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.

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.

非最小相位的单电感双输出Buck-Boost变换器的复合控制方法

单电感双输出Buck-Boost (SIDO Buck-Boost)变换器在电感电流连续模式(CCM)下工作存在交叉影响以及非最小相位特性的问题.为了解决上述问题,提出基于储能函数的扩张状态观测器(ESO)的改进非奇异快速终端滑模(NFTSM)和自抗扰控制(ADRC)相结合的控制策略.设计主路控制器,对系统的传递函数进行拟合得到ADRC范式,利用该范式对主路进行解耦控制.设计支路控制器,采用改进型ESO对储能函数进行观测,并将观测值反馈补偿到非奇异快速终端滑模控制律中,达到支路解耦的效果.为了抑制滑模控制的抖振问题,对趋近律进行改进.利用Lyapunov理论证明系统稳定性.基于硬件在环(HIL)实验平台进行实验验证.结果表明,所提控制策略与PI控制策略以及基于ESO的滑模控制策略相比,在超调量和响应时间上具有较好的效果.

Instantaneous Current Feedback Control Strategy on Buck Mode Inverter

Buck型逆变器的电感电流瞬时值反馈控制和电容电流瞬时值反馈控制存在本质区别。以差动正激直流斩波器型高频环节逆变器为例，采用理论推导方法，研究这两种电流控制逆变器的稳定性、输出外特性、短路能力、输出功率特性、带非线性负载能力及动态响应特性。研究结果表明，电感电流瞬时值反馈控制逆变器具有电感电流和输出功率受限、较强的过载和短路能力、较软的输出外特性、较弱的带非线性负载能力、较差的动态响应等特点；而电容电流瞬时值反馈控制逆变器具有电感电流和输出功率不受限、较弱的过载能力、无短路能力、硬的输出外特性、较强的带非线性负载能力、较好的动态响应等特点。研究成果为Buck型逆变器电流型控制策略的选择及其设计提供重要的理论依据。

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.

自适应可调恒定导通时间Buck型直流电压变换器设计

为提高开关电源输出纹波电压、负载调整率、线性调整率和瞬态响应时间等性能指标,采用纹波控制的方法,研究出一款自适应可调恒定导通时间(adjustable-constant-on-time,ACOT)Buck型直流电压变换器。基于TSMC0.18μmCMOS工艺完成了电路设计,并用Cadence平台Spectre仿真器进行了仿真验证。结果表明:该电路的恒定导通时间可以精准灵活调节,纹波电压、线性调整率和瞬态响应时间均较低,与相关文献对比可知,本文设计在负载调整率上具有明显优势。

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.

混合工作模态的高功率因数无桥Buck PFC变换器

AC-DC降压型功率因数校正PFC(power factor correction)变换器广泛应用于低压场合,为解决该类拓扑因输入电流死区导致功率因数PF(power factor)低、输入电流总谐波THDi(total harmonic distortions of input current)高的问题,首先引入Buck-Boost单元以构建1种高PF的混合工作模态降压型无桥PFC变换器,其在正、负半个工频周期分别工作在Buck和Buck-Boost模式。虽然Buck-Boost单元效率低于Buck单元,但所提变换器在负半工频周期运行于Buck-Boost模式,可以避免输入电流死区以提高PF并降低THDi。在正半工频周期运行于Buck模式,变换器仍保留Buck单元的高效率优势。其次,通过分析所提无桥变换器工作模态与PF值来证明变换器的高PF特性。最后,通过仿真实验,验证所提变换器的可行性和理论分析的正确性,并比较所提变换器与传统Buck PFC变换器的性能。

