A switched-inductor (SL) multi-cell boost converter is analyzed in this paper for a high-voltage gain application, stepping up a dc voltage from 36 V to 380 V in the first stage of a photovoltaic (PV) conversion chain. A fast maximum power point tracker (MPPT), processing the system input voltage, is used to extract the maximum power from the PV generator regardless of atmospheric conditions. A single sliding-mode control (SMC) loop forces the PV generator voltage to follow the maximum power point (MPP) voltage provided by a Perturb and Observe (P&O) algorithm. The sliding-mode analysis uses the equivalent control approach to demonstrate that the linearized ideal sliding dynamics are unconditionally stable. Theoretical predictions are corroborated by simulations and experimental measurements of the system under step-type changes in input irradiance and output load. The MPPT performance is experimentally evaluated against two classical approaches applied to a canonical boost converter: a current-based SMC and a voltage-based PWM. Both approaches track the MPP current and voltage, respectively, as given by the P&O algorithm. The proposed system outperforms the two classical systems, showing a better tracking accuracy.

Over the decades, bifurcation theory has emerged as a significant area of research, providing deep insights into the complex dynamics of systems across multiple disciplines. Moreover, it serves as a foundation for devising effective control methodologies aimed at avoiding or delaying undesirable dynamical transitions. This paper deals with both local and global dynamics of a bidirectional dc-dc boost converter supplying a constant power load (CPL) with a stabilizing resistor inserted in series with the main inductor. Numerical simulations performed on the averaged model of the system show interesting bifurcation phenomena explaining its local and global dynamical behavior. In particular, it is shown that in some parametric region, the system has two coexisting equilibria, one of them being a saddle and the other one an anti-saddle. The latter can be stable or unstable. An unstable limit cycle also coexists with the stable anti-saddle equilibrium. This limit cycle disappears through a homoclinic bifurcation. Moreover, a parameter space reduction is carried out by choosing suitable bifurcation parameters, and the normal form of the Bogdanov-Takens bifurcation is obtained hence mathematically demonstrating its existence. Finally, the analytical and simulation results on the switched model are partially validated by experimental measurements from a laboratory prototype.

This paper outlines a detailed design methodology for a digital multi-loop control strategy for an electric vehicle (EV) battery charger based on interleaved buck converters. The proposed control strategy implements the constant-power constant-voltage (CP-CV) protocol. Specifically, a first outer loop regulating the output voltage, enforces the CV phase, and a second outer loop controlling the battery power imposes the CP phase. An inner loop implements the democratic current sharing technique for the regulation of the inductor currents. Proportional-integral (PI) controllers are designed via the root locus method using a discrete-time model that considers parasitic resistances on the converter. A multi-rate sampling strategy is employed to follow conventional rules of cascade control systems ensuring that each control loop operates at the appropriate sampling frequency according to its dynamic characteristics. The entire proposal is validated through numerical simulations performed in PSIM© software.

This paper presents a comprehensive investigation into the analysis, design, and fixed frequency digital control of a three-phase four-wire (3P4W) ac-dc rectifier followed by a CLLC resonant converter, targeting 11 kW battery charging applications. First, the 3P4W front-end rectifier is characterized under steady-state and dynamic conditions, emphasizing on achieving a near-unity power factor, input-current harmonic mitigation, and neutral-point voltage stabilization in both bal¬anced and unbalanced loading scenarios. Second, the CLL- Cresonant converter is designed and analyzed to achieve zero-voltage and zero-current switching (ZVZCS) in both charging and discharging modes to minimize switching losses in wide load ranges. Fixed-frequency operation is maintained through phase-shift modulation for the constant-current/constant-voltage (CC-CV) charging protocol, ensuring robust performance despite wide variations in battery voltage and load current. Fixed-frequency control simplifies electro-magnetic interference (EMI) filtering and facilitates predictable timing. The simulation results show power factor exceeding 0.99 and a total harmonic distortion below 5%.

