Switched affine systems with hysteresis-based switching control: application to power converters

Many power electronic converters can be modeled using the theoretical framework of switched affine systems, which considers the instantaneous dynamics of the converter instead of its averaged model. In this class of systems, a certain number of subsystems is present and a control law is designed to orchestrate the switching among them. When the switching law is state-dependent, the closed-loop system is stabilized at the desired equilibrium through sliding mode dynamics, leading to infinite-rate switching. In this paper, a control strategy is proposed using constant-width hysteresis as a way of bounding the switching frequency at a finite value when two subsystems are present. In addition, an upper bound on the hysteresis width is provided so that the system is not stabilized at the equilibrium of a subsystem. Finally, simulation results illustrating the application of the proposed method to power electronic converters are presented. The relation between the switching law parameters and the current ripple is discussed for a dc-dc Boost converter and a Buck converter.