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Stability Analysis for Peak Current-Mode Controlled Buck LED Driver Based on Discrete-Time Modeling
Abstract
Considering that the state equations of peak current-mode (PCM) controlled buck light-emitting diode (LED) driver with proportion-integration (PI) compensator are third-order singular matrices with maximum rank 2, it is not invertible and may lead to non-convergent problem under certain circuit parameters. Therefore, an improved discrete-time modeling is performed by substituting state variables of power stage circuit for PI compensator equivalently in this paper. Based on this modeling, the stability of PCM controlled buck LED driver is investigated by analyzing bifurcation diagram and the maximum Lyapunov exponent spectrum, while the conduction-mode boundary and stability boundary are deduced which indicate the operation regions of the system intuitively, providing design guidelines for LED driver. Experimental results are further presented to verify the theoretical analysis.
... However, to achieve a high control bandwidth by designing feedback compensators, a highly accurate small-signal model is required to predict loop stability. Although some prior works such as discrete-time modeling methods [14]- [18] target stability issues, they generally deviate from the small-signal concept. Furthermore, some modeling methods [16]- [18] are stability-oriented and do not contain frequency-domain information for transient response behavior estimation. ...
... Although some prior works such as discrete-time modeling methods [14]- [18] target stability issues, they generally deviate from the small-signal concept. Furthermore, some modeling methods [16]- [18] are stability-oriented and do not contain frequency-domain information for transient response behavior estimation. Therefore, those methods are not as widely adopted in the industry by engineers as frequency-domain small-signal models do. ...
... where r 0 is the DC component, v c4 (t) has already been given in (12), and v c1 (t), v c2 (t), v c3 (t) can be expressed as (16) to (18) ...
High-bandwidth buck voltage regulator with peak current-mode control is a commonly-used scheme, especially for CPU power applications. However, the conventional single-frequency and three-frequency models are inaccurate in modeling the loop gain stability when the control bandwidth is close or higher than one-third of the converter switching frequency. A more accurate four-frequency small-signal model for a high-bandwidth buck converter with peak current-mode control is proposed in the present paper. The describing function approach is used to model the duty-cycle modulator. The effects of the four-frequency components, including the modulating frequency, the two sideband harmonics, and the switching frequency, are considered. Simulations and experiments verified the results.
... To solve the inaccuracy caused by the approximation used in [20], an accurate discrete-time model combined with the Floquet theory was proposed to analyze the subharmonic oscillation in a V 2 IC controlled buck converter with a Type-I compensator in [22]. In addition, an improved discrete-time model was proposed to investigate the stability of a peak-current-mode controlled buck LED driver in [23]. However, the design-oriented closed-loop stability criterion has not been found in [20]- [23], which makes it inconvenient to choose the circuit parameters of converters. ...
... In addition, an improved discrete-time model was proposed to investigate the stability of a peak-current-mode controlled buck LED driver in [23]. However, the design-oriented closed-loop stability criterion has not been found in [20]- [23], which makes it inconvenient to choose the circuit parameters of converters. ...
... i.e. (23) when (24) the CC controlled buck converter with a PI compensator is stable, otherwise it is unstable. It is necessary to note that the feedback gain g of the outer voltage loop as well as the capacitance C and ESR r of the output capacitor can affect the stability of the buck converter when the outer voltage loop is closed, which has not been previously considered [25]. ...
Due to the inherent feedforward of load current, capacitor current (CC) control shows a fast transient response that makes it suitable for the power supplies used in various portable electronic devices. However, considering the effect of the outer voltage loop, the stable range of the duty-cycle is significantly diminished in CC controlled buck converters. To investigate the stability effect of the outer voltage loop on buck converters, a CC controlled buck converter with a proportion-integral (PI) compensator is taken as an example, and its second-order discrete-time model is established. Based on this model, the instability caused by the duty-cycle is discussed with consideration of the outer voltage loop. Then the dynamical effects of the feedback gain of the PI compensator and the equivalent series resistance (ESR) of the output capacitor on the CC controlled buck converter with a PI compensator are studied. Furthermore, the design-oriented closed-loop stability criterion is derived. Finally, PSIM simulations and experimental results are supplied to verify the theoretical analyses.
... Peak current mode (PCM) control has been widely used in power electronic converters due to its accuracy, fast dynamic response and software flexibility [1,2]. Flying capacitor Buck converters [3], flyback converters [4] and Buck LED drivers [5] are some examples of this PCM control. In fullbridge DC-DC converter applications, PCM control has a simple structure and an inherent built-in overcurrent protection mechanism [6]. ...
... Subharmonic oscillation and instability are the two main problems of PCM control [5,24,25]. When V C /V D is close to 0.5, the angle between the rising curves of I L and I set is smaller than the angle between the falling curves of I L and I set . ...
Traditional local-averaged state-space modeling for peak current mode (PCM) controls fails to explain the subharmonic oscillation phenomenon when the spectrum is higher than half of the switching frequency. To address this problem, this paper presents a small-signal modeling method in the z-domain, and builds a discrete linear model for the current loop of a full-bridge DC-DC converter. This discrete model is converted into a second-order continuous model that is able to represent the system performance with a wider frequency range. A frequency-domain analysis shows that this model can be used to explain the subharmonic oscillations and unstable characteristics. This provides an engineering guideline for the practical design of slope compensation. The effectiveness of the proposed modeling method has been verified by simulation and experimental results with a prototype working in the Buck mode.
... For example, in the process of burning coal, a lot of dust will be produced, which has a great impact on the air. Although my country has taken various countermeasures to control the increasing area of acid rain to a certain extent, acid rain in some areas is still increasing, and problems such as automobile exhaust pollution are becoming more and more prominent, especially in metropolises [5]- [8]. Air pollution has gradually turned into a mixture of smoke and exhaust gas. ...
With the rapid progression of new energy resources technology and the increasing application of new energy resources, solar energy, fuel cell and other new energy resources power generation systems have higher requirements for the input voltage range of DC-DC converter. When the input voltage range of traditional DC-DC converter is wide, its duty cycle must be changed in a relatively large range to keep the output voltage stable, which leads to complex controller design and low system stability. The quadratic Boost converter can achieve high voltage gain with squared duty cycle using only a single switch. Thus, it has a wider input voltage range than the traditional switching Boost converter in the same duty cycle range and reduces the design difficulty of the control system. At the same time, the large range undulation of the output voltage of the new energy power generation system also puts forward higher demands for the load transient response speed of the circuit. Therefore, it is very important to study the control technology of quadratic Boost converter with fast load transient response.
... The step-up operation is widely known as the boost operation, and the step-down operation is widely known as the buck operation. These DC/DC converters are used in consumer electronics, electric transport [3]- [5], LED lighting [6], renewable energy systems [7], [8], electric aircraft [9], and many other applications. Again, the constant output voltage is preferable with variations in the input voltage, current, or load [10]- [11]. ...