In this paper, a control strategy is proposed to implement the constant power (CP)-constant voltage (CV) charging protocol for the ultrafast charging of electric vehicles (EV). The battery charger consists in a four-phase interleaved buck converter, with a multiple-loop controller in cascade configuration. Each of the three loops has its dedicated proportional integral (PI) controller for the control of a specific variable of the system. Namely, i) an inner loop to control the inductor current of each leg, ensuring equal distribution of the current between the four phases, ii) a first outer loop regulating the output voltage and providing the reference of the inner loop, and iii) a most outer loop to regulate the battery power by modifying the reference of the voltage loop. The correct operation of the system is validated by means of numerical simulation performed using the switched model implemented in PSIM©software.

A constant power (CP)-constant voltage (CV) protocol for battery charging is implemented in a conventional boost converter with output filter (BOF) by imposing loss-free resistor (LFR) behavior during the CP phase. To compare on equal basis the performance of the new CP-CV technique with the classical constant current (CC)–CV protocol, the latter is also implemented in the same power stage. The CC phase in BOF is attained by imposing a G-gyrator of type II behavior to the converter. A versatile controller uses the same voltage regulation loop for both protocols during the CV phase and a slightly different loop for the CP and CC phases. The latter loop is based in both CP and CC phases on the sliding-mode control (SMC) of the input inductor current of BOF, which in steady-state is made proportional to the input voltage in the LFR case or to the output voltage in the gyrator implementation. To compensate for the slow variations of the battery voltage during the CC phase, a proportional-integral (PI) current regulator has been added in the gyrator realization. The comparison of the corresponding experimental results shows identical behavior in both approaches in the measured waveforms, component stress, efficiency and external temperature. The simplicity of the CP-CV implementation based on LFR allows the extension of the proposed protocol to other hard-switching converters.

This paper presents the detailed design of an active damping system for the stabilization of an open-loop boost converter in constant-power load (CPL) operation. The reported work analyzes the steady-state regime of the interconnection of a boost converter supplying a CPL, and a loss-free resistor (LFR) in series with the converter input port (SLFR) performing the active damping. The LFR behavior is obtained by peak current mode control (PCMC) imposing proportionality between the steady-state average values of current and voltage in the SLFR input port. The isolated SEPIC fulfills the topological constraints of the interconnection and is selected to implement the SLFR. Finally, PSIM simulations and measurements from a 500 W prototype are in good agreement with the theoretical predictions and illustrate the system stabilization around the specified steady-state operating point for different values of the CPL power.

Modern DC-DC power conversion represents an important challenge because connected loads are not purely resistive as it has been conventionally considered. Furthermore, the corresponding power converters perform functions which are not limited to regulate either a specific output voltage or output current. One of these new functions is the transfer of a regulated power to different types of loads, which emerge in the context of microgrids and electric vehicles, in which the sliding-mode control (SMC) is an important actor because of its versality, robustness and systematic design. This paper presents SMC of a boost converter operating as a loss-free resistor (LFR), which supplies a constant power to the parallel connection of three canonical elements, namely, a constant power load (CPL), a constant current load (CCL) and a dc voltage source with internal resistance. The studied load is defined as a generic nonlinear static load (GNSL). The subsequent analysis of the connection of the controlled power converter and the GNSL reveals the existence of a single equilibrium point, which is unconditionally stable. This feature is preserved when the GNSL is particularized in the single load cases of battery, current source or resistor, and in all cases of two-element and three-element load combinations. The exception is the supply of a single CPL, which results in an infinite number of equilibrium points with marginally stable behavior. Simulation and measurements in a 1 kW prototype are in perfect agreement with the theoretical predictions.

The unstable ON and OFF state trajectories of a boost converter supplying a constant power load (CPL) are appropriately combined using sliding-mode control (SMC) with a suitable surface to yield a stable trajectory that reaches a specified equilibrium point. Selecting the optimum surface involves a comparative analysis among potential candidates in terms of stability, disturbance rejection, conduction losses and inrush current. The performance as switching function of polynomials of degree zero (non-zero constant), degree one (affine function) and degree 2 (quadratic function) are analyzed in depth to conclude that the affine function leads to the best static and dynamic results. The theoretical predictions are verified by means of simulations and measurements in a prototype.

