Transfer function modeling and analysis of the open-loop Buck converter using the fractional calculus

Based on the fact that the real inductor and the real capacitor are fractional order in nature and the fractional calculus,the transfer function modeling and analysis of the open-loop Buck converter in a continuous conduction mode（CCM） operation are carried out in this paper.The fractional order small signal model and the corresponding equivalent circuit of the open-loop Buck converter in a CCM operation are presented.The transfer functions from the input voltage to the output voltage,from the input voltage to the inductor current,from the duty cycle to the output voltage,from the duty cycle to the inductor current,and the output impedance of the open-loop Buck converter in CCM operation are derived,and their bode diagrams and step responses are calculated,respectively.It is found that all the derived fractional order transfer functions of the system are influenced by the fractional orders of the inductor and the capacitor.Finally,the realization of the fractional order inductor and the fractional order capacitor is designed,and the corresponding PSIM circuit simulation results of the open-loop Buck converter in CCM operation are given to confirm the correctness of the derivations and the theoretical analysis.

Dynamical analysis and experimental verification of valley current controlled buck converter

The dynamical behaviours of valley current controlled buck converter are studied by establishing its corresponding discrete iterative map model in this paper. Time-domain waveforms and phase portraits of valley current controlled buck converter are obtained by Runge-Kutta algorithm through a piecewise smooth switching model. The research results indicate that the valley current controlled buck converter exhibits rich nonlinear phenomena, and it has routes to chaos through period-doubling bifurcation and border-collision bifurcation in a wide parameter range. Interesting inverse nonlinear behaviours compared with peak current controlled buck converter are observed in the valley current controlled buck converter. Analysis and simulation results are verified by experimental results.

Dynamics and stabilization of peak current-mode controlled buck converter with constant current load

The discrete iterative map model of peak current-mode controlled buck converter with constant current load（CCL）,containing the output voltage feedback and ramp compensation, is established in this paper. Based on this model the complex dynamics of this converter is investigated by analyzing bifurcation diagrams and the Lyapunov exponent spectrum. The effects of ramp compensation and output voltage feedback on the stability of the converter are investigated. Experimental results verify the simulation and theoretical analysis. The stability boundary and chaos boundary are obtained under the theoretical conditions of period-doubling bifurcation and border collision. It is found that there are four operation regions in the peak current-mode controlled buck converter with CCL due to period-doubling bifurcation and border-collision bifurcation. Research results indicate that ramp compensation can extend the stable operation range and transfer the operating mode, and output voltage feedback can eventually eliminate the coexisting fast-slow scale instability.

Pole placement method of controlling chaos in DC-DC buck converters

Based on the mechanism for the generation of chaos in a buck converter, a pole placement method is proposed and applied to controlling the chaos in a circuit. The control circuit is designed and tested. Numerical calculation and circuit implementation demonstrate the validity of this chaos control method.

Design of Second Order Sliding Mode and Sliding Mode Algorithms:A Practical Insight to DC-DC Buck Converter

This paper presents a simple and systematic approach to design second order sliding mode controller for buck converters.The second order sliding mode control(SOSMC)based on twisting algorithm has been implemented to control buck switch mode converter.The idea behind this strategy is to suppress chattering and maintain robustness and finite time convergence properties of the output voltage error to the equilibrium point under the load variations and parametric uncertainties.In addition,the influence of the twisting algorithm on the performance of closed-loop system is investigated and compared with other algorithms of first order sliding mode control such as adaptive sliding mode control(ASMC),nonsingular terminal sliding mode control(NTSMC).In comparative evaluation,the transient response of the output voltage with the step change in the load and the start-up response of the output voltage with the step change in the input voltage of buck converter were compared.Experimental results were obtained from a hardware setup constructed in laboratory.Finally,for all of the surveyed control methods,the theoretical considerations,numerical simulations,and experimental measurements from a laboratory prototype are compared for different operating points.It is shown that the proposed twisting method presents an improvement in steady state error and settling time of output voltage during load changes.

Study of Sliding Mode Control of DC-DC Buck Converter

In this paper, a robust sliding mode controller for the control of dc-dc buck converter is designed and analyzed. Dynamic equations describing the buck converter are derived and sliding mode controller is designed. A two-loop control is employed for a buck converter. The robustness of the sliding mode controlled buck converter system is tested for step load changes and input voltage variations. The theoretical predictions are validated by means of simulations. Matlab/Simulink is used for the simulations. The simulation results are presented. The buck converter is tested with operating point changes and parameter uncertainties. Fast dynamic response of the output voltage and robustness to load and input voltage variations are obtained.

