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

Abstract
Figure/Table
References
Related Citation (15)

Download: PDF (2726 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

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 -20 dB 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 4.8 h and case Ⅱ takes up to 3.8 h. The proposed optimal controller design method takes only 55 s and 53 s 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

Received: 07 October 2022

PACS:

TM46

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Cheng Xiangpeng
	Liu Jinjun
	Shao Yu
	Liu Zeng

Cite this article:

Cheng Xiangpeng,Liu Jinjun,Shao Yu等. High-Frequency Modeling for Peak Current-Model Buck Converters and Optimal Controller Design by Combining Genetic Algorithm[J]. Transactions of China Electrotechnical Society, 2024, 39(1): 217-232.

URL:

https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.221916 OR https://dgjsxb.ces-transaction.com/EN/Y2024/V39/I1/217

[1] Texas Instruments, LM25149 datasheet (2020) [R/OL]. https://www.ti.com.cn/cn/lit/ds/symlink/lm25149. pdf.
[2] Texas Instruments. TPS2585x datasheet (2021) [R/OL]. https://www.ti.com.cn/cn/lit/ds/symlink/tps25850-q1. pdf.
[3] Texas Instruments. LM5143Q1 datasheet (2021) [R/OL]. https://www.ti.com.cn/cn/lit/ds/ symlink/lm5143-q1.pdf.
[4] 何亮, 方宇, 李吉, 等. 峰值电流控制DC/DC变换器的恒值限流方法[J]. 电工技术学报, 2006, 21(10): 86-89, 105.
He Liang, Fang Yu, Li Ji, et al.Over Current protection for peak current controlled DC-DC converter[J]. Transactions of China Electrotechnical Society, 2006, 21(10): 86-89, 105.
[5] Suntio T.On dynamic modeling of PCM-controlled converters—Buck converter as an example[J]. IEEE Transactions on Power Electronics, 2018, 33(6): 5502-5518.
[6] Ridley R B.A new, continuous-time model for current-mode control (power convertors)[J]. IEEE Transactions on Power Electronics, 1991, 6(2): 271-280.
[7] James D.Moore’s law continues into the 1x-nm era[C]//2016 21st International Conference on Ion Implantation Technology (IIT), Tainan, Taiwan, China, 2017: 1-10.
[8] Borkar S, Dubey P, Kahn K C, et al.Platform 2015: intel ® processor and platform evolution for the next decade[N]. Technology, 2005: 1-10
[9] Stanford E.New processors will require new powering technologies[J]. Power Electronics Technology, 2002, 28(2): 32-42.
[10] Wong P L, Lee F C, Xu Peng, et al.Critical inductance in voltage regulator modules[J]. IEEE Transactions on Power Electronics, 2002, 17(4): 485-492.
[11] Qiu Yang, Yao Kaiwei, Meng Yu, et al.Control-loop bandwidth limitations for multiphase interleaving Buck converters[C]//Nineteenth Annual IEEE Applied Power Electronics Conference and Exposition, 2004. APEC '04, Anaheim, CA, USA, 2004: 1322-1328.
[12] Middlebrook R D. Topics in multiple-loop regulators and current-mode programming[J]. IEEE Transactions on Power Electronics, 1987, PE-2(2): 109-124.
[13] 高国庆, 雷万钧, 袁晓杰, 等. 双有源全桥变换器全状态离散迭代建模与输出电压纹波分析[J]. 电工技术学报, 2021, 36(2): 330-340.
Gao Guoqing, Lei Wanjun, Yuan Xiaojie, et al.Full-state discrete-time model and the output-voltage-ripple analysis of the dual active bridge converter[J]. Transactions of China Electrotechnical Society, 2021, 36(2): 330-340.
[14] Li Jian.Current-mode control: modeling and its digital application[D]. Virginia: Virginia Tech Dissertation, 2009.
[15] Yan Na, Ruan Xinbo, Li Xin.A general approach to sampled-data modeling for ripple-based control—part I: peak/valley current mode and peak/valley voltage mode[J]. IEEE Transactions on Power Electronics, 2022, 37(6): 6371-6384.
[16] Qiu Yang, Xu Ming, Sun Juanjuan, et al.A generic high-frequency model for the nonlinearities in Buck converters[J]. IEEE Transactions on Power Electronics, 2007, 22(5): 1970-1977.