This paper deals with nonlinear control of a single-phase half-bridge interleaved buck shunt active power filter (HBIB-SAPF) with a nonlinear load. The control objective for the system is twofold: performing power factor correction by compensating for harmonics and reactive current consumed by the nonlinear load from one hand and tightly regulating the HBIB converter DC capacitor voltage. Both objectives are accomplished using a two-loop nonlinear controller. The inner loop acts on the switching devices so that the active filter current tracks its reference with the aim of ensuring a unity power factor. This loop is tackled using backstepping technique and Lyapunov approach. The outer loop is responsible for regulating the DC capacitor voltage to its desired value, using a PI controller with a pre-filter. The stability analysis of the closed-loop system is formally performed by using the averaging theory. The validity of the designed nonlinear controller is checked by simulations in Matlab/SimpowerSystem showing its robustness and accuracy under various operating conditions.

This paper presents a systematic approach to synthetize constant power loads using switching converters under sliding-mode control. The generation of sliding motions is analyzed in converters with a series inductor in the input port and a switching function representing the error between the input power and a suitable power reference. The analysis establishes the existence conditions for sliding-mode and the stability of the resulting ideal dynamics. Simulation and experimental results verifying the theoretical predictions in boost, Ćuk and SEPIC converters illustrate the proposal. The design procedure yields a simple, economical and small-size prototype that can be useful in the experimental validation of converters supplying constant power loads.

In this paper, the steady-state performances of a piecewise quadratic auto-tuned slope compensation technique proposed recently to eliminate subharmonic oscillations in dc-dc switching converters are evaluated. With this technique, a self-generated compensating signal is used resulting in a naturally full duty cycle stability domain by appropriately self-adapting the amplitude of the generated signal both in transient and in steady-state regimes. The circuit corresponding to the proposed technique can be implemented using standard analog devices. A boost converter under current mode control is used to validate the theoretical results both by numerical simulations and by experiments showing that the technique efficiently eliminate subharmonic oscillation and is robust against parameter variations such as load current and inductor value.

Switched inductor (SL) step-up dc-dc converters can be used for high voltage gain applications such as in PV systems. In this paper, a study of a N-cell high voltage gain boost dc-dc converter performing maximum power point tracking from a PV source is presented. First, the time domain dynamic model is derived. Then, the linearized s- domain model is first obtained. It is obtained that contrarily to the conventional canonical boost converter, the N-cell switched inductor converter presents a stable zero in the duty-cycle-to-PV-voltage transfer function which can be considered as an advantage to design a fast voltage-based MPPT control having the same response speed that corresponds to current mode control. Using the resulting control-to-output transfer function, a fast voltage-based MPPT controller is designed. Finally, numerical simulation are used to evaluate the performances of the converter when used in PV applications under different weather conditions.

An implicit first-order non-dimensional model of open loop dc-dc boost converter operating in Discontinuous Conduction Mode (DCM) with Constant Power Load (CPL) is derived. Analysis of this model shows that successive period doubling bifurcations and subharmonic oscillation take place when certain parameters such as the switching period, the operating duty cycle and the load power are varied. The resulting typical period-doubling route to chaos is confirmed by numerical simulations under the mentioned operating conditions.

Switching converters may exhibit unsuitable inrush current and an unacceptable transient response during startup. This phenomenon is mainly due to saturation of the duty cycle at the initial switching cycle and is more pronounced with nonlinear loads and reactive components and in the presence of unavoidable delays in the feedback. This paper proposes solutions to mitigate such problems in a digitally sliding-mode controlled dc-dc boost converter loaded with a constant power load and taking into account nonlinearities in the inductor. Numerical simulations from a detailed switched model validate the proposed approach and experimental measurements verify the mathematical analysis and the numerical simulation showing a good agreement.

In this paper, a study of the nonlinear dynamics of a boost converter performing maximum power point tracking from a PV source and charging a battery is presented. Numerical simulations shows that the system can exhibit subharmonic oscillations under the variation of suitable parameters such as those related to weather conditions (irradiance) and those related to the controller and the pulse width modulator. A state space switched model was developed for simulating the dynamic behavior and validating the desired working regime of the system in terms of the different parameters taking into account the nonlinearity of the PV source and the inductor. Analog-mixed-signal circuit simulation performed by the MATLAB-PAN (MP) simulation environment is used to explore the dynamical behavior that the system can exhibit. Stability boundaries are determined revealing the effect of the parameters on the system behavior by doing harmonic analysis of the circuit through simulations.