This research compares the output voltage and harmonics of open-loop and closed-loop PID-controlled boost converters. Open-loop systems produce output based on their input voltage. The output voltage's THD & the capacitor's and inductor's input and output currents' THD don't change much with voltage. Using the same circuit and setting the reference voltage at half the open loop output voltage, the closed-loop system's output voltage remains almost constant for input voltages below the reference value. If the input voltage crosses the reference voltage, the output voltage jumps up somewhat. The closed-loop system is less effective than the open-loop system since the THD of the output voltage and the input and output currents of the inductor and capacitor are higher and vary more with voltage. Open loop output voltage THD was 375.06% and closed loop THD was 1742.84% for a 17-volt input.
... Switching power converters are widely used in different industrial applications such as in portable devices, solid-state lighting drivers and technologies [Leng et al., 2018], electric vehicles, aircraft and ships [Griffo & Wang, 2012;Rivetta et al., 2004;Rahimi & Emadi, 2009;Sulligoi et al., 2014], renewable energy production such as in PV systems [Kwasinski & Onwuchekwa, 2011;Al-Nussairi et al., 2017], among others. Apart from inductive and capacitive energy storage elements, elementary switching converters use two basic switching devices for their operation: a controlled switch (transistor S) and an uncontrolled one (diode D). ...
This paper presents a study of the existence conditions of limit cycles and mechanisms when losing their stability in an open-loop DC–DC boost converter loaded with a constant power load and operating in discontinuous conduction mode. First, the existence conditions are determined. Then, boundaries associated with different kinds of instabilities such as the classical smooth fold and period-doubling bifurcations and nonsmooth border-collision bifurcations such as fold border-collision bifurcations are elucidated. To perform the stability analysis, an implicit 1D map for the system is derived. From this model, it is obtained that smooth period-doubling and fold bifurcations may occur at certain values of the circuit parameters. Some results from numerical simulations performed on the circuit-based switched model are provided showing consistency with the theoretical analysis from the derived model.
... LED 负载特性为非线性指数函数且受温度影响，不便于控制设计，为此，大量学者对其近似模型进行了研究，主 4 要包括动态电阻模型 [31] 、DUR(Diode, Voltage and Resistance)串联模型 [32] 、多分支等效电路模型 [33] 、泰勒级数展开 模型 [34] 、状态空间平均模型 [35] 和热电模型 [36] 等。其中，由理想二极管、电压源和动态电阻构成的 DUR 模型，尽管在 低于 10mA 的非线性区域很难描述光源的真实特性，但能准确反应截止和导通段的伏安特性，且结构简单，已被成功 应用于 LED 驱动电源的设计 [37] 。 开关型 DC-DC 变换器常采用平均技术法 [38] 和离散时间法 [39] 建立其小信号模型。平均小信号模型能够准确描述变 换器的低频动态特性，已成功应用于模拟控制器设计，但对高频动态特性的描述非常不准确 [40] ，而且，应用于数字控 制器设计时，只能采用近似方法对环路延迟等进行补偿 [41] 。离散时间小信号模型能够精确描述 DC-DC 变换器的高频 动态特性 [39] ，但模型中包含大量的矩阵指数，导致计算推导非常复杂 [42] ，近年来，随着高频数字化的发展趋势，该建 模方法越来越受到人们的关注 [42] 。 对于 AC-DC LED 驱动控制系统，其闭环传递函数基于 LED 近似模型和 DC-DC 变换器的小信号模型，并充分考 虑采样、调制、延迟等因素进行建立 [43,44] 。对于某些特定应用，如纹波补偿控制等，还会建立纹波电流与控制量之间 的传递函数 [45] 。2018 年，冷敏瑞等人 [46] 则针对峰值电流模式控制的 Buck 型 LED 驱动电源，采用离散时间建模法建立 了系统的改进型三阶离散模型，该模型能有效而准确的描述系统的动态特性。 总之，由于 LED 光源和 DC-DC 变换器的非线性、时变和离散特性，建立能准确描述变换器动态特性、且易于控 制器设计的数学模型比较困难，但这又是高性能 LED 驱动电源设计的关键所在。 ...
随着 LED 照明领域的不断拓展和人们对健康光源的迫切需要，LED 光源的频闪问题备受关注。流经 LED 光源的纹波电流不但会引起频闪，还会对光度、比色性能和光效等造成不良影响。无电解电容 LED 驱动电源纹波补偿控制能有效兼顾长寿命和低纹波等性能指标的优化设计，从而为人们提供高效节能且更加健康的 LED 光源。通过归纳分析无电解电容 AC-DC LED 驱动电源的关键技术和纹波补偿控制策略，对大功率无电解化 LED 驱动电源合理化指标要求、拓扑结构、小信号模型、自适应数字电流预测控制、自适应纹波补偿控制和高频能量同步传输控制等进行了展望，并针对工程应用提出了相应的实现思路，以期助推绿色健康 LED 驱动电源的研究。
... For Buck LED driver controlled by peak current mode, Leng Minrui established an improved third-order DTM. And, the stability analysis shows that the model is an effective and accurate small-signal model [27]. ...
The high-power Asymmetric half-bridge Converter (AHBC) LED constant current driver controlled by digital current mode is a fourth-order system. Static operating point, parasitic resistance, load characteristics, sampling effect, modulation mode and loop delay will have great influence on its dynamic performance. In this paper, the small-signal pulse transfer function of the driver is established by the discrete-time modeling method for two operating points with three modulation modes of trailing-edge, leading-edge and double-edge. And, the effects of parasitic parameters, delay, sampling and load etc. are fully considered in modeling. For a large number of complex exponential matrix operations, the first order Taylor formula is used for approximate calculation after the coefficient matrix is obtained by substituting the data. Then, the designed average current mode compensators based on state-space averaging small-signal model(SSA) are used for analog and digital control, and the loop characteristics and control performance are analyzed. Simulation and experimental comparison results show that the proposed discrete-time model(DTM) can more accurately describe the characteristics of resonant peak, high-frequency dynamic and loop delay, and is very suitable for the design of high frequency digital controller.
... For Buck LED driver controlled by peak current mode, Leng Minrui established an improved third-order discrete-time model. And, The stability analysis shows that the model is an effective and accurate small-signal model [27]. ...
The high-power Asymmetric half-bridge Converter (AHBC) LED constant current driver controlled by digital current mode is a fourth-order system. Static operating point, parasitic resistance, load characteristics, sampling effect, modulation mode and loop delay will have great influence on its dynamic performance. In this paper, the small-signal pulse transfer function of the driver is established by the discrete-time modeling method for the two operating points corresponding to the three modulation modes of the trailing edge, leading edge and double edge. And, the effects of parasitic parameters, delay effect, sampling effect and load effect are fully considered in modeling. For a large number of complex exponential matrix operations, the first order Taylor formula is used for approximate calculation after the coefficient matrix is obtained by substituting the data. Then, Matlab software is used to compare and analyze the discrete-time model and the discrete-average model. The results show that the proposed discrete-time model can more accurately characterize the resonant peak and high-frequency dynamic characteristics, and is very suitable for the design of high frequency digital controller.
... Therefore, understanding these nonlinear phenomena, their analysis, prediction and control have increasingly become of great concern of many researchers all over the world [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The major part of the analytical results on subharmonic oscillation in power electronics converters has been achieved for DC-DC converters [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. DC-AC inverters are more difficult to deal with, since their dynamics is governed by two vastly different frequencies, namely the high switching frequency and the low frequency of the output voltage reference sinewave. ...
