Unified Approach for Robust Stability Analysis of Buck Converters with Discrete-Time Sliding Mode Control

Yanmin Wang,Ping Zhang,Yang Ge,Guangxin Duan,Yuqiang Wu

doi:10.1155/2021/5527047

Abstract

This paper proposes a novel discrete-time sliding mode (DTSM) control approach to address the robust stability problem of buck converters with multiple disturbances. The contributions lie in the “unified” modelling and controller design. In modelling, all the possible model uncertainties and external disturbances are considered and further classified into two cases. It can also be extended to the situations with individual/several disturbances. While for the controller design, differing from the traditional DTSM based on the nominal model, the disturbances are directly introduced in the process, giving the robust stability condition and four new regulation subranges. It is suitable for both nominal and perturbed systems. Finally, the influences of the sampling time and disturbances on the control performance are investigated. Simulations and experiments confirm the benefits of the unified approach with greater accuracy and wider applications.

Highlights

With the rapid development of programmed microprocessor chips, the discretization is another issue not to be avoided for SM controlled converters [24,25,26]
The contributions of this paper can be concluded as follows: (1) all possible model uncertainties and external disturbances of buck converters are considered in modelling and control, including the variations of input and reference output voltage, parameter uncertainties of load resistor, inductor, and capacitor, and time-varying external disturbances; (2) differing from the traditional discrete-time sliding mode (DTSM) approach [1, 24, 27, 31], four more accurate subranges of controller parameter can be achieved by the stability analysis; and (3) the influences of the sampling time and disturbances on the controller regulation and control performance are investigated simultaneously
If we fix the sampling time h, the bigger the DTSM parameter λ is, the smaller the response time is, while the values of steady error and the relative steady error of the output voltages vc are maintained. It means that the sampling time h is more sensitive to the system than the DTSM parameter λ. erefore, it is recommended to determine the value of h prior to that of λ

Summary

Introduction

With the rapid development of programmed microprocessor chips, the discretization is another issue not to be avoided for SM controlled converters [24,25,26]. The contributions of this paper can be concluded as follows: (1) all possible model uncertainties and external disturbances of buck converters are considered in modelling and control, including the variations of input and reference output voltage, parameter uncertainties of load resistor, inductor, and capacitor, and time-varying external disturbances; (2) differing from the traditional DTSM approach [1, 24, 27, 31], four more accurate subranges of controller parameter can be achieved by the stability analysis; and (3) the influences of the sampling time and disturbances on the controller regulation and control performance are investigated simultaneously. T denotes the transpose of the matrix, I∈Rn denotes the n × n identity matrix, O(.) denotes the infinitesimal term of the corresponding parameter, and the items with “Δ” represent the disturbances of the corresponding nominal variables

Methods

Results

Conclusion