In this paper, a polytopic control approach is applied to a PV-fed single-ended primary-inductance (SEPIC) dc-dc converter. In a clear-cut-contrast with conventional control techniques based on averaging procedures, the polytopic control approach is applied to the switched model of the system. In particular, the switching control signal is synthesized using a Lyapunov function which has polytopic level sets. The validity of the approach is illustrated and verified using numerical simulations showing that the controller can achieve good performance in terms of fast recovery due to input voltage variations.

In this paper, analytical and numerical tools are combined to explore the dynamics of a quadratic boost converter supplied with a PV source and interlinked to a grid-tied dc-ac inverter with the aim to determine its subharmonic instability boundary in terms of different system parameters. First, numerical simulations from the detailed switched model of the system shows that it can exhibit subharmonic instability at relatively high irradiance levels. A simplified dynamical model is derived mathematically by taking into account the power stage, the controller, the PV generator working at the maximum power point. Using the simplified model of the system and a closed-form expression for predicting subharmonic oscillations, the stability boundaries are located in terms of weather conditions as well as circuit parameters, hence, obtaining the system safe operation domain. The dependence of the inductance values on the operating current, determined from a linear regression analysis and a least square algorithm applied to experimental data, is also taken into account in the analysis.

In this paper, a systematic approach is presented to synthesize constant power loads using switching converters under sliding mode control. The study shows that switching converters with a series inductor at the input port may behave as an instantaneous constant power load under sliding-mode control based on a nonlinear switching surface representing the error between the input power of the converter and a suitable power reference. With the proposed approach, the synthesis and design of constant power loads is simple. The synthesized loads can offer an inexpensive alternative to analyze switching converters feeding constant power loads such as in dc distributed power systems and electric vehicles. The theoretical derivations are validated by numerical simulations performed on the detailed switched model of boost, SEPIC and Cuk converters.

In this paper a novel modulation technique is proposed to eliminate instabilities such as subharmonic and chaotic oscillations in dc-dc switching converters. This modulation technique injects a stabilizing signal which is generated internally from its own state variables so that the system is free from the problems due to externally injected signal, such as frequency mismatch, phase shift, etc. Stability analysis of the system is carried out using Floquet theory taking into account its switching nature. Our results show that the system has larger stable region in the parameter space compared to the conventional modulation techniques. Numerical simulations illustrate the performance of the proposed technique under line and load disturbances.

This paper deals with the global dynamical analysis of a self-oscillating resonant inverter which is based on switching between two symmetrical circuit configurations. The analysis predicts coexisting steady-state solutions, which are increasingly relevant for low values of the quality factor of the resonant circuit, thus likely driving to an improper system operation. A repelling sliding region is found to be connected with the two unstable limit cycles that split the phase plane in three basins of attraction. To avoid the presence of multiple steady-state solutions, a viable solution consisting of a modification of the control is proposed and validated by numerical simulations.

Power electronic systems exhibit different types of fast- and slow-scale instabilities which limit the stable operating range of the parameters. It has been shown that the stability of complex power electronic systems can be fruitfully investigated using the Filippov method, where the stability of the system is given by the eigenvalues of the monodromy matrix, which is a combination of the state transition matrices through each subsystem and those across the switching events, called saltation matrix. In this paper we show that the components of the saltation matrix can be used to change the stability status of the system, and propose three specific techniques, which can be used individually or together to extend the range of stability significantly. The performance of these techniques are shown using line and load disturbances.

A combination of two switching surfaces for the sliding-mode control of a boost converter feeding a constant power load is presented. It allows the converter start-up with small inrush current and permits the output voltage regulation by minimizing the effect of external perturbations on the steady-state operation. The resulting sliding-regime for each switching surface is analyzed and the conditions for the existence of sliding-mode are derived. PSIM simulations are in perfect agreement with the theoretical predictions.

