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Article(id=1322161859269083329, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322161751467078485, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1728835200000, receivedDateStr=2024-10-14, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793157551829, onlineDateStr=2026-10-28, pubDate=1758729600000, pubDateStr=2025-09-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793157551829, onlineIssueDateStr=2026-10-28, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793157551829, creator=13701087609, updateTime=1793157551829, updator=13701087609, issue=Issue{id=1322161751467078485, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='9', pageStart='1', pageEnd='314', issueExtLink='null', onlineDate='null', pubDate='1758729600000', pubDateStr='2025-09-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793157526127, creator='13701087609', updateTime=1793158877659, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1322167420266074322, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322161751467078485, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1322167420266074323, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322161751467078485, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=176, endPage=183, ext={EN=ArticleExt(id=1322161859478798531, articleId=1322161859269083329, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Research on Intelligent Control System of Belt Conveyor Based on Multiverse Optimizer Algorithm, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to achieve the goals of balanced coal flow control, energy saving, and efficiency improvement for the belt conveyor in the mining area of the 4205 working face at Longquan Coal Mine, a mathematical model of the belt conveyor was established. The Multiverse Optimizer (MVO) algorithm was employed to optimize the fuzzy PID controller. Simulations were conducted based on MATLAB, and the results were compared and validated against actual field data. The results are as follows. Firstly, compared with the traditional PID control, the fuzzy PID control optimized by MVO algorithm reduces the adjustment time and overshoot by 46.4% and 34.49 percentage points respectively, and the fitness value converges from 1 022 of the initial iteration to 901.8, indicating that the response speed, stability and anti-interference ability of the system are significantly improved. Secondly, by comparing and analyzing the actual belt speed of the belt conveyor and the regulated belt speed of MVO-Fuzzy-PID within 300 s of five time periods on the belt conveyor, it is verified that the regulated belt speed can be closer to the set value more accurately. Thirdly, from the power point of view, the total power of the motor after MVO-Fuzzy-PID control is significantly reduced. Therefore, the MVO algorithm optimizes the belt speed to achieve energy-saving control and fast matching of coal flow.

, authors=Runhua ZHANG, Qiaorong MENG, Jialong XIN, Chen ZHANG, Zhikun MA, authorsList=Runhua ZHANG, Qiaorong MENG, Jialong XIN, Chen ZHANG, Zhikun MA, authorCompany=null, correspAuthors=Qiaorong MENG, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322161866734944518, articleId=1322161859269083329, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=基于多元宇宙优化算法的带式输送机智能控制系统研究, columnId=1226462295946085268, journalTitle=矿业研究与开发, columnName=矿山机电与矿业智能化, runingTitle=null, highlight=null, articleAbstract=

为实现龙泉煤矿4205工作面采区巷道带式输送机的煤流均衡控制及节能提效的目标，通过建立该带式输送机的数学模型，采用多元宇宙算法(MVO)优化模糊PID控制器，并基于MATLAB进行仿真与现场实际数据对比验证。结果表明：(1)相较于传统PID控制，MVO算法优化模糊PID控制使调节时间和超调量分别下降了46.4%和34.49个百分点，适应度值从初始迭代的1 022收敛至901.8，表明系统的响应速度、稳定性和抗干扰能力显著提升；(2)对比分析带式输送机上5个时间段300 s内带式输送机的实际带速与MVO-Fuzzy-PID的调控带速，验证调控带速能更准确地接近设定值；(3)从功率角度分析，MVO-Fuzzy-PID调控后所对应的电动机总功率显著降低。因此，MVO算法优化带速实现了节能控制与煤流量快速匹配。

, authors=张润华, 孟巧荣, 辛佳龙, 张琛, 马志坤, authorsList=张润华, 孟巧荣, 辛佳龙, 张琛, 马志坤, authorCompany=null, correspAuthors=孟巧荣, authorNote=

张润华（1998—），男，山西太原人，硕士研究生，主要从事煤矿智能化方面的研究。E-mail:

, correspAuthorsNote=
孟巧荣（1974—），女，山西朔州人，博士，副教授，主要从事原位改性采矿、智能开采方面的研究。E-mail:
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张润华（1998—），男，山西太原人，硕士研究生，主要从事煤矿智能化方面的研究。E-mail:

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张润华（1998—），男，山西太原人，硕士研究生，主要从事煤矿智能化方面的研究。E-mail:

