A consistent framework for robust linear quadratic regulators (LQRs) control of power converters is presented. Systems with conventional LQR controllers present good stability properties and are optimal with respect to a certain performance index. However, LQR control does not assure robust stability when the system is highly uncertain. In this paper, a convex model of converter dynamics is obtained taking into account uncertainty of parameters. In addition, the LQR control for switching converters is reviewed. In order to apply the LQR control in the uncertain converter case, we propose to optimize the performance index by using linear matrix inequalities (LMIs). As a consequence, a new robust control method for dc-dc converters is derived. This LMI-LQR control is compared with classical LQR control when designing a boost regulator. Performance of both cases is discussed for load and line perturbations, working at nominal and non nominal conditions. Finally, the correctness of the proposed approach is verified with experimental prototypes.

A novel dc-dc switching converter consisting of a boost stage cascaded with a buck converter with their coils magnetically coupled is presented. The disclosed converter has the same step-up or step-down voltage conversion properties than the single inductor noninverting buck-boost converter but exhibits nonpulsating I/O currents. The converter control-to-output transfer function is continuous between operation modes if a particular magnetic coupling is selected. The addition of a damping network improves the dynamics and results in a control-to-output transfer function that has, even in boost mode, two dominant complex poles without right-half-plane zeros. An example shows that an output voltage controller can be designed with the same well-known techniques usually applied to the second-order buck regulator. Details of a prototype and experimental results including efficiency, frequency, and time domain responses are presented. The experimental results validate the theoretical expected advantages of the converter, namely, good efficiency, wide bandwidth, and simplicity of control design.

Switching dc–dc converters are widely used to interface the dc output of renewable energy resources with power distribution systems in order to facilitate the use of energy at the customer side. In the case of residential photovoltaic (PV) applications, high conversion ratio is usually required, in order to adapt the low output voltages of PV modules to a dc bus voltage, while dealing with the appropriate impedance matching. In this paper, a system connected to a PV panel consisting of two cascaded dc–dc boost converters under sliding-mode control and working as loss-free resistors is studied. The modeling, simulation, and design of the system are addressed. First, an ideal reduced-order sliding-mode dynamics model is derived from the full-order switched model taking into account the sliding constraints, the nonlinear characteristic of the PV module, and the dynamics of the MPPT controller. For this model, a design-oriented averaged model is obtained and its dynamic behavior is analyzed showing that the system is asymptotically globally stable. Moreover, the proposed system can achieve a high conversion ratio with an efficiency close to 95 $\%$ for a wide range of working power. Numerical simulations and experimental results corroborate the theoretical analysis and illustrate the advantages of this architecture in PV systems.

In distributed power generation systems a pivotal role is played by DC-DC power converters that are employed to connect local loads to local power sources. These converters are used either in combinations of series/parallel connections or as stand-alone devices. A lot of work has taken place in the stability analysis of these converters and several methods have been used/proposed with different properties, strengths and weaknesses. Describing all existing methods is probably a never ending task and therefore in this tutorial paper four different methods will be presented by pointing out their main properties and explaining briefly how they can be used in applications that involve power converters. More specifically, the chosen methods are based on 1) the Poincaré map, 2) Saltation matrix, 3) trajectory sensitivity, and 4) steady-state-response analysis of the discrete-time model. Simple case studies from previous publications are collected and presented in order to further explain these methodologies. Finally, this paper intents to describe some of the future challenges that exist in the area of stability analysis of power converters especially when these are employed in distributed generation applications.

The cascade connection of two dc–dc switching converters for constant power supply is studied. The source converter is of boost type while the load converter is of buck type. The natural unstable behaviour of the cascade connection for both on and off states of the boost converter is counteracted by a sliding‐mode control strategy that combines unstable trajectories to generate a stable one for the regulated boost converter dynamics. Experimental results using an electronic load to emulate a buck converter‐based constant power load are in good agreement with the theoretical predictions. A similar agreement is later obtained when a buck converter with a dynamic behaviour close to an instantaneous constant power load is employed instead of the electronic load.

Switched power converters are used to interface the dc output in modern distributed power generation systems, which are usually aggregated to the main grid to yield the necessary power using interconnected modules. Synthesis, modeling, and stability analysis of interconnected systems using cascaded converters working under sliding-mode control are considered in this paper. A systematic procedure to synthesize cascaded connection of dc-dc boost converters is introduced. The approach is based on making each module to behave as a suitable canonical element for power processing. Three different elements are considered, which are the dc power gyrator, the dc transformer, and the dc loss-free resistor. These canonical elements are designed by means of a sliding-mode control theory and then their dynamic behavior is studied in detail. The sliding-mode conditions for each case are derived in closed form to obtain design-oriented criteria for selecting the parameters of the system. The aforementioned canonical elements are compared to select the most suitable one for a distributed power system. Simulation results ensure the correctness of the proposed approach. Experimental measurements corroborate the theoretical predictions and the numerical simulations.