This paper focuses on the steady-behavior of a differential boost inverter used for generating a sinewave AC voltage in rural areas. The analysis of its dynamics will be performed using an accurate approach based on discrete time models and Floquet theory and adopting a quasi-static approximation. In particular, the undesired subharmonic oscillation exhibited by the inverter will be analyzed and its boundary in the parameter space will be predicted and delimited. Combining analytical expressions and computational procedures to determine the quasi-static duty cycle, subharmonic oscillation is accurately predicted. It is found that subharmonic oscillation takes place at critical values of the sinewave voltage reference cycle, which can cause distortion to the input current and degrade the harmonic content of the output voltage. The results provide useful information for the design of the boost inverter to avoid distortion caused by subharmonic oscillation. Namely, the minimum value of the compensation slope and the maximum proportional gain of the AC output voltage controller guaranteeing a pure sinewave voltage and clean inductor current during the entire AC cycle will be determined. Numerical simulations performed on the switched model implemented using PSIM© software confirm the theoretical predictions.
... In this paper, the value of k is chosen as 100 to achieve better dynamic performance of the controller. The equation (3) in z domain is obtained using trapezoidal method [14] ...
This paper proposes a novel control algorithm for a four-leg converter to compensate unbalanced non-linear loads in three-phase four-wire system. The detection and compensation for unbalanced non-linear load currents is implemented using double reduced order generalized integrators (DROGI) with proportional resonant (PR) controller. One integrator of DROGI is used to extract the reference compensation harmonics, and the second integrator is applied to decompose compensation currents and rectification currents at the converter side. The compensation currents are regulated by multi-PR controller, and the rectification currents are controlled by proportional controller. As a result, the compensation mode (DC-AC) and rectification mode (AC-DC) of converter are decoupled. More flexibility and selectivity in terms of control methods are achieved. The effectiveness of the control algorithm is verified by simulation and experiment. Keywords-Four-leg inverter, double reduced-order generalized integrator (DROGI), power quality, non-linear loading balancing, compensation.
... Direct-inductance-current control strategies have become very popular to improve dynamic performances of Buck and Boost converters [93,94]. Similarly, some peak, valley and even average current mode controls are proposed to improve dynamic responses of NSDAB dc-dc converter [86,95,96]. ...
The non-resonant single-phase dual-active-bridge (NSDAB) dc-dc converter has been increasingly adopted for isolated dc-dc power conversion systems. Over the past few years, significant research has been carried out to address the technical challenges associated with modulations and controls of NSDAB dc-dc converter. The aim of this paper is to review and compare these recent state-of-the-art modulation and control strategies. Firstly, the modulation strategies for NSDAB dc-dc converter are analyzed. All possible phase-shift patterns are demonstrated, and the correlation analysis of the typical phases-shift modulation methods for NSDAB dc-dc converter is presented. Then, an overview of steady-state efficiency optimization strategies is discussed for NSDAB dc-dc converter. Moreover, a review of optimized techniques for dynamic responses is also provided. For both the efficient and dynamic optimizations, thorough comparisons and recommendations are provided in this paper. Finally, to improve both steady state and transient performances, a combination approach to optimize both efficiency and dynamics for NSDAB dc-dc converter based on the reviewed methods is presented in this paper.
High-order power electronics converters are switching systems with multiple switching conditions and multiple operating modes. It is challenging to analyze their dynamics and stability based on traditional models, because of their multimodal nature. To address this issue, a sigmoid function-based two-piece switching system model was proposed in this paper. Using the voltage-controlled series-series inductive wireless power transfer (SS-IWPT) system as an example, this study adopts the sigmoid function to construct a two-piece switching system model for the system. Filippov’s theory and the Floquet method were used to analyze the dynamic behavior of such systems. And, Floquet multipliers were employed to compute the stable domains of the system’s parameter space, which can be used to guide parameter design. Theoretical analysis based on the proposed model indicates that SS-IWPT systems could exhibit Neimark-Sacker bifurcation under certain conditions, and that their dynamic behaviors can range from periodic states to quasiperiodic states. These findings are consistent with the time-domain waveforms obtained from circuit simulation and an experimental prototype. Both simulation and experimental results validate the accuracy of the proposed model, which can significantly reduce the difficulty of analyzing high-order power electronics systems dynamics.
Dual active bridge DC-DC (DAB) converters have a wide range of applications. However, the stability of DAB converters may be destroyed by the output voltage disturbance, which is caused by variations in input voltage and load conditions. To improve dynamic performance of DAB converters, many optimization schemes are proposed and require additional voltage and current sensors. In this paper, a model predictive control (MPC) method is proposed to achieve fast dynamic performance in load-current sensorless condition, which leads to cost reduction of the hardware system. The proposed MPC method is insensitive to circuit parameters and easy to implement. Moreover, combined with inductor current stress optimization (CSO), the proposed method can achieve multi-object optimization of DAB converters, including improving dynamic response, reducing the cost of the hardware system, etc. Firstly, the transmission power model under dual-phase-shift (DPS) of DAB converters is analyzed. Then, some typical methods, such as the PI control, the load current feedforward (LCFF) control, and the sliding mode based direct power control (SM-DPC), are introduced. Finally, an experiment phototype of DAB converters is developed, and comprehensive experiments with resistive load and 3-phase inverter load are employed to verify the correctness and effectiveness of the proposed method.
An inductive wireless power transmission (IWPT) system is a high-order nonlinear switching system with multiple operating modes. It is challenging to analyze the dynamic characteristics of such a system using the extended describing function, generalized state-space averaging, or other existing modeling methods. To address this challenge, this study proposes a modeling and dynamic characteristics analysis method for a closed-loop IWPT control system based on a sigmoid function model. A sigmoid function with a large steepness factor is adopted to approximate the switching process of the switch and a unified smooth continuous dynamic model is established for a phase-shift controlled IWPT system. Because this model is infinitely differentiable, a stability theory of continuous systems can be directly applied to analyze the bifurcation type of the system and stability of periodic solutions. Analysis results reveal the transition of the phase-shift-controlled WPT system from periodic behavior to chaotic behavior through saddle-node bifurcation and Neimark-Sacker bifurcation. A stable domain in the two-parameter space of the controller proportional coefficient and load is also obtained. Both simulation and experimental results validate the accuracy of the proposed model and theoretical analysis method, which can significantly reduce the difficulty of analyzing IWPT system dynamics.
Safety first-Save Lives/Systems is the main agenda in the design process of any safety-critical electrical drive system. Critical electrical drive systems are those systems,
breakdown of which might cause loss of life and significant resource damage. The
main application fields are such as automotive, aircraft flight control and railway
traction systems. Many modern electric drive systems change into critical electrical
drives system to save human life or protect system from failure. In future, critical
electrical drive system will become more widespread and dominant [1]. Due to recent
advancements in electrical drive and power converters, the industrial process systems
and electrical drives received increased attention [2]. The reliable and fault-tolerant
operation of these critical electrical drives is the main area of interest. In any electrified
drive system, the operations like steering control, brake-by-wire system and fuel
pump control play a vital role in the uninterrupted operation of the system. Hence,
parallel redundancy has been widely employed in many safety-critical electrical drive
applications such as space machines, aerospace, defence, electric vehicle, and many
other industrial applications.
