Advanced control laws of DC-DC converters based on piecewise affine modelling. Application to a stepdown 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.