward explanation of state-space control design which you may find helpful:
ctms.engin.umich.edu/CTMS/index.php?example=Introduction&section=ControlStateSpace