A new general mathematical technique for stability and bifurcation analysis of DC-DC converters applied to one-cycle controlled buck converters with non-ideal reset

This paper brings two major contributions: the first investigates and draws conclusions about stability and bifurcation phenomena related to one-cycle controlled dc-dc converters when non-ideal reset is encountered. The second introduces a new general mathematical technique for deriving stability and bifurcation behavior in continuous conduction mode operated dc-dc converters. Up to now, one-cycle control analysis assumed the integrator is instantly reset and in these conditions it was demonstrated that one-cycle control is always stable. In the present work it is proven that even with an ideal converter, when the integration capacitor is discharged over a nonzero resistor the system becomes unstable at high duty cycles. The stability condition with respect to the control voltage is analytically derived using a new general proposed technique. This approach can be applied to any control such as: traditional current mode control, predictive current control, charge control, one cycle control or feedback loops employing different regulators. Moreover, it can be used with different types of modulation: leading-edge, trailing-edge or double-edge modulation. When applied to one-cycle controlled buck converters employing a non-ideal resettable integrator, it is proven that bifurcation phenomena are encountered. This behavior with period doubling instability is confirmed by Matlab and Caspoc simulations.