Global Hybrid Modeling and Control of a DC-DC Buck-Boost Converter via Mixed Logical Dynamical Systems

This paper presents a new model for a DC-DC buck-boost converter considering its all controlled and uncontrolled switching phenomena in both continuous and discontinuous conduction modes. The proposed model is developed based on hybrid systems theory using mixed-logical dynamical (MLD) systems, and an improved version of these systems called as extended mixed-logical dynamical (EMLD) Systems. Compared to the existing MLD and EMLD models of the DC-DC converters, the proposed model contains fewer numbers of integer variables and inequalities, and, as a result, leads to the less complexity and solution time of the mixed integer optimization problems arising from the corresponding hybrid model predictive controllers. The advantage of the proposed modeling and control method is evaluated via the comparison of the existing MLD models and hybrid predictive controllers as well as classic proportional-integral (PI) controllers. Moreover, the theoretical challenges for the closed-loop stability proof are discussed and in this regard some future research outlines and ideas are introduced. The steady state and transient performance of the closed-loop control system over a wide range of the operation points show the satisfactory operation of the proposed modeling and control scheme for the DC-DC buck-boost converter.