This paper investigates the effect of the integrator gain on subharmonic oscillation boundary in switching converters with fixed frequency pulse width modulation (PWM) with an integrative feedback loop. First, the exact state-space switched model of the converter is revisited and then a closed-form expression for predicting this phenomenon is presented. The use of this expression is illustrated by means of two different examples f switching converters. While in voltage mode control, the integral action can be ignored for predicting subharmonic oscillation, it is shown the integral action in the current loop has a significant effect on this phenomenon.

The dynamic behavior and stability analysis of a quadratic boost converter for high conversion ratio applications is addressed. After studying the stability of the system by using the monodromy matrix, a closed form stability condition is used for predicting the boundary of subharmonic oscillation in the system in terms of the duty cycle and the slope of the ramp modulator. The derived theoretical conditions are validated by numerical simulations using a system-level switched model obtaining a good matching between the results. This work provides a convenient means of stability boundary determination in the parameter space hence facilitating the design of quadratic boost converters.

In this paper a stability condition is obtained for predicting the boundary of subharmonic oscillation in dc-ac H-bridge inverters under double edge modulation. This condition is analytically derived and expressed in terms of the system state-space model matrices. The availability of such analytical expression reveals the effect of all the parameters of the inverter on its dynamical behavior. The derived theoretical condition is validated by numerical simulations using a system-level switched model obtaining a good matching between the results. This work provides a convenient means of predicting subharmonic oscillation boundary in the parameter space hence facilitating the design of dc-ac inverters free from this kind of instability.

Coupled magnetic resonance is considered to be a key enabling technology for mid-range wireless power transfer. Models and systems have hitherto considered linear resonators as underlying dynamics, thereby limiting practical deployability due to the extreme sensitivity in front of parameter mismatch and resonance detuning. In this work, structural nonlinear modeling of constituent elements of the resonant link-resonant coils- is considered to unveil the existence of nonlinear dynamic regimes. The methodology considered to explore the nonlinear behavior is based on a behavioral model consisting of state equations, Floquet theory and Filippov method to study the stability of the periodic regime through the associated monodromy matrix. The ultimate aim of the investigation is a design-oriented parameter space exploration which characterizes the border of occurrence of the different dynamic modes in wireless power transfer links.

This paper discusses the influences of non-ideal current sensor on the stability and subharmonic oscillation boundaries in current mode controlled switching converters. First, a general-purpose simplified model is built applicable to any switching converter working in continuous conduction mode. Then, a steady-state asymptotic Fourier-series-based method is applied to obtain a boundary condition in the frequency domain and expressed in terms of the system state-space matrices. Using the Poisson sum formulae, this condition is transformed into the time-domain. The approach is applied to dc-dc switching converters with current mode control (CMC) taking into account finite current sensor bandwidth. Design-oriented equations describing the occurrence of subharmonic oscillations are derived for any single-switch dc-dc converter. These equations are expressed explicitly in terms of operating converter parameters and duty cycle making them directly applicable for design purposes. Some problems with influence of the limited bandwitdh of the current sensor on the ramp compensator design and system dynamics are discussed, along with some proposed solutions.

The significant improvements that have been recently achieved in HBLEDs technology in terms of lifetime, luminous efficacy, and power rating, make these devices one the most promising candidates to replace conventional light sources in various residential and industrial applications, despite their high cost. The efficiency requirement should be completed by means of the voltage conversion stage by performing Power Factor Corrector. In this paper we consider the problem of Power Factor Corrector and output current regulation for a group of HBLEDs by using a Ćuk converter under a Sliding-Mode Control which must be ultimately implemented by a hysteretic comparator to limit the switching frequency to practical values. However, with a constant hysteresis width, the system exhibits harmful harmonic distortion in the input line current waveform. Therefore, a variable hysteresis window is used thereby avoiding this distortion near the zero crossing of the input current. Using the Ćuk converter under a Sliding-Mode Control with variable hysteresis window, the converter will be forced to behave as a Loss Free Resistor. Simulation and experimental results are presented in this paper to demonstrate the functionality of the proposed technique.

In this paper, a system consisting of two cascaded dc-dc boost converters under sliding-mode control, working as loss free resistors, connected to a PV panel 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 and stability analysis is carried out. It is shown that the cascade connection of boost-based loss free resistors can be a good solution for the impedance matching in PV systems with the standard 380 V dc bus voltage.

