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The switching behavior of power converters with 'ideal' electronic devices (EDs) makes it difficult to define a switched model that describes the dynamics of the converter in all possible operating conditions, i.e., a 'complete' model. Indeed, simplifying assumptions on the sequences of modes are usually adopted, also in order to obtain averaged models and discrete--time maps. In this paper, we show how the complementarity framework can be used to represent complete switched models of a wide class of power converters, with EDs having characteristics represented by piecewise-affine (even complicated) relations. The model equations can be written in an easy and compact way without the enumeration of all converter modes, eventually formalizing the procedure to an algorithm. The complementarity model can be used to perform transient simulations and time-domain analysis. Mathematical tools coming from nonlinear programming allow to simulate numerically the transient behavior of even complex power converters. Also rigorous time-domain analysis is possible without excluding pathological situations like, for instance, inconsistent initial conditions and simultaneous switchings. Basic converter topologies are used as examples to show the construction procedure for the complementarity models and their usefulness for simulating the dynamic evolution also for nontrivial operating conditions. Index Terms--Modeling, piecewise linear approximation, power conversion, simulation, switched systems, switching circuits.

In this paper, we propose a novel approach to the modeling and controller design of the synchronous step-down dc-dc converter. We introduce a hybrid converter model that is valid for the whole operating regime and captures the different modes of operation. Based on this model, we formulate and solve a constrained optimal control problem. This allows a systematic controller design that achieves the regulation of the output voltage to its reference despite input voltage and output load variations while satisfying the constraints on the duty cycle and the inductor current. The resulting state-feedback control law is of piecewise affine form, which can be easily stored and implemented in a lookup table. A Kalman filter is added to account for unmeasured load variations and to achieve zero steady-state output voltage error. Experimental results demonstrate the potential advantages of the proposed control methodology. Index Terms--DC-DC converter, power electronics, model predictive control (MPC), optimal control, hybrid system, piecewise-affine (PWA) system.

Dithering is proposed as a technique for the regulation of the boundary layer for switched systems under sliding-mode control. It is proved that dithering maintains the state of the system close to the ideal sliding manifold and that state error and practical stability depend on the dither amplitude, period, and shape, all by preserving the natural switching mode of the system. Experiments on a dc/dc buck power converter confirm the theoretical results. Index Terms--Dither techniques, power electronics, sliding mode, switched systems.