Stability Analysis and Control of Nonlinear Phenomena in Boost Converters Using Model-Based Takagi–Sugeno Fuzzy Approach

The application of a novel Takagi-Sugeno (TS) fuzzy-model-based approach to prohibit the onset of subharmonic instabilities in dc-dc power electronic converters is presented in this paper. The use of a model-based fuzzy approach derived from an average mathematical model to control the nonlinearities in power electronic converters has been reported in the literature, but this is known to act as a low-pass filter, thus ignoring all nonlinear phenomena occurring at converter clock frequency. This paper shows how converter fast-scale instabilities can be captured by extending the TS fuzzy modeling concept to nonsmooth dynamical systems by combining the TS fuzzy modeling technique with nonsmooth Lyapunov stability theory. The new method is applied to the current-mode-controlled boost converter to demonstrate how the stability analysis can be directly applied by formularizing the stability conditions as a numerical problem using linear matrix inequalities. Based on this methodology, a new type of switching fuzzy controller is proposed. The resulting control scheme is able to maintain the stable period-one behavior of the converter over a wide range of operating conditions while improving the transient response of the circuit.