A high performance adaptive on-time controlled valley-current-mode DC–DC buck converter

This paper presents an AOT-controlled(adaptive-on-time,AOT)valley-current-mode buck converter for portable application.The buck converter with synchronous rectifier not only uses valley-current-mode control but also possesses hybridmode control functions at the same time.Due to the presence of the zero-current detection circuit,the converter can switch freely between the two operating modes without the need for an external mode selection circuit,which further reduces the design difficulty and chip area.The converter for the application of high power efficiency and wide current range is used to generate the voltage of 0.6–3.0 V with a battery source of 3.3–5.0 V,while the load current range is 0.05–2 A.The circuit can work in continuous conduction mode with constant frequency in high load current range.In addition,a stable output voltage can be obtained with small voltage ripple.In pace with the load current decreases to a critical value,the converter transforms into the discontinuous conduction mode smoothly.As the switching period increases,the switching loss decreases,which can significantly improve the conversion efficiency.The proposed AOT controlled valley current mode buck converter is integrated with standard 0.18μm process and the simulation results show that the converter provides well-loaded regulations with power efficiency over 95%.When the circuit switches between the two conduction modes drastically,the response time can be controlled within 30μs.The undershoot voltage is controlled within 25 mV under a large current hopping range.

Effects of electron radiation on commercial power MOSFET with buck converter application

Microelectronic power converters such as buck and boost converter are required to be tolerant to radiations including electron radiation. This paper examines electron radiation effects on the Ⅰ-Ⅴ characteristics of VDMOSFET and its corresponding effects in buck converter. Analysis of the electrical characteristics shows that after irradiation the threshold voltage and drain current for all VDMOSFETs degraded more than two orders of magnitude. The impact of this electrical degradation has been investigated in an application of typical buck converter circuit. The buck converter with n-channel switching transistor shows that after irradiation its output voltage increased with the drain current in the n-channel ZVN4424 A VDMOSFET, while the buck converter with p-channel switching transistor shows its output voltage decreased with the drain current in the p-channel ZVP4424 A VDMOSFET after irradiation.

Notch filter feedback controlled chaos in buck converter

A method of controlling chaos in the voltage-mode buck converter is presented by using an improved notch filter feedback control in this paper. The proposed control part comprises a notch filter and a low-pass filter. The discrepancy between the outputs of the two filters is introduced into the control prototype of the power converter. In this way, the system period-1 solution is kept unchanged. The harmonic balance method is applied to analysing the variation law of the system bifurcation point, and then the stable range of the feedback gain is ascertained. The results of simulation and experiment are also given finally.

Equivalent-resistance based on the analysis of inductor-disconnected discharge behavior for intrinsic safety Buck converters

An Equivalent-Resistance based Analysis Method (ERAM) was proposed, which can convert the Inductor-Disconnected Discharge (IDD) behavior of the Intrinsically Safe Buck Converter (ISBC) into that of an Equivalent Simple-Inductive-Circuit (ESIC). According to the inductor disconnected equivalent circuit corresponding to the most dan- gerous operating case of the converter,the arc discharge time and the variation of out- put-voltage during the IDD were deduced based on the simple current linear attenuation model.According to the energy equivalence,the equivalent inductor-current of the ESIC was obtained.It is pointed out that although the inductor-current of the Buck converter is much lower than that of the published ignition curve,ignition still occurs and the ignition ability is strengthened with increase of the output capacitance.The proposed analyzing method is verified by the experiment results on IEC standard spark ignition apparatus.

Modeling and Dynamic Analysis of Fractional-Order Buck Converter in Continuous Conduction Mode

According to the fact that the actual inductor and actual capacitor are fractional, the mathematical and state-space averaging models of fractional order Buck converters in continuous conduction mode(CCM) are constructed by using fractional calculus theory. Firstly, the parameter conditions that ensure that the converter working in CCM is given and transfer functions are derived. Also, the inductor current and the output voltage are analyzed. Then the difference between the mathematical model and the circuit model are analyzed, and the effect of fractional order is studied by comparing the integer order with fractional order model. Finally, the dynamic behavior of the current-controlled Buck converter is investigated. Simulation experiments are achieved via the use of Matlab/Simulink. The experimental results verify the correctness of theoretical analysis, the order should be taken as a significant parameter. When the order is taken as a bifurcation parameter, the dynamic behavior of the converter will be affected and bifurcation points will be changed as order varies.

Mode shift and stability control of a current mode controlled buck-boost converter operating in discontinuous conduction mode with ramp compensation

By establishing the discrete iterative mapping model of a current mode controlled buck-boost converter, this paper studies the mechanism of mode shift and stability control of the buck-boost converter operating in discontinuous conduction mode with a ramp compensation current. With the bifurcation diagrazn, Lyapunov exponent spectrum, time- domain waveform and parameter space map, the performance of the buck-boost converter circuit utilizing a compensating ramp current has been analysed. The obtained results indicate that the system trajectory is weakly chaotic and strongly intermittent under discontinuous conduction mode. By using ramp compensation, the buck-boost converter can shift from discontinuous conduction mode to continuous conduction mode, and effectively operates in the stable period-one region.

