Based on a recently obtained Lemma about periodic orbits in linear systems with a piecewise-linear non-autonomous periodic control, we describe analytically the bifurcation structures in a ZAD-controlled buck converter. This analytical description shows that the period doubling bifurcation in this system may be both subcritical or supercritical. Considering virtual orbits we show how a saddle-node bifurcation becomes feasible and how it is destroyed at a new codimension-2 bifurcation point, where the subcritical period doubling bifurcation becomes supercritical. We also show that this phenomenon does not take place when the error surface in the ZAD conditions piecewise-linear defined.
- Non-smooth systems
- Virtual orbits
- Zero average dynamics
- Power electronics
Avrutin, V., Fossas, E., Granados, A., & Schanz, M. (2011). Virtual orbits and two-parameter bifurcation analysis in ZAD-controled buck-converter. Nonlinear Dynamics, 63(1), 19-33. https://doi.org/10.1007/s11071-010-9782-7