同步BUCK电路中的新型非奇异终端滑模控制性能研究

针对传统滑模控制趋近速度较慢、抖振较大,应用在同步Buck变换器中响应速度较慢、精度较低等问题,提出了一种新型非奇异终端滑模控制的方法。首先对传统的滑模面函数进行了修改,通过引入非线性函数并附上积分项,可以迫使系统快速收敛,从而缩短响应时间。其次在传统趋近律的基础上引入了形式为sigmoid的函数,并用饱和函数来替代符号函数,避免了符号函数在零附近高频切换,因此降低了传统滑模控制带来抖振影响。最后在MATLAB/Simulink仿真平台搭建相应的模型,结果显示,其调整时间为90μs,突加负载后恢复时间为20μs。并通过实验验证,在转速指令发生改变时,所设计的方法调整时间更快,在突加负载后,抗干扰能力更强。

峰值电流控制Buck变换器高频建模及结合遗传算法的控制器优化设计

峰值电流控制Buck变换器广泛应用于电源管理芯片。小信号建模是设计其控制器的关键。现有模型忽略电压外环引入的稳态控制信号纹波与小信号扰动延拓频谱对系统的影响,在高控制带宽场景下失效,从而无法指导控制器的设计。该文首先指出控制器设计决定了控制信号纹波类型,进而研究了可导型纹波对系统建模的影响;然后综合考虑电压、电流环导致的频谱耦合,得到精确的高频模型;最后基于高频模型,提出一种结合遗传算法的高带宽控制器优化设计方法。仿真与实验证明了该模型的精确性与设计方法的优越性。

Bifurcation and chaos in high-frequency peak current mode Buck converter

Bifurcation and chaos in high-frequency peak current mode Buck converter working in continuous conduction mode（CCM） are studied in this paper. First of all, the two-dimensional discrete mapping model is established. Next, reference current at the period-doubling point and the border of inductor current are derived. Then, the bifurcation diagrams are drawn with the aid of MATLAB. Meanwhile, circuit simulations are executed with PSIM, and time domain waveforms as well as phase portraits in i_L–v_C plane are plotted with MATLAB on the basis of simulation data. After that, we construct the Jacobian matrix and analyze the stability of the system based on the roots of characteristic equations. Finally, the validity of theoretical analysis has been verified by circuit testing. The simulation and experimental results show that,with the increase of reference current I_（ref）, the corresponding switching frequency f is approaching to low-frequency stage continuously when the period-doubling bifurcation happens, leading to the converter tending to be unstable. With the increase of f, the corresponding Irefdecreases when the period-doubling bifurcation occurs, indicating the stable working range of the system becomes smaller.

带恒功率负载多电平Buck变换器逆解耦自适应滑模控制

针对带恒功率负载(CPL)多电平Buck变换器的强耦合问题及负阻抗特性引起的不稳定问题,提出一种逆解耦自适应滑模控制策略。建立带CPL多电平Buck变换器的非线性数学模型,基于逆系统方法证明系统的可逆性,并推导逆系统表达式,将模型线性化解耦为多个伪线性子系统,抵消负阻抗特性的影响。通过选取线性滑模面和指数趋近律以减弱滑模抖振,并将自适应机制引入到滑模控制中,进而为线性子系统分别设计自适应滑模控制器,进一步提高系统控制性能。基于李雅普诺夫理论对控制系统的稳定性和鲁棒性进行验证。与现有控制方法进行比较,仿真结果表明,所提控制策略具有更强的鲁棒性和优越性。最后,搭建原理样机进行实验对比,实验结果验证了所提控制策略的正确性和有效性。

基于逆系统解耦的三电平Buck变换器反步滑模控制

多电平变换器因其可以降低开关管承受的电压应力、减小滤波电感和滤波电容体积,被广泛应用在直流微电网中。三电平Buck变换器的飞跨电容电压和输出电压存在耦合,是一个多输入多输出、强耦合的非线性系统。针对这一问题,提出一种逆系统解耦反步滑模控制方法。采用逆系统方法实现输出电压控制和飞跨电容电压控制的解耦,采用反步滑模法控制保证输出电压的稳定性和鲁棒性,通过状态反馈控制将飞跨电容电压平衡在输入电压的1/2处。仿真和实验结果表明,所提控制策略能使得飞跨电容电压和输出电压均具有良好的稳态和动态特性。