[17] 岳小龙, 卓放, 杨书豪, 等. Buck变换器的多频率矩阵模型及其在分布式供电系统中的应用[J]. 电工技术学报, 2017, 32(4): 250-259.
Yue Xiaolong, Zhuo Fang, Yang Shuhao, et al.A multifrequency matrix model for Buck converters and its application in distributed power system[J]. Transactions of China Electrotechnical Society, 2017, 32(4): 250-259.
[18] Hsiao S F, Chen Dan, Chen C J, et al.A new multiple-frequency small-signal model for high-bandwidth computer V-core regulator applications[J]. IEEE Transactions on Power Electronics, 2016, 31(1): 733-742.
[19] Cheng Xiangpeng, Liu Jinjun, Liu Zeng.A generalized multifrequency small-signal model for high-bandwidth Buck converters under constant-frequency voltage-mode control[J]. IEEE Transactions on Power Electronics, 2020, 35(8): 8186-8199.
[20] Cheng Xiangpeng, Liu Jinjun, Liu Zeng.Accurate small-signal modeling and stability analysis of wide-input Buck converter considering modulation waveform ripples[J]. IEEE Transactions on Power Electronics, 2022, 37(6): 6962-6971.
[21] Xu Shen, Li Fei, Yao Yunpeng, et al.A high-frequency model for a PCM Buck converter[J]. IEEE Transactions on Power Electronics, 2015, 30(4): 2304-2312.
[22] Hung M H, Shu Lisun, Ho S J, et al.A novel intelligent multiobjective simulated annealing algorithm for designing robust PID controllers[J]. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 2008, 38(2): 319-330.
[23] 李家祥, 汪凤翔, 柯栋梁, 等. 基于粒子群算法的永磁同步电机模型预测控制权重系数设计[J]. 电工技术学报, 2021, 36(1): 50-59, 76.
Li Jiaxiang, Wang Fengxiang, Ke Dongliang, et al.Weighting factors design of model predictive control for permanent magnet synchronous machine using particle swarm optimization[J]. Transactions of China Electrotechnical Society, 2021, 36(1): 50-59, 76.
[24] 江凌峰, 龚邻骁, 金新宇, 等. 基于遗传算法的多模块IPOP双有源全桥DC-DC变换器总电流有效值优化策略[J]. 电工技术学报, 2023, 38(24): 6782-6797.
Jiang Lingfeng, Gong Lingxiao, Jin Xinyu, et al.Total root mean square current optimization of IPOP dual active bridge DC-DC converter based on genetic algorithm[J/OL]. Transactions of China Electrotechnical Society, 2023, 38(24): 6782-6797.
[25] 袁立强, 陆子贤, 孙建宁, 等. 电能路由器设计自动化综述—设计流程架构和遗传算法[J]. 电工技术学报, 2020, 35(18): 3878-3893.
Yuan Liqiang, Lu Zixian, Sun Jianning, et al.Design automation for electrical energy router-design workflow framework and genetic algorithm: a review[J]. Transactions of China Electrotechnical Society, 2020, 35(18): 3878-3893.
[26] Divakar A, Jacob J.Genetic algorithm based tuning of nonfragile and robust PI controller for PSFB DC-DC converter[C]//2019 International Conference on Communication and Electronics Systems (ICCES), Coimbatore, India, 2020: 1846-1851.
[27] Peng C C, Lee C L.Performance demands based servo motor speed control: a genetic algorithm proportional-integral control parameters design[C]//2020 International Symposium on Computer, Consumer and Control (IS3C), Taichung City, Taiwan, China, 2021: 469-472.
[28] Wang Chang, Zsurzsan T G, Zhang Zhe.Genetic algorithm assisted parametric design of splitting inductance in high frequency GaN-based dual active bridge converter[J]. IEEE Transactions on Industrial Electronics, 2023, 70(1): 522-531.
[29] Kostov K S, Kyyra J J.Genetic algorithm optimization of peak current mode controlled Buck converter[C]// Proceedings of the 2005 IEEE Midnight-Summer Workshop on Soft Computing in Industrial Applications, 2005, SMCia/05, Espoo, Finland, 2005: 111-116.
[30] 蔡子龙, 束洪春, 单节杉. 考虑运营成本的电动公交车集群换电优化调度策略[J]. 电力系统自动化, 2022, 46(17): 205-217.
Cai Zilong, Shu Hongchun, Shan Jieshan.Optimal dispatching strategy for battery swapping of electric bus cluster considering operation cost[J]. Automation of Electric Power Systems, 2022, 46(17): 205-217.