The dual active bridge converter (DAB) is one of the recent topologies for isolated dc–dc converters. The isolation provided by the DAB converter is among the essential features used for renewable energy applications as it dissociates the grounds of source and load, enhancing the safety and protection of the renewable energy installation. In recent years, substantial investigations have been reported to discuss the technical challenges accompanying the DAB converter’s modulations and controls for renewable energy systems. This chapter presents the overview of control methods and parameter designing of the DAB power converter, applicable in the renewable energy system. The control algorithm and DAB parameter design considered renewable energy sources like PV, subsequently providing efficient power handling and voltage regulation. A brief overview of various control schemes is presented in this chapter, which is broadly classified into three categories. The renewable energy systems suffer from frequent voltage change; thereby, the control method plays a vital role in providing a satisfactory output. The direct power control strategy for DAB is proposed and discussed in this chapter to provide a fast transient response, stable steady-state response and improved voltage regulation. The performance of the suggested controller algorithm is evaluated in MATLAB/Simulink, and the outcomes demonstrate the suggested control method's effectiveness.
Multi-loop constant on-time (COT) controlled buck converter uses two weight resistors for sensing inductor current and detecting output voltage in its inner loop. When an output capacitor with a small ESR is employed, the converter will suffer the risk of instability due to different weight settings of inductor current and output voltage using a proportional-integral (PI) compensation gain in the outer voltage loop. However, no attention has been paid for their stability effects, which are important for designing the inner loop and outer voltage loop. To address these issues, a piecewise linear model is established for multi-loop COT controlled buck converter. Circuit parameterrelated bifurcation behaviors and control weight-related dynamical distributions are explored to demonstrate these stability effects. Further, through deriving an approximate discrete model, a control weight-related stability criterion is expressed explicitly, from which stability boundaries for dividing the normally stable and abnormally unstable operation parameter regions are thereby yielded. Besides, control weight-related transient performances under different circuit parameter settings are analyzed. Finally, PSIM circuit simulations and hardware circuit experiments verify the theoretical analysis well.
Average small signal model, known as a simple and powerful tool, is widely used to provide design guidance for switching converters. Due to the ignorance of high-frequency characteristics, conventional average small signal model fails to reveal dynamics of switching converters with ripple-based control. Improved small signal models for ripple-based controls, including peak and valley ripple-based controls, are proposed in this paper, which can be accurate to half of the switching frequency. Specifically, as for peak or valley current control, the uniform gain representing sample-and-hold (SAH) effect is derived and suitable for different averaging ways. With regard to
control, the improved small signal model can predict sub-harmonic oscillation caused by duty cycle and reveal the influence of the equivalent series resistance (ESR) of output capacitor. Moreover, by combining the improved small signal models of ripple-based current-mode control and
control, small signal model of
control can be analyzed. The relationship among these ripplebased control methods is revealed, and the stability analysis as well as the transient response are carried out. Finally, experimental results turn out to agree well with the theory analysis.
This paper focuses on analyzing the fast scale stability in a peak current-mode-controlled boost converter with a constant power load. Since with this kind of nonlinear loads the analytical expression of the discrete time model is not available and the existing averaged models are inadequate in describing accurately the fast scale dynamics of these converters, a piecewise linear switched model is established by approximating the constant power load by a composite linear load. The model is first demonstrated to predict accurately the same bifurcation points predicted by the switched model using the nonlinear load. The bifurcation analysis using Floquet theory and the resulting monodromy matrix and its eigenvalues loci clearly shows the effect of system parameters on its stability. The fast scale stability boundaries in terms of suitable parameters are obtained by using eigenvalues analysis. The effect of the proportional gain of the voltage controller is studied. Finally, experimental results are further given to verify the theoretical analysis and simulation results obtaining a good agreement.
Through analyzing the operating principles of V
2
controlled buck converters, 2-D discrete-time models and accurate switched models of V
2
controlled buck converters with trailing-edge and leading-edge modulations are established, respectively. The discrete-time models demonstrate the advantages of simple modeling and less computational complexity. Based on this, the dynamical behaviors of V
2
controlled buck converters are revealed through bifurcation diagrams and the boundary equations are derived by using the Jacobian matrix. Meanwhile, the operating regions with varying output capacitor time-constants are divided effectively by the boundary equations. The time-domain waveforms and phase portraits are also obtained through time-domain simulation. The research results indicate that trailing-edge- and leading-edge-modulated buck converters have symmetrical dynamical behaviors, such as symmetrical bifurcation, symmetrical time-domain waveforms, symmetrical phase portraits, and symmetrical period-doubling bifurcation boundaries. A symmetrical axis (SA) or a symmetrical point (SP) can be found in bifurcation diagrams, time-domain waveforms, phase portraits, and period-doubling bifurcation boundaries with varying output capacitor time-constants and duty ratios. By ramp compensation, the operating states of V
2
controlled buck converters with trailing-edge and leading-edge modulations could be effectively stabilized from unstable to stable periodic state. Experimental results are further given to verify the theoretical analysis and simulation results.
we propose an adaptive ramp control strategy with self-tuning offset and amplitude, as a simple yet effective solution for controlling DC-DC power converters despite load and input voltage variations. It is shown that our control technique is able to suppress chaos and sub-harmonic oscillations for a wide range of input voltage and loads. Furthermore, a systematic methodology based on bifurcation diagrams for tuning the controller is proposed. Stability and performance analysis have been done together with a proper comparison of our technique, and the classical control strategies often used in the literature. Particularly, Vin feed-forward and adaptive slope compensation controllers have been considered for the buck and boost converters, respectively. Finally, the effectiveness of the control technique is validated for the buck converter via experimental setup.
In general, DC-DC converter is a highly nonlinear system. More than one decade ago, many researchers have approved that DC-DC converters are experiencing bifurcation and chaotic oscillations. In this paper, both DC-DC Buck and Boost converters are been studied and analyzed. The study showed that such DC-DC converters are experiencing a nonlinear behavior (chaotic behavior) under certain operation conditions. In this paper, we studied the bifurcation and chaos in the DC-DC buck converter with changing different control parameters. In addition, the bifurcation theory will be applied to DC-DC Boost converter. Bifurcation diagrams and state-space diagrams have been shown for changing some control parameters.
V2Ic control provides very fast dynamic performance to the Buck converter both under load steps and under voltage reference steps. However, the design of this control is complex since it is prone to subharmonic oscillations and several parameters affect the stability of the system. This paper derives and validates a very accurate modeling and stability analysis of a closed-loop V2Ic control using the Floquet theory. This allows the derivation of sensitivity analysis to design a robust converter. The proposed methodology is validated on a 5-MHz Buck converter. The work is also extended to V2 control using the same methodology, showing high accuracy and robustness. The paper also demonstrates, on the V2 control, that even a low bandwidth-linear controller can affect the stability of a ripple-based control.
