Advanced control laws of DC–DC converters based on piecewise affine modelling. Application to a step-down converter

This study proposes two control techniques for a buck converter operating in continuous conduction mode at a fixed switching frequency. The non-linear behaviour of this switched system is represented by a discrete piecewise affine (PWA) model. The PWA representation offers a precise approximation of the converter's dynamics in the whole operating domain and also allows the investigation of system's stability and the design of different control laws. The first control approach corresponds to a piecewise linear (PWL) state-feedback controller, designed by using a piecewise quadratic Lyapunov function and by solving a set of linear matrix inequalities. This control method guarantees the stability of the closed-loop system for a wide range of operating points. The second control strategy is a model predictive control. The constrained optimal control problem is formulated and solved using the PWA approximation as a prediction model. The explicit form of the control law is derived off-line as an affine state-feedback controller and stored in a look-up table for implementation. Both PWL and PWA controllers are validated experimentally, showing better performances in comparison with a proportional–integral or constant state-feedback controller.