Modular System of Cascaded Converters Based onModel Predictive Control

A modular system of cascaded converters based on model predictive control(MPC)is proposed to meet the application requirements ofmultiple voltage levels and electrical isolation in renewable energy generation systems.The system consists of a Buck/Boost+CLLLC cascaded converter as a submodule,which is combined in series and parallel on the input and output sides to achieve direct-current(DC)voltage transformation,bidirectional energy flow,and electrical isolation.The CLLLC converter operates in DC transformer mode in the submodule,while the Buck/Boost converter participates in voltage regulation.This article establishes a suitable mathematical model for the proposed system topology,and uses MPC to control the system based on this mathematical model.Module parameters are designed and calculated,and simulation is built in MATLAB/Simulink to complete the simulation comparison experiment between MPC and traditional proportional integral(PI)control.Finally,a physical experimental platform is built to complete the physical comparison experiment.The simulation and physical experimental results prove that the control accuracy and response speed ofMPC are better than traditional PI control strategy.

An Analysis of Buck Converter Efficiency in PWM/PFM Mode with Simulink

This technical paper takes a study into efficiency comparison between PWM and PFM control modes in DC-DC buck converters. Matlab Simulink Models are built to facilitate the analysis of various effects on power loss and converting efficiency, including different load conditions, gate switching frequency, setting of voltage and current thresholds, etc. From efficiency vs. load graph, a best switching frequency is found to achieve a good efficiency throughout the wide load range. This simulation point is then compared to theoretical predictions, justifying the effectiveness of computer based simulation. Efficiencies at two different control modes are compared to verify the improvement of PFM scheme.

Modeling and dynamics analysis of the fractional-order Buck-Boost converter in continuous conduction mode

In this paper, the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode （CCM） are established based on the fractional calculus and the Adomian decomposition method. Some dynamical properties of the current-mode controlled fractional-order Buck- Boost converter are analysed. The simulation is accomplished by using SIMULINK. Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary. At the same time, the simulation results show that the converter goes through different routes to chaos.

Analysis of Discharge Spark Energy in Buck Converter of a Continuous Mode of Inductive Current

The basic idea of intrinsically safe circuit and the discharge spark in the Buck converter in the explosive at- mospheres were introduced. The Buck converter is the main topological structure of the switch type of intrinsically safe circuit, which has two working modes: continuous inductive current (CCM — continuous conduction mode) and dis- crete inductance current (DCM — discontinuous conduction mode). The operating state of the continuous inductive current mode is analyzed in detail and the energy of discharge spark in various operating modes is discussed. The total energy will decrease with the increase of switch frequency, in a switching cycle; the discharge spark energy has a maxi- mum and a minimum value. Therefore, the Buck converter has smaller discharge spark energy than the linear power circuit and the switch type of intrinsically safe circuit can enhance the output power and the conversion efficiency of the intrinsically safe power.

Sampled-data modeling and dynamical effect of output-capacitor time-constant for valley voltage-mode controlled buck-boost converter

By analyzing the output voltage ripple of a buck-boost converter with large equivalent series resistance（ESR） of output capacitor, one valley voltage-mode controller for buck-boost converter is proposed. Considering the fact that the increasing and decreasing slopes of the inductor current are assumed to be constant during each switching cycle, an especial sampleddata model of valley voltage-mode controlled buck-boost converter is established. Based on this model, the dynamical effect of an output-capacitor time-constant on the valley voltage-mode controlled buck-boost converter is revealed and analyzed via the bifurcation diagrams, the movements of eigenvalues, the Lyapunov exponent spectra, the boundary equations,and the operating-state regions. It is found that with gradual reduction of output-capacitor time-constant, the buck-boost converter in continuous conduction mode（CCM） shows the evolutive dynamic behavior from period-1 to period-2, period-4, period-8, chaos, and invalid state. The stability boundary and the invalidated boundary are derived theoretically by stability analysis, where the stable state of valley voltage-mode controlled buck-boost converter can enter into an unstable state, and the converter can shift from the operation region to a forbidden region. These results verified by time-domain waveforms and phase portraits of both simulation and experiment indicate that the sampled-data model is correct and the time constant of the output capacitor is a critical factor for valley voltage-mode controlled buck-boost converter, which has a significant effect on the dynamics as well as control stability.

Analysis of Output Characteristics of Buck Converter

This Article introduced the concept, topology and function of voltage type Buck converter, built a small signal model, analysis the negative impedance character of converter, then simulated a Buck-type DC/ DC through MATLAB, observed the dynamic response of converter to pulse-type power load, verified the small-signal theoretical by simulation, lay the foundation for analyzing DC system stability.

Analysis and Modeling of Buck Converter in Discontinuous-Output-Inductor-Current Mode Operation

The Buck converter with LC input filter operating in discontinuous output current mode has a high power factor with a constant duty cycle. A Buck converter in this operation mode can reduce the reverse recovery loss of the freewheeling diode thus increase the efficiency. The operation, power factor analysis and modeling of the converter are studied in this paper. Experimental results are presented to verify the theoretical predictions.