It has been reported that subharmonic instability exists in the V2 controlled buck converter in continuous conduction mode (CCM) when the duty ratio is above 0.5 (D > 0.5) and no stability issue exists in discontinuous conduction mode (DCM) when 0 < D < 1. However, the CCM and DCM instabilities will appear in the safe duty ratio range when the equivalent series resistance (ESR) of the output capacitor is below a critical value. The critical output-capacitor ESR for the stabiiity of a V2 controlled buck converter in CCM and DCM is investigated by using the discrete-time model and verified by circuit simulations.
This paper proposes a small-signal model for average current mode control based on an equivalent circuit. The model uses a three-terminal equivalent circuit model based on a linearized describing function method to include the feedback effect of the sideband frequency components of the inductor current. The model extends the results obtained in peak current mode control to average current mode control. The proposed small-signal model is accurate up to half switching frequency, predicting the subharmonic instability. The proposed model is verified using SIMPLIS simulation and hardware experiments, which show good agreement with the measurement results. Based on the proposed model, new feedback design guidelines are presented. The proposed design guidelines are compared with several conventional, widely used design criteria. By designing the external ramp following the proposed design guidelines, the quality factor of the double poles at half of the switching frequency in the control-to-output transfer function can be precisely controlled. This helps the feedback loop design to achieve wide control bandwidth and proper damping.
Power factor correction (PFC) converters using conventional control strategies have been reported tremendously as exhibiting slow- and fast-scale bifurcations. This study investigates the fast-scale and slow-scale instabilities in a PFC ĆUK converter under non-linear carrier (NLC) control, which is proved advantageous compared with other conventional control strategies. It is found that the fundamental periodic orbit loses its stability via period-doubling bifurcation and later bifurcates to chaos. Bifurcation studies of NLC controlled higher-order converters have not been reported so far in literature. Computer simulations as well as experimental investigations are performed to study the qualitative behaviour of the system under variations of different parameters. It is found that both the fast- and slow-scale instabilities may cause distortion in the line current and degrade the supply power factor. The results offer useful information of parameter space for the design and operation of the converter in the desired fundamental stable regime.
The complex dynamics and coexisting fast-slow scale instability in current-mode controlled buck converter with constant current load (CCL), operating in both continuous conduction mode (CCM) and discontinuous conduction mode (DCM), are investigated in this paper. Via cycle-by-cycle computer simulation and experimental measurement of current-mode controlled buck converter with CCL, it is found that a unique fast-slow scale instability exists in the second-order switching converter. It is also found that a unique period-doubling accompanied by Neimark–Sacker bifurcation exists in this simple second-order converter, which is different from period-doubling or Neimark–Sacker bifurcations reported previously. Based on a nonlinear discrete-time model and the corresponding Jacobian, the effects of CCL and input voltage on the dynamics of current-mode controlled buck converter are investigated and verified theoretically. Fixed point analysis for slow-scale low-frequency oscillation is also given to verify the dynamics and the coexisting fast-slow scale instability.
In this paper, period-doubling bifurcation in a two-stage power factor correction converter is analyzed by using the method of incremental harmonic balance (IHB) and Floquet theory. A two-stage power factor correction converter typically employs a cascade configuration of a pre-regulator boost power factor correction converter with average current mode control to achieve a near unity power factor and a tightly regulated post-regulator DC—DC Buck converter with voltage feedback control to regulate the output voltage. Based on the assumption that the tightly regulated post-regulator DC—DC Buck converter is represented as a constant power sink and some other assumptions, the simplified model of the two-stage power factor correction converter is derived and its approximate periodic solution is calculated by the method of IHB. And then, the stability of the system is investigated by using Floquet theory and the stable boundaries are presented on the selected parameter spaces. Finally, some experimental results are given to confirm the effectiveness of the theoretical analysis.
This paper presents a new control strategy for power factor correctors (PFCs) that are used to drive high-brightness LEDs. This control strategy is extremely simple and is based on the use of a conventional peak-current-mode controller with a suitable selection of the compensation ramp waveform. Neither an analog multiplier nor an input voltage sensor is needed to achieve quasi-sinusoidal line waveforms at nominal conditions and full load. If the converter belongs to the flyback family (flyback, buck-boost, SEPIC, Cuk and Zeta), the line waveform appears notably distorted if the compensation function is a linear ramp, but becomes almost sinusoidal if the linear ramp is substituted by a properly chosen exponential function. The line waveform is slightly distorted when the load varies or when the converter works under either overvoltage or undervoltage conditions. However, the waveform maintains a very high power factor (PF) even under these conditions. Moreover, the line current is cycle-by-cycle-controlled due to the peak-current-mode control, and hence, the input-current feedback loop is extremely fast, thereby allowing this type of control to be used with high-frequency lines (above 400 Hz).
A unified approach for the stability analysis of both preregulator and two-stage power factor correction (PFC) ac-dc converters is presented. Practical and accurate analytical expressions for the stability boundary are obtained by studying the dynamics of the first harmonic component. The resulting model of this dynamics has an equilibrium point at the origin of the harmonic state space. In the case of a stable equilibrium point, the first-order component converges to zero, and the system oscillates at twice the line frequency. If the equilibrium point loses stability, another equilibrium point depending on high-order harmonics will be reached while the real system will exhibit a period-doubling phenomenon leading to subharmonic oscillations. It is demonstrated that the stability boundaries depend on the power level. Numerical simulations and experimental results in both a preregulator and a complete two-stage PFC converter validate the approach.
In parameter ranges where conventional methods break down, DC-DC
converters may be described by iterated mappings, a nonlinear discrete
modeling technique. The underlying principles are explained and are
applied to the example of a PWM-controlled buck converter. Stable
behavior and bifurcations to chaos are predicted by numerical evaluation
of the governing mapping and are confirmed by experiment
A current-mode control power convertor model that is accurate at
frequencies from DC to half the switching frequency is described for
constant-frequency operation. Using a simple pole-zero transfer
function, the model is able to predict subharmonic oscillation without
the need for discrete-time z -transform models. The accuracy of
sampled-data modeling is incorporated into the model by a second-order
representation of the sampled-data transfer function which is valid up
to half the switching frequency. Predictions of current loop gain;
control-to-output; output impedance; and audio susceptibility transfer
functions were confirmed with measurements on a buck converter. The
audio susceptibility of the buck converter can be nulled with the
appropriate value of external ramp. The modeling concentrates on
constant-frequency pulse-width modulation (PWM) converters, but the
methods can be applied to variable-frequency control and discontinuous
conduction mode
The discrete mapping model of current-mode controlled buck converter with constant current load, taking account of composite output capacitors (parallel connection of two different types of capacitor branches, i.e. electrolytic capacitors and ceramic capacitors), is established. Based on the model, dynamical effects of varying output capacitance and equivalent series resistance (ESR) are investigated by bifurcation behaviours. The period of low-frequency oscillation among coexisting fast-slow scale instability is derived by exploring the loci of eigenvalues, while the operating regions are estimated. Time-domain simulation and experimental waveforms are provided for verification of the theoretical analysis, indicating the existences of subharmonic oscillation and coexisting fast-slow scale instability in the converter with variation of output capacitance and ESR. Research results reveal that the low-frequency oscillation can be eventually eliminated due to a relatively large (or small) ESR and the capacitance in the same branch presents to identical tendency of dynamical effects on the converter. Moreover, the interaction effects between two parallel capacitor branches are demonstrated. It illustrates that the low-frequency oscillation can be removed with smaller (or larger) ESR or capacitance in one branch of the composite output capacitors while larger (or smaller) ESR or capacitance in the other branch.
