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

Abstract

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.

Is exponential stability achievable in singular perturbed delayed systems with time-varying parameters? A comprehensive analysis

“…Traditional methodologies employed in these studies have commonly assumed exponential stability in the fast subsystem, yielding valuable insights across diverse contexts [ [56] , [57] , [58] ]. Notably, the emergence of LMI methods has revolutionized the analysis of singularly perturbed systems, offering efficient techniques for stability analysis and providing a deeper understanding of their dynamic behavior [ [59] , [60] , [61] ]. Despite the significant advancements in stability analysis facilitated by LMI methods, a notable limitation persists in the existing literature [ 62 , 63 ].…”

Design of a Switching Strategy for Output Voltage Tracking Control in a DC-DC Buck Power Converter

“…A robust state-feedback switching law for the switched system utilizing the sliding mode theory was developed in [14] to ensure the robust asymptotic stability of the desired equilibrium point for the Buck converter. While Hejri, in [15], using switched Lyapunov functions, a set of sufficient conditions based on matrix inequalities, reduced the computational complexity and solved the stabilization problem for the DC/DC converter, de Souza et al in [16] developed a strategy to limit the switching frequency using a state-dependent switching law for switched systems for stabilization at the desired equilibrium. Another switching strategy consists of an adaptive sliding mode control that combines a robust proportional-derivative control law for the regulation of the DC/DC Buck converter-DC motor system presented in [17].…”

“…Motivated by the benefits of a commutated control strategy [12][13][14][15][16][17][18][19], the design of a suitable switching function by means of the application of convex sets for the output trajectory tracking of a Buck power electronic converter is presented here. Unlike in [12][13][14][15][16][17][18][19], this control resolves voltage tracking at the converter load.…”

“…Motivated by the benefits of a commutated control strategy [12][13][14][15][16][17][18][19], the design of a suitable switching function by means of the application of convex sets for the output trajectory tracking of a Buck power electronic converter is presented here. Unlike in [12][13][14][15][16][17][18][19], this control resolves voltage tracking at the converter load. The use of convex sets in the commutated control strategy presented here allows for resolving the tracking for different desired voltage trajectories for the Buck converter in milliseconds, even in the presence of abrupt disturbances in the load and source.…”