Piecewise affine modeling of parallel boost converter in a DC microgrid and its control application by utilizing a Linear Matrix Inequality approach

The Piecewise Affine (PWA) model approximates nonlinear systems using linear models within specific regions. This approach offers advantages for designing DC microgrid control systems with linear controllers, mainly when the system includes several nonlinear DC–DC boost converters. The boundaries of the PWA model can be established using straightforward methods based on duty cycle partitions. Each duty-cycle region represents a distinct operational mode of the system characterized by unique dynamic equations. This study presents a formulation for deriving the PWA model of a parallel boost converter based on its nonlinear average dynamics resulting from the multiplication of states and inputs. An average dynamics model for the parallel boost converter is also introduced and employed in the deriving formulation. Moreover, computer simulations were conducted to analyze the PWA models of parallel boost converter dynamics, employing various partitions, comparing their behaviors among themselves and against those of the Matlab Simulink model. Furthermore, laboratory experiments were conducted by implementing a controller based on Linear Matrix Inequalities (LMI), designed using the PWA model of the parallel boost converter, to regulate the converter’s output voltage. The simulation and experimental results demonstrate that the PWA models of parallel boost converter dynamics closely align with those of the average model, making it well-suited for being controlled using a linear controller.