The usual method of estimating the onset of bifurcation and studying non-linear phenomena in power electronic devices consists of defining the discrete-time model. This model provides more precise results than an averaged model. However, the discrete-time model cannot be developed easily for some particular systems. In this study, a continuoustime averaging model is developed for a boost converter in the continuous-conduction mode (CCM). This proposed model is used to obtain the eigenvalues of the system to predict the stable operation of the period-1 orbit. It is observed that the loss of the asymptotic stability of the proposed model corresponds to the onset of period-doubling bifurcation in the discrete-time model. The generalisation of this method is investigated by applying the proposed method to a DC active filter converter connected in parallel with a CCM boost converter. Using this model, it is possible to obtain the eigenvalues of the system to investigate robustness properties with regards to system parameter variations. To confirm the validity of the proposed method, simulation and experimental results are presented.
The second-order discrete iterative map model of V2-controlled Buck converter is established, based on which, the bifurcation diagrams with variation of output capacitance and its equivalent series resistance (ESR) are obtained, and the effect of output capacitance time-constant on the dynamic characteristics of V2-controlled Buck converter is investigated. It is found that with gradual reduction of output capacitance time-constant, the V2-controlled Buck converter shows the evolutive dynamic behavior from continuous conduction mode (CCM) period-1 to CCM period-2, CCM period-4, CCM period-8, CCM chaos, and discontinuous conduction mode (DCM) chaos. Jacobi matrix at a fixed point is also derived. According to this, the converter stability is analyzed by using characteristic values and maximum Lyapunov exponent, which validates the correctness of bifurcation analysis. Finally, the simulation and experimental circuits are set up, and the correctness of the theoretical analysis is verified by simulation and experimental results.
Based on the piecewise smooth model, the smooth model and the discrete iterative model of proportion-integration (PI)-based voltage-mode Buck converter are derived. In this paper, it is proved that the chaotic attractor moves on the load line and is controlled by duty cycle, and that the manifold of the model moves around the chaotic attractor accompanied by the occurrences of period 1, period 2 and chaos phenomenon. The linear relationship between output voltage of the PI-controller and output voltage of Buck converter is derived, and then reveals that the proportional factor is a dominant one in PI controller. The period-doubling bifurcation, border collision and chaos are analyzed, and the state transfer process is exhibited. Experimental results verify that the theoretical modeling analysis and the simulation are correct.
In this paper, a single-stage LED driver is proposed for a street lighting system. Two boost circuits that share a single inductor are formed by integrating the switches of a half-bridge LLC resonant converter. Both boost circuits operate in the boundary conduction mode, which realizes a power-factor correction function. Because the input voltage of the LED driver is divided by two capacitors, the bus voltage is considerably reduced to almost the input peak voltage, rendering the novel single-stage LED driver to work suitably under high-input-voltage conditions. The soft-switching characteristics of the half-bridge LLC resonant circuit are not affected by the integration of the switches; thus, the converter has a low cost and a high efficiency. A 100-W prototype was developed, and the efficiency was determined to be as high as 91.1% in a full-load state under a 220-V ac input.
This paper presents the optimal design of the light-emitting diode (LED) array combinations for three typical nonisolated continuous-conduction mode single-loop control LED drivers. Based on the LED Taylor series model and the equivalent circuits of these three LED drivers, the quality factor functions in their transfer functions of the control-to-output current are derived to predict the optimal combination of the LED arrays according to the given circuit and LED parameters to fulfill the requirement of critical damping and maximum efficiency power conversion, which happen at unity quality factor. The three prototype circuits of three LED drivers with 120 LEDs are presented to verify the optimal design of the corresponding LED array combinations through the theoretical, simulation, and experimental results.
This paper presents a light-emitting-diode (LED) model based on the four-parameter Taylor series to describe the – characteristic of the LED at different junction temperatures. Therefore, in order to precisely model the LED nonlinear characteristics at different junction temperatures, an improved Taylor series-based LED model is proposed according to the four available parameters: 1) maximum operating point; 2) rated operating point; 3) knee point; and 4) temperature coefficient obtained from the LED – curves. Furthermore, in order to perform the dc and small-signal simulation and analyses of the LED drivers at different junction temperatures, the proposed model can be used to derive the LED dc and small-signal equivalent resistances at different junction temperatures. Finally, the measured results are compared with the modeled – curves, dc equivalent resistances, and small-signal equivalent resistances of the experimental LED at different junction temperatures.
Based on a survey on over 1400 commercial LED drivers and a literature review, a range of LED driver topologies are classified according to their applications, power ratings, performance and their energy storage and regulatory requirements. Both passive and active LED drivers are included in the review and their advantages and disadvantages are discussed. This paper also presents an overall view on the technical and cost aspects of the LED technology, which is useful to both researchers and engineers in the lighting industry. Some general guidelines for selecting driver topologies are included to aid design engineers to make appropriate choices.
This study deals with the analysis and implementation of an HPF (high power factor) single-stage, single switch buck converter-based power supply design for an LED (light emitting diode) lamp load of 13 W operated at the universal ac mains. In general purpose lighting applications, a buck converter is a good candidate for power factor correction with low component count and reduced cost. In low-power lighting, it is a tough task to control the THDi (total harmonic distortion) of ac mains current under the limits of strict international standards such as IEC-61000-3-2 with universal ac mains for class D equipments. In the proposed optocouplerless topology, HPF operation at input ac mains is achieved by operating the buck ac-dc converter in continuous conduction mode. The design, modelling and simulation of the proposed topology are executed using MATLAB-Simulink and sim-power system toolboxes. A prototype of the power supply for LED lamp is developed for multiple LEDs connected in series configuration. The efficiency of the proposed LED lamp driver is observed as 83.76% at rated voltage of 220 V and the THD of ac mains current less than 17.27% for a wide range of voltages of 90-270 V.
This paper proposes a novel light-emitting diode (LED) driver consisting of a buck-boost converter and a buck converter. Each converter adopts a power MOSFET as the active switch. With no need to use any auxiliary switches or snubber circuits, both active switches can operate at zero-voltage switching on (ZVS) by freewheeling the inductor current of the converters to flow through the intrinsic diodes of the MOSFETS. The buck-boost converter is operated at discontinuous-conduction mode (DCM) to perform the function of power-factor correction to ensure almost unity power factor at the input line. The buck converter steps down the output voltage of the buck-boost converter to drive LEDs. It could be designed to operate at either DCM or continuous-conduction mode. The detailed circuit operations and analysis are provided. A prototype 60-W LED driver was built and tested. Experimental results show that the switching losses can be effectively reduced by operating the active switches at ZVS. The measured power factor and circuit efficiency are as high as 0.99% and 93%, respectively.