Nonlinearities have been shown to play an important role in increasing the extracted energy of energy harvesting devices at the macro and micro scales. Vibration-based energy harvesting on the nano scale has also received attention. In this paper, we characterize the nonlinear dynamical behavior of a strained nanostructured graphene for its potential use in energy harvesting applications. A compressed vibrating membrane graphene sheet free from any external excitation is first studied. We present a continuous time dynamical model of the system in the form of a double-well single degree of freedom system. Equilibrium points are obtained and their stability analysis is carried out. Then, random vibrations are considered as the main ambient energy source for the system and its performances in terms of the well occupation zones, RMS value of the position, and the corresponding energy harvested are presented in the steady state non-equilibrium regime when the noise level is considered as a control parameter. From this model, nonlinear analysis is carried out by computing state space trajectories, probability density and FFT spectra under a deterministic excitation. The ultimate goal of this parameter space exploration based upon a behavioral model is to provide design-oriented guidelines for engineering graphene-based mechanical harvesters.

Microgrids consist of distributed electrical generation architectures which have some instability problems due to the cascade interconnection of the converters and their related negative impedance effect. In electric power distribution system, a point of load converter behaves as constant power load (CPL) which result in a well known destabilizing effect. In this paper, different strategies that have been used to eliminate this undesirable behavior will be discussed. Then, an alternative approach based on sliding mode control (SMC) and using canonical elements for power processing will be proposed to stabilize cascaded converters. The proposed approach will be illustrated using a system consisting of two cascaded boost converters behaving as Loss Free Resistors (LFR) supplied from a PV panel and connected to a 380 V dc bus of a microgrid. It will be shown that using LFRs and SMC could be a good strategy to stabilize cascaded boost converters. The theoretical results are verified using simulations and experimental measurements.

In this paper a closed-form stability condition is obtained for predicting the boundary of fast-scale instability in a buck switching power converter. This design-oriented condition is obtained from the discrete-time model and it is validated by means of numerical simulation under different cases, including only the voltage-mode loop, current-mode along with voltage-mode loop open or closed, or adding an external compensating ramp. The availability of such design-oriented expression allows to understand the effect of the different parameters of the regulator upon the stability boundary along with facilitating the design and synthesis of new controllers to avoid these instabilities.

In this paper a SEPIC converter, operating as an AC-DC adaptation stage, is studied. It is shown that the system has high efficiency and good power factor being able to work both as a boost (step-up) or buck (step-down) converter. To impose a loss free resistor (LFR) behavior, sliding-mode control is applied. It is shown that the LFR acts as an ideal rectifier with a power factor near the unity. The output of the system is used to power supply a group of HBLEDs, and its brightness (luminosity) is controlled by the output current. The design and the models are validated by mathematical, numerical and experimental results.

Discrete-time modeling approach is used to analyze the non-smooth bifurcation phenomena in a single-inductor two- output DC-DC converter under interleaved control scheme. In particular, a four-piece linear map is derived, which models the dynamical behavior of the converter when the waveforms of the inductor current are assumed to be linear during each switching sub-interval. The domain of the parameters is constrained by the interleaving control and the physical parameters. This paper focuses on the existence and stability conditions of the rich variety of k-periodic orbits and the different bifurcation patterns that can be exhibited. The analytical results in the form of 2-D bifurcation diagrams are compared with numerical simulations obtained from the circuit-based switched model getting a good agreement between the two approaches.

The synthesis of a boost-converter-based loss-free resistor (LFR) operating in PWM is presented. The resulting LFR can be used as a preregulator for power factor correction in one-phase circuits. PSIM simulations are in good agreement with the theoretical predictions.

The purpose of this paper is the synthesis from the frequency domain standpoint of a controller for switching power converters with the aim to eliminate bifurcation and chaotic behavior. Firstly the paper analyzes the frequency response of previous delay-based chaos controllers unveiling that they are based in comb-filtering at multiples of the sub-harmonic half of the switching frequency. Secondly, chaos control is explored by using both a single notch filter and a bandstop filter at half of the switching frequency. It is demonstrated that the latter achieves chaos rejection while being an implementation-aware simplification of delay-based methods.

