  The Equivalent Series Resistance (ESR) of the output capacitor may cause
output voltage Vo jumps, that are not modeled commonly for second order DC-DC
converters, i.e., converters with two second order switched subsystems. These
jump discontinuities in Vo lead to performance issues in Switching Surface (SS)
controllers. In this paper, these ESR effects are modeled using switched
systems with state jumps, called Jump-Flow Switched (JFS) systems. Furthermore,
it is shown that approximating the capacitor voltage (Vc), with Vo, can cause
undesired limit cycles, oscillations, chattering or instability issues. To
resolve these issues, a non-jumping normal switched system is defined for JFS
systems, that is equivalent to the internal continuous dynamics. Also, the
challenges of designing SS controllers, for this equivalent switched system is
studied, and the Constrained Near Optimal (CNO) SS is designed for the
equivalent switched system of buck, boost, and buck-boost converters. To
eliminate the required estimations, a general class of switching methods are
defined, that also avoids chattering and eliminates the conventional hysteresis
blocks. The proposed controller is implemented using analog op-amp circuits.
Experimental results show fast and robust responses of the controller board
with buck, boost, and buck-boost converters.