Electrical lighting has seen many advancements since Edison first patented his version of the incandescent lamp. From those early days, lighting technology eventually changed with the introduction of mercury vapor, fluorescent, metal halide, and high-pressure sodium lamps. While each of these new light sources offered tremendous benefits over the incandescent lamp, their acceptance and any further advancement happened over a number of decades. Light-emitting diodes (LEDs) as a method of general lighting entered the market in the early 2000s. They were expensive and not very energy efficient. Within a few years, these lighting LEDs had dramatically improved. By 2006, they became trendy for residential and commercial applications, crossing over into the roadway lighting market a couple of years later. By 2010, they had become very “popular” as an industrial light source. In 2011, LEDs became mainstream and more affordable. Moving forward, LEDs are poised to dominate. Over the next decade, it is expected that LEDs will render most other light sources obsolete. The dilemma is that just about every evaluation method used for the past 140 years for every other light source cannot be applied directly to LED light sources. This paper will examine the LED revolution and what you need to know to survive.
Equivalent series resistance (ESR) of output capacitor has a significant effect on the control performance of constant on-time (COT) controlled switching dc-dc converters. In this paper, a discrete-time model of COT-controlled buck converter, with variable sampling frequency, is established. Based upon which, the dynamical effects of the ESR of output capacitor on COT-controlled buck converter are revealed and analyzed. The time-domain numerical simulations of the exact switched state equations, the bifurcation diagrams, and maximal Lyapunov exponents of the discrete-time model are obtained. These results verified by experimental circuit indicate that the ESR of output capacitor is a critical factor for COT-controlled buck converter, which can eliminate the unique pulse bursting phenomenon and shift operation mode from discontinuous conduction mode to continuous conduction mode, as well as control stability.
In this study, the non-linear dynamics of a two-stage cascaded-boost converter, which is a popular choice, for solar energy systems is investigated. The stability of the system is studied with the aid of non-linear state equations derived from an averaged continuous model. Analysis of the describing autonomous equations reveals that the system loses stability via supercritical Hopf bifurcation. Extensive computer simulations are performed to capture the system??s dynamic behaviour and demarcate the bifurcation boundaries. Furthermore, the possibility of subcritical Hopf bifurcation for variation in input voltage is also examined. Trajectory and Poincar?? section before and after the bifurcation are shown. Experimental results are also provided to confirm the observed bifurcation scenario.
Small-signal models are developed for two circuit versions of the basic
push-pull current-fed converter operating in the continuous-mmf modes.
The model for each circuit version leads to different small-signal
characteristics when the controlled-switch duty cycle is above 50
percent and when it is less than 50 percent. The models are verified by
comparisons with experimentally obtained results.
A valley current-mode (VCM) controlled buck converter with current source load (CSI) has complex phenomena of fast-scale and slow-scale subharmonic oscillations. The piecewise smooth switching model of the VCM controlled buck converter with CSI is established. It is found that attractive regions of fast-scale and slow-scale subharmonic oscillations exist in the bifurcation diagram, and two tori exist in the corresponding Poincaré mapping. The research results by time-domain simulation indicate that U-type subharmonic oscillation (SO) constituted by SO and frequency-reduced subharmonic oscillation (FSO) exists in inductor current, and sine-type SO constituted by fast scale and low scale exists in output voltage respectively. Experimental results are given to verify the analysis and simulation results.
The significant improvements recently achieved in LED technology in terms of lifetime, luminous efficacy, power rating, and color property render LED one of the most promising candidates to replace conventional light sources in various residential and industrial applications. The rapid advancement in the device characteristics has simultaneously stimulated interests in developing efficient LED drivers with optimized control circuitries. The two conventional techniques currently employed in most LED drivers, namely the amplitude-mode and pulsewidth modulation (PWM) mode driving techniques, suffer from the disadvantage that high luminous efficacy in the amplitude mode has to be traded for control flexibility in the PWM mode and vice versa . In this paper, a method is proposed to improve the luminous efficacy of conventional PWM-mode driving technique while retaining their control flexibility by introducing a dc-offset component into the PWM current. Two LEDs were used in the experimental verifications. Improvements of 17.6% and 18.1% on average were measured by maintaining a dc offset of 100 and 200 mA, respectively, in the LED current. Further improvement can be achieved by increasing the dc-offset current. The main tradeoff is the reduction of the dynamic range over which the average LED current can be controlled. For a given set of performance criteria, the proposed method offers designers of LED drivers the flexibility of balancing between luminous efficacy and dynamic range for control.
A general sampled-data representation of the dynamics of arbitrary power electronic circuits is proposed to unify existing approaches. It leads, via compact and powerful notation, to disciplined modeling and straightforward derivation of small-signal models that describe perturbations about a nominal cyclic steady state. Its usefulness is further illustrated by considering the representation and analysis of a class of symmetries in circuit operation. The results of the application of this methodology to modeling the small-signal dynamics of a series resonant converter are described. The results correlate well with simulation results obtained on the Massachusetts Institute of Technology's Parity Simulator. What is of greater significance is the fact that the small-signal model is obtained in a completely routine way, starting from a general formulation and working down to the actual circuit; this contrasts with the circuit-specific analyses that are more typical of the power electronics literature. The automatability of this procedure is also discussed, and it is pointed out that the key ingredients for automatic generation of dynamic models from a circuit specification are now available.
This paper investigates the coexisting fast-scale and slow-scale bifurcations in simple dc/dc converters under peak current-mode control operating in continuous conduction mode. Our focus is the boost converter as it is a representative form of dc/dc converter requiring current-mode control. Effects of varying the input voltage and some chosen parameters on the qualitative behavior of the system are studied in detail. Analysis based on a nonlinear simplified discrete-time model, which takes into account the effects of parasitics, is performed to investigate the coexistence of fast-scale and slow-scale bifurcations, and to identify the different types of bifurcation. Boundaries of stable region, slow-scale bifurcation region, fast-scale bifurcation region, coexisting fast and slow-scale bifurcation region are identified. Experimental measurements of the boost converter are provided for verification of the analytical results.
In this paper, an integrated double buck-boost (IDBB) converter is proposed as a high-power-factor offline power supply for power-LED lamps. The IDBB converter features just one controlled switch and two inductors and is able to supply a solid-state lamp from the mains, providing high power factor and good efficiency. In this paper, the IDBB converter is analyzed, and a design methodology is proposed. It is demonstrated that, with a careful design of the converter, the filter capacitances can be made small enough so that film capacitors may be used. In this way, the converter mean time between failures can be made as high as that of the solid-state lamp. A design example for a 70-W converter supplied from a 230 V/50 Hz mains for street lighting applications is shown. Finally, experimental results from a laboratory prototype are also presented.
With the variation of circuit parameters, the operation-state regions of current-mode-controlled switching dc-dc converters can shift among stable period region, robust chaos region in continuous conduction mode, and intermittent chaos region in discontinuous conduction mode. This paper presents a unified approach to the operation-states analysis of switching dc-dc converters with ramp compensation. The piecewise map model of the converters is first derived. With the bifurcation analyses, two boundary classification equations of the orbit state shifting are then obtained. Finally, the operation-state regions are well classified. To verify the theoretical analysis results, 2-D bifurcation diagrams are simulated and experimentations with current-mode-controlled buck converter are conducted. It is revealed that regular and irregular (chaotic or intermittent) operation states can be generated depending on circuit parameters or control of ramp-compensation current.