In this paper a simplified model based on the exact discrete-time map of a buck switching power converter with proportional control, which captures all its dynamics, allows deriving a closed-form stability condition for predicting fast-scale instability boundary. This condition analytically demonstrates the validity of the recently proposed ripple-based index to predict fast-scale period-doubling, hitherto based on an a priori hypothesis and simulation validation, thereby demonstrating the use of the ripple index as a design-oriented tool. The equivalence of the ripple index to the condition derived from the discrete-time map endorses its use as a means to characterize the complete design space against fast-scale instabilities.

This paper provides a first exploration of fast-scale stability borders for switching power converters operating as wideband switching amplifiers. Such operation is required in audio amplifiers, envelope trackers in polar RF transmitters and line drivers for Power Line Communications. A buck converter with output voltage proportional feedback in a signal tracking configuration with a sinusoidal reference is considered (Figure 1). The work first characterizes the effect of the classical set of parameters used in regulation stability analysis (output resistance, reactive components, switching frequency, feedback gain), and considers the output voltage to cover the complete dynamic range and hence disappear as a variable in the parametric space. Complementarily, the effect of the ratio of the tracking or baseband frequency to the switching frequency is added as a new variable in the design space indicative of wideband tracking operation. Characterization tools encompass families of time domain simulations as dynamic bifurcation diagrams for the time-varying reference. The paper concludes by exploring the effect of momentarily losing fast-scale stability upon the output signal spectrum, since applications such as adaptive supply of RF power amplifier are subject to strict spectral masks.

This paper extends the validity of a ripple-based index able to predict the frontier of fast-scale instability bifurcation in switching power converters, for the whole design-space and for different conduction modes. Hitherto a first validation of the index, based on the approximated ripple level in the PWM modulator, was carried out for a basic proportional voltage feedback PWM buck converter and for L, C, fs, Kpparameters. This article has carried out a complete design-space analysis and has found the stability boundary dependence on converter parameters. Besides, the circuit-based approach has been validated through a comparison between the proposed index and the classical analytical methods based in the linearization of the discrete-time nonlinear map. The paper also proposes improved ripple approximations, by obtaining the exact analytic ripple expression for a buck converter derived from Laplace transform. The index is also validated for a buck converter operating in DCM, through time domain simulations and bifurcation diagrams.

This paper presents a re-examination of conditions for lost of period-1 bifurcation appearance in switching power converters. A unified index based on the ripple level in the PWM modulator is able to predict first occurrence of fast-scale instability. Previous parametric design space explorations have been presented to explore the rich complex behaviour phenomena in switching power converters. The bifurcation-avoiding design-oriented index presented herein allows the designer to collect in a unified index the effect of several circuit parameters, such as input and output voltage, reactive component values and switching frequency, together with feedback parameters. The approach is validated through time domain simulations and bifurcation diagrams for a basic proportional voltage feedback PWM buck converter. Alternative topologies such as multilevel converters and interleaved parallel-connected converters, as well as more practical control methods such as dynamic compensators, current-mode control, and hysteretic control are discussed as well. Proof-of-concept experimental results are reported to demonstrate the approach

The main drawback of the discrete time models reported in the literature for predicting nonlinear phenomena in power electronic circuits is their complexity which make their use in system design very minted. The availability of approximated discrete time models that retain the accuracy of the exact model and at the same time makes the system design simple would give new perspectives in the control design of such systems. In this paper we give a detailed analytical study of a two-cell DC-DC buck converter for high voltage applications by using discrete time formulation. Different operating modes are possible and they can be modeled by a unified discrete time model. A digital controller is considered for the system. This controller includes a dynamic compensator in the form of digital integrator for the output variable regulation. An approximated discrete time model in the form of current recurrence equation which accurately describes the dynamical behavior of the system is derived. This model is use to predict instabilities when some design parameters are varied. The Jury test is applied to the characteristic polynomial in order to obtain boundary of stability in the design parameter space. Numerical simulations confirm the theoretical predictions

This paper describes a design method for robust control of dc-dc switched converters using quantitative feedback theory (QFT). The chief advantage of this approach is that the method takes into account plant uncertainties from a frequency point of view in a systematic way. This clarifies how the design can fulfil the requirements, simplifying the designer's task