Abstruct-A dc-dc buck converter controlled by naturallysampled, constant-frequency pulsewidth modulation in continuous conduction mode gives rise to a great variety of behavior, depending on the values of the parameters of the circuit. We analyze the one-periodic and two-periodic orbits which cross the voltage ramp once per cycle, and we study their stability by computing the characteristic multipliers associated with each one. Subharmonics, bifurcations, and the presence of a strange attractor are also studied. A plot of the number of crossings in the ramp is drawn. This becomes a helpful tool for investigating the evolution of the trajectories when they are close to the attractor. When analytic computations are impossible, we resort to numerical algorithms to simulate the orbits.

Abstract-Shunt active power filters have been proved as useful elements to correct distorted currents caused by nonlinear loads in power distribution systems. This work presents an all-digital approach, based on the repetitive control technique, for their control. In particular, a special digital repetitive plug-in controller for odd-harmonic discrete-time periodic references and disturbances is used. This approach does not introduce high gain at those frequencies for which it is not needed, and thus it improves robustness. Additionally, the necessary data memory capacity is lower than in traditional repetitive controllers.The design is performed for the particular case of single-phase shunt active filter with a full-bridge boost topology. Several experimental results are also presented to show the good behavior of the closed-loop system.

Abstract-In this paper a fixed-frequency quasi-sliding control algorithm based on switching surface zero averaged dynamics (ZAD) is reported. This algorithm is applied to the design of a Buck-based inverter, and implemented in a laboratory prototype by means of a field programmable gate array (FPGA), taking into account processing speed versus computational complexity trade-off. Three control laws, namely sliding control (SC), fixed-frequency quasi-sliding ZAD and PWM-based control have been experimentally tested to highlight the features of the proposed algorithm. According to the experimental results presented in the paper, the ZAD algorithm fulfills the requirement of fixed switching frequency and exhibits similar robustness properties in the presence of perturbations to those of sliding control mode.

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Abstract-Shunt active power filters have been proved as useful elements to correct distorted currents caused by nonlinear loads in power distribution systems. This paper presents an all-digital approach based on a particular repetitive control technique for their control. Specifically, a digital repetitive plug-in controller for odd-harmonic discrete-time periodic references and disturbances is used for the current control loops of the active filter. This approach does not introduce a high gain at those frequencies for which it is not needed and, thus, improves robustness of the controlled system. The active power balance of the whole system is assured by an outer control loop, which is designed from an energy-balancing perspective. The design is performed for a three-phase four-wire shunt active filter with a full-bridge boost topology. Several experimental results are also presented to show the good behavior of the closed-loop system. Index Terms-Active power filters, digital repetitive control, three-phase four-wire power distribution systems, unbalanced systems.