Enric Fossas

Study of chaos in the buck converter

A DC-DC buck converter controlled by naturally-sampled, 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.

Digital Repetitive Control of a Three-Phase Four-Wire Shunt Active Filter

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

A fixed-frequency quasi-sliding control algorithm: application to power inverters design by means of FPGA implementation

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.

Sliding-mode control design of a boost-buck switching converter for AC signal generation

This paper presents a sliding-mode control design of a boost-buck switching converter for a voltage step-up dc-ac conversion without the use of any transformer. This approach combines the step-up/step-down conversion ratio capability of the converter with the robustness properties of sliding-mode control. The proposed control strategy is based on the design of two sliding-control laws, one ensuring the control of a full-bridge buck converter for proper dc-ac conversion, and the other one the control a boost converter for guaranteeing a global dc-to-ac voltage step-up ratio. A set of design criteria and a complete design procedure of the sliding-control laws are derived from small-signal analysis and large-signal considerations. The experimental results presented in the paper evidence both the achievement of step-up dc-ac conversion with good accuracy and robustness in front of input voltage and load perturbations, thus validating the proposed approach.

Application of sliding-mode control to the design of a buck-based sinusoidal generator

This paper is devoted to the design of a sliding-mode control scheme for a buck-based inverter, with programmable amplitude, frequency, and DC offset, with no external sinusoidal reference required. A general procedure for obtaining an autonomous (time independent) switching surface from a time-dependent one is presented. For this surface, the system exhibits a zeroth-order dynamics in sliding motion. On the other hand, from the sliding-domain analysis, a set of design restrictions is established in terms of the inverter output filter Bode diagram and the output signal parameters (amplitude, frequency and DC offset), facilitating the subsequent design procedure. The control scheme is robust with respect to both power-stage parameter variations and external disturbances and can be implemented by means of conventional electronic circuitry. Simulations and experimental results for both reactive and nonlinear loads are presented.

Analysis of a bidirectional coupled-inductor Cuk converter operating in sliding mode

Analytic models for a bidirectional coupled-inductor Cuk converter operating in sliding mode are described. Using a linear combination of the converter four state variable errors as a general switching surface, the expression for the equivalent control is derived and the coordinates of the equilibrium point are obtained. Particular cases of the general switching surface are subsequently analyzed in detail: (1) surfaces for ideal line regulation, (2) surfaces for ideal load regulation, and (3) surfaces for hysteretic current control. Simulation results verifying the analytical predictions are presented.

Stabilization of periodic orbits of the buck converter by time‐delayed feedback

Time-delay autosynchronization (TDAS) can be used to stabilize unstable periodic orbits in dynamic systems. The technique involves continuous feedback of signals delayed by the orbits period so that the feedback signal vanishes on the target orbit and hence the latter is a solution of the original dynamic system. Furthermore, this control method only requires the knowledge of the period of the unstable orbit. The feedback gain needed to achieve stabilization varies with the bifurcation parameter(s) of the system, resulting in a domain of control, the computation of which requires, in general, detailed information about the target orbit(s). In this paper we compute the domain of control of the unstable periodic orbits of the PWM controlled buck converter for a couple of TDAS schemes. For both schemes we get an analytical expression for the closed curve whose index determines the stability, and this index is then numerically computed. We run several simulations of the controlled systems and discuss the results. The main result is that TDAS greatly increases the range of values of the input voltage where the PWM control yields a periodic orbit with a small rippling. Copyright

SECONDARY BIFURCATIONS AND HIGH PERIODIC ORBITS IN VOLTAGE CONTROLLED BUCK CONVERTER

Period doubling route to chaos has been shown to occur in the voltage controlled DC/DC buck converter, both experimentally and numerically. A chaotic attractor was found at the end of the sequence, suddenly followed by an increase of its size. In this paper new secondary bifurcations and high periodic phenomena, coexisting with the main sequence are detected and analyzed over the same range of parameters. A(synchronous)-switching and stroboscopic maps, unstable orbits, bifurcation diagrams, invariant manifolds and basins of attraction are outlined. These tools are put together to reveal the dynamical richness of this nonsmooth system.

Application of sliding mode control to the design of a buck-based sinusoidal generator

This work is devoted to the design of a sliding feedback control scheme for a buck-based AC generator where amplitude, frequency and offset can be externally adjusted. A sliding control law over an autonomous switching surface is proposed. As a result, the control scheme is found to be robust with respect to parameters variations and external disturbances. Simulation and experimental results validating the design are also presented.

TRANSITION FROM PERIODICITY TO CHAOS IN A PWM-CONTROLLED BUCK CONVERTER WITH ZAD STRATEGY

The transition from periodicity to chaos in a DC-DC Buck power converter is studied in this paper. The converter is controlled through a direct Pulse Width Modulation (PWM) in order to regulate the error dynamics at zero. Results show robustness with low output error and a fixed switching frequency. Furthermore, some rich dynamics appear as the constant associated with the first-order error dynamics decreases. Finally, a transition from periodicity to chaos is observed. This paper describes this transition and the bifurcations in the converter. Chaos appears in the system with a stretching and folding mechanism. It can be observed in the one-dimensional Poincare map of the inductor current. This Poincare map converges to a tent map with the variation of the system parameter ks.