Total ampere-turns of the primary and secondary windings of a transformer are taken as one of variables to analyze the bifurcation behaviors and the border collision phenomenon on voltage-mode-controlled flyback converter. Six operation modes which are separated by the two borderlines of capacitor voltage and the three borderlines of total ampere-turns are obtained. A class of explicit piecewise smooth discrete-time maps with six operation modes is derived to describe the dynamics of the system. The numerical calculations are carried out, the bifurcation diagrams and the maximal Lyapunov exponent spectrums with the control period as a parameter are obtained. Then, the paper particularly analyzes the stability and existence conditions of main periodic orbits. The structure of bifurcation diagrams and the characteristics of operation modes at the border collision points are studied too. Finally, PSIM simulation and experimental results testify the validity of theoretical analysis.
A simplified method for finding and using discrete small-signal models for switching regulators is presented. With introduction of a new "straight-line" approximation, and application of root locus techniques, it is demonstrated that discrete models may be used accurately to predict wide bandwidth closed-loop behavior with methods simple enough to be useful in the initial design phase of a switching regulator. The principal result is a set of converter transfer functions comparable to the set derived by describing function techniques, but not subject to the low frequency restriction of describing function models. Also presented is a set of pulse-width modulator transfer functions which indicates that the potential small-signal transient behavior of a switching regulator is independent of the choice of modulator.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1989. Includes bibliographical references. by Seth R. Sanders. Ph.D.
This paper provides an analysis result of current control accuracy in driving power LEDs from widely varied DC input voltage. The detail analysis results show that the RMS LED current with Buck converter by using Peak Current Control (PCC) decreases according to increasing input voltage. Since the LED driver needs to be simple and low cost, the Buck converter is popular because it can allow continuous flowing current operation without an output bulky capacitor. Based on the simulation and experimental result, it is discussed how to improve current accuracy by using large a inductor size with PCC in Buck converter over wide input voltage variations. The result of PCC in Buck converter is also compared with Hysteretic Current Control (HCC) LED driver. Experimental results with PCC and HCC show that the RMS current accuracy with HCC is much better than that of PCC in Buck converter. In the experiment, the peak current level is set to 800[mA] both in PCC and HCC with the varied input voltage from 14V to 28V DC. 262 [KHz] fixed switching frequency is used in PCC and 1.2 [MHz] switching frequency is obtained with 33 [muH] inductor in HCC. The PCC and HCC are tested to drive two HB-LEDs rated of 750 [mA]. Finally, the current accuracies of 1% with HCC and 10% with PCC are obtained in the test range.
This paper investigates issues in modeling of current-mode
controlled DC-DC converters. The effects of the current-sampling
intrinsic to current-mode control are analyzed, and inadequately
recognized limitations of linear, time invariant models at high
frequencies are exposed. The paper also examines the geometric methods
used to derive duty ratio constraints in averaged models of current-mode
control. The conclusions are supported by simulation and experimental
results
A unified model is established for a current-programmed converter,
which is both a modification and an extension of familiar models.
Inclusion of the sampling effect allows the presence of an additional
pole in the current-loop gain to be inferred. The resulting final
double-slope asymptote is fixed in position, and the crossover frequency
cannot exceed half the switching frequency. A new stability parameter, Q
s, determines the additional pole and describes the degree of
peaking in the closed-loop transfer functions. Experimental verification
uses an analog signal injection technique
A correction to the usual derivation of state-space averaged
models for constant frequency, current mode controlled converters
produces average models. Using a buck-boost example, the authors compare
frequency responses of the model, the usual model, and an exact
sampled-data model. Approximate sampled-data models, often written down
but seldom exploited, are highlighted
A generalized discrete time-domain modeling and analysis technique is presented for all types of switching regulators using any type of duty-cycle controller and operating in both continuous and discontinuous inductor currents. State-space techniques are employed to derive an equivalent nonlinear discrete time model that describes the converter exactly. The system is linearized about its equilibrium state to obtain a linear discrete time model for small signal performance evaluations, such as stability, audiosusceptibility, and transient response. The analysis makes extensive use of the digital computer as an analytical tool. It is universal, exact, and easy to use.
The letter presents an exact small-signal discrete-time model for digitally controlled pulsewidth modulated (PWM) dc-dc converters operating in constant frequency continuous conduction mode (CCM) with a single effective A/D sampling instant per switching period. The model, which is based on well-known approaches to discrete-time modeling and the standard Z-transform, takes into account sampling, modulator effects and delays in the control loop, and is well suited for direct digital design of digital compensators. The letter presents general results valid for any CCM converter with leading or trailing edge PWM. Specific examples, including approximate closed-form expressions for control-to-output transfer functions are given for buck and boost converters. The model is verified in simulation using an independent system identification approach.
As the performance of microcontrollers has increased rapidly during the last decade, there is a growing interest to replace the analog controllers in low power switching converters by more complicated and flexible digital control algorithms. Compared to high power converters, the control loop bandwidths for converters in the lower power range are generally much higher. Because of this, the dynamic properties of the uniformly-sampled pulse-width modulators (PWMs) used in low power applications become an important restriction to the maximum achievable bandwidth of the control loop. Though frequency- and Laplace-domain models for uniformly-sampled PWMs are very valuable as they improve the general perception of the dynamic behavior of these modulators, the direct discrete design of the digital compensator requires a z -domain model for the combination modulator and converter. For this purpose a new exact small-signal z -domain model is derived. In accordance with the zero-order-hold equivalent commonly used for “regular” digital control systems, this z -domain model gives rise to the development of a uniformly-sampled PWM equivalent of the converter. This z -domain model is characterized by its capability to quantify the different dynamics of the converter for different modulators, its ease of use and its ability to predict the values of the control variables at the true sampling instants of the real system.
The possibility of obtaining the frequency-domain dynamic model of
a circuit from transient analysis data provided by a circuit simulator
is shown. The computer-aided design (CAD) program FREDOMSIM, which
governs the simulations, processes the output data, and supplies the
results in a well suited manner for design optimization, is introduced.
Feedback circuits are modeled with all their feedback loops open, so
that the designer can optimize systems by proper a posteriori loop
closures. The characterization with the loops closed is also given
A general small-signal model for current-programmed
switching power stages is used for design-oriented analysis of a 150-W buck regulator and of a 280-W boost regulator. The model, into which the current-programming minor feedback loop is absorbed, exposes the desired tendency towards “constant” output current. The regulator
voltage loop remains the only explicit feedback loop, allowing the regulator closed-loop properties to be easily obtained from those of the open-loop current-programmed power stage. The design-oriented analytic results allow easy inference of the effects of element changes on
the regulator performance functions. Results are obtained for the regulator line-to-output transfer function (audio susceptibility) and output impedance.
Accurate analysis of subharmonic oscillations of
- J Cortés
- V Šviković
- P Alou
- J A Oliver
- J A Cobos
- R Wisniewski