交错并联BUCK电源CE102超标问题及解决措施

针对交错并联BUCK电源在10 kHz~10 MHz频率范围内传导噪声超标严重的问题,分析了交错并联BUCK电源的工作过程、纹波抑制和原始噪声,提出了EMI滤波器的设计方法,通过对差模电容高频特性、抑制原理的分析,结合插入损耗测试,对差模电容的选型进行了优化。实验结果表明,加装EMI滤波器后的交错并联BUCK电源能够达到GJB 151B—2013中CE102的测试标准,证明了设计的有效性。

基于自适应非奇异终端滑模的Buck变换器控制

为了提高滑模控制下Buck变换器的控制性能并降低抖振,提出一种自适应非奇异终端滑模控制方法.首先,对Buck变换器进行建模与分析,得到存在扰动时的数学模型;其次,设计非奇异终端滑模面,进行控制器设计和稳定性分析,使得闭环系统在有限时间内收敛并避免控制奇异问题,同时利用自适应律得到尽量小且足够抑制扰动的动态控制增益以削弱抖振;最后,通过理论分析和仿真实验验证所提控制方法的有效性.结果表明:该控制方法可以在减弱控制抖振的同时使得Buck变换器的输出电压在有限时间内跟踪上参考电压;当Buck变换器中的负载电阻和输入电压突变时,所提方法亦能表现出良好的抗干扰能力.

基于自适应超螺旋滑模观测器的Buck变换器无模型预测控制

针对三相交错并联Buck变换器在外部干扰下影响系统鲁棒性和动态性能的问题,本文提出一种基于自适应超螺旋滑模观测器的无模型预测控制策略。首先,建立超局部模型代替原有的数学模型,设计自适应超螺旋滑模观测器估计超局部模型中的动态部分。然后,引入最小二乘法预测电流误差趋势,动态调整观测器增益矩阵。最后,构建离散方程,设计代价函数,实现无模型预测控制。实验结果验证了所提算法可以有效抑制因外部扰动产生的稳态误差,且相较于传统无模型预测控制具有更好的鲁棒性和动态性能。

宽转换范围的峰值电流模式BUCK电源环路设计

宽转换范围的BUCK电源芯片使用峰值电流控制模式设计需要考虑全工作范围内的稳定性。首先分析了峰值电流型BUCK变换器的小信号模型,归纳了其稳态工作时的传输函数。然后描述了控制环路的设计过程,尤其是Type Ⅱ和Type Ⅲ型跨导运放的补偿网络的选择和设计方法。最后通过Mathcad及Simplis电路仿真对宽转换范围的BUCK电源芯片环路设计结果进行了验证和总结。

控制受限滑模控制Buck变换器设计

分析控制受限的传统滑模控制Buck变换器的滑动模态区与滑模系数和Buck变换器电路参数的数量关系,结合滑模控制开关变换器的主电路参数和性能要求,给出实现系统期望性能指标的滑模系数的设计方法,获得无输出电压振荡的滑模控制Buck变换器。仿真和实验结果验证了提出的滑模系数设计方法的有效性和可行性。

脉冲序列Buck变换器的控制规律及特性

研究了开关DC-DC变换器电压型和电流型脉冲序列控制的特点和实现方式,分析和对比了脉冲序列控制Buck变换器的稳态工作特性、控制规律和启动特性.理论分析、仿真和实验结果表明:电压型和电流型脉冲序列控制变换器在负载变化时控制规律基本相同,即负载增大时控制器产生较多的高能量脉冲.当输入电压升高时,电压型和电流型脉冲序列控制器分别产生较多的低能量脉冲和高能量脉冲.与电压型相比,电流型脉冲序列控制变换器具有更平稳的启动特性.