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

doi:10.19595/j.cnki.1000-6753.tces.221916

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摘要

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。本文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。

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	程翔鹏
	刘进军
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	刘增

关键词 ： Buck变换器, 峰值电流控制, 高带宽, 高频建模, 遗传算法

Abstract：

Peak current-model (PCM) Buck converters are widely employed in power management ICs. As microprocessors integrate continuously, high-bandwidth design has become a requisite for the front-end Buck converters. Accurate small-signal modeling is crucial for analyzing system stability and designing high-performance controllers. Existing models neglect control signal ripples (CSRs) in steady-state and extended-spectrum under small-signal perturbation transferred by voltage-loop, which makes significant errors under high control bandwidth and fails to guide controller design. To portray the high-frequency characteristics of the system and direct the design of high-bandwidth controllers, this paper proposed a high-frequency model for PCM Buck converters. An optimal controller design method was conducted based on the proposed model and genetic algorithm.
Firstly, this paper emphasized that different types of CSRs are initiated by different types of controllers. Subsequently, influences caused by differentiable CSRs were analyzed, wherein the impact of differentiable ripples on the system can be equivalent to the derivative values at crossing points. The spectrum coupling from the voltage-loop and current-loop was incorporated, and the maximum frequency point corresponding to -20dB amplitude of the single-frequency loop gain was taken as the selection boundary of the extended spectrum to simplify the model. Thereby an accurate small-signal model was obtained. Analytical expressions for loop gain, audio susceptibility, input impedance, and output impedance were derived based on matrix operations. Lastly, based on the proposed high-frequency model, an efficient optimization design of high-bandwidth controllers was conducted by combining genetic algorithm.
To assert the accuracy of the proposed model and the effectiveness of the optimal controller design method, this paper devised two cases and conducted simulations and experimental verifications. For case I, the loop gain predicted by the proposed model (Bandwidth: 222.5 kHz, Phase margin: 29.9°) matches well with the simulated results (Bandwidth: 224.3 kHz, Phase margin: 29.8°). For case II, the loop gain predicted by the proposed model (Bandwidth: 161.9 kHz, Phase margin: 13.1°) also matches well with the simulated results (Bandwidth: 162.0 kHz, Phase margin: 12.8°). The parameters of case II were leveraged to construct an experimental platform. The loop gain of the system is measured using a Venable Frequency Analyzer. The experimental results (Bandwidth: 162.5 kHz, Phase margin: 16.4°) further confirm the accuracy of the proposed model. Deviations between them are mainly due to parameter variations and measurement errors in the real system. The simulation-based genetic algorithm optimization method in Simulink was redone to illustrate the efficiency of the proposed optimal controller design method. To achieve a fair comparison, the genetic algorithm optimization calculation was also carried out in Matlab, and even with the same computer settings, case I takes up to 4.8h and case II takes up to 3.8h. The proposed optimal controller design method takes only 55s and 53s respectively, which are hundreds of times more efficient, showcasing its effectiveness. Compared with the time-domain simulation-based parameter search method, the ability to attain a quantitative stability margin design by setting L_{pm_limit} is another advantage by utilizing the precise analytical model.
Simulation and experimental results demonstrate that the proposed high-frequency model is accurate enough to portray frequency domain characteristics and forecast system stability precisely, compared with existing models. Additionally, the proposed optimal controller design method enables fast and efficient implementation of high-bandwidth controller designs. The proposed high-frequency model belongs to an analytical model and significantly reduces the computational burden on computers. Combining it with a genetic algorithm results in complementary benefits. This combination facilitates quick and precise appraisal of individual fitness during the iteration process, thereby reducing design time considerably and offering practical value in engineering applications.

Key words： Buck converter peak current-mode high-bandwidth high-frequency modeling genetic algorithm

收稿日期: 2022-10-07

PACS:

TM46

基金资助:

国家自然科学基金资助项目（51437007）

通讯作者: 刘进军, 男,1970年生,教授,博士生导师,研究方向为电力电子技术在电能质量控制、输配电系统以及分布式发电系统中的应用、电力电子电路和系统的建模、仿真、分析和控制等。E-mail：jjliu@mail.xjtu.edu.cn

作者简介: 程翔鹏, 男,1994年生,博士,研究方向为DC-DC变换器精确小信号建模、基于智能算法的控制器设计与多电力电子变换器系统稳定性分析。E-mail：alexcheng1994@163.com

引用本文:

程翔鹏, 刘进军, 邵钰, 刘增. 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[J]. 电工技术学报, 0, (): 8906-. Cheng Xiangpeng, Liu Jinjun, Shao Yu, Liu Zeng. High-Frequency Modeling for PCM Buck Converters and Optimal Controller Design by Combining Genetic Algorithm. Transactions of China Electrotechnical Society, 0, (): 8906-.

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