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Xuzhou: China University of Mining and Technology, 2022., articleTitle=Research on coal flow visual detection and energy saving control system for belt conveyor, refAbstract=null)], funds=[Fund(id=1322162674394321460, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, awardId=51974191, language=CN, fundingSource=国家自然科学基金资助项目(51974191), fundOrder=null, country=null), Fund(id=1322162674469818933, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, awardId=2021-059, language=CN, fundingSource=山西省省筹资助回国留学人员项目(2021-059), fundOrder=null, country=null), Fund(id=1322162674742448694, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, awardId=J20230222, language=CN, fundingSource=2023年山西省高等学校教学改革创新项目(J20230222), fundOrder=null, country=null), Fund(id=1322162674834723383, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, awardId=HBIR 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tableContent=null), ArticleFig(id=1322162671361839655, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, language=CN, label=图9, caption=智能控制仿真对比, figureFileSmall=Kjkw+N192ErSgSkZ2ko7xg==, figureFileBig=EcU5qpvze+v4A74W4w1tBA==, tableContent=null), ArticleFig(id=1322162672850817576, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, language=EN, label=Table 1, caption=

Permanent magnet synchronous motor parameters

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反电动势常数 ke/(V/(rad·min－1))定子励磁电感Ls/H电驱电阻R/Ω转动惯量 J/(kg·m2)电机极对数np/对
0.090.0851.50.42523
), ArticleFig(id=1322162672938897961, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, language=CN, label=表1, caption=

永磁同步电机参数

, figureFileSmall=null, figureFileBig=null, tableContent=
反电动势常数 ke/(V/(rad·min－1))定子励磁电感Ls/H电驱电阻R/Ω转动惯量 J/(kg·m2)电机极对数np/对
0.090.0851.50.42523
), ArticleFig(id=1322162673035366954, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, language=EN, label=Table 2, caption=

Fuzzy control rules

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Kp/Ki/Kd隶属度速度偏差 e0
1(NB)2(NM)3(NS)4(Z)5(PS)6(PM)7(PB)
速度偏差变化率 ec1(NB)7/1/57/1/56/1/46/2/45/1/45/4/74/4/7
2(NM)7/1/37/1/36/2/36/2/35/4/44/4/34/4/6
3(NS)6/2/16/2/16/3/25/3/34/5/43/5/52/5/6
4(Z)6/2/15/3/25/3/24/4/33/5/42/5/52/6/6
5(PS)5/3/15/3/24/4/33/5/33/2/42/6/52/6/5
6(PM)4/4/24/4/33/5/32/6/32/6/42/7/51/7/5
7(PB)4/4/53/4/43/5/45/6/42/6/41/7/71/7/7
), ArticleFig(id=1322162673136030251, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, language=CN, label=表2, caption=

模糊控制规则

, figureFileSmall=null, figureFileBig=null, tableContent=
Kp/Ki/Kd隶属度速度偏差 e0
1(NB)2(NM)3(NS)4(Z)5(PS)6(PM)7(PB)
速度偏差变化率 ec1(NB)7/1/57/1/56/1/46/2/45/1/45/4/74/4/7
2(NM)7/1/37/1/36/2/36/2/35/4/44/4/34/4/6
3(NS)6/2/16/2/16/3/25/3/34/5/43/5/52/5/6
4(Z)6/2/15/3/25/3/24/4/33/5/42/5/52/6/6
5(PS)5/3/15/3/24/4/33/5/33/2/42/6/52/6/5
6(PM)4/4/24/4/33/5/32/6/32/6/42/7/51/7/5
7(PB)4/4/53/4/43/5/45/6/42/6/41/7/71/7/7
), ArticleFig(id=1322162673467380268, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, language=EN, label=Table 3, caption=

Response performance indexes

, figureFileSmall=null, figureFileBig=null, tableContent=
控制器ts/str/sMp/%tp/s
传统PID20.3114.55734.500 07.067
Fuzzy-PID17.14410.9800.530 028.825
MVO-Fuzzy-PID10.8857.5820.002 527.029
), ArticleFig(id=1322162673563849262, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, language=CN, label=表3, caption=

响应性能指标

, figureFileSmall=null, figureFileBig=null, tableContent=
控制器ts/str/sMp/%tp/s
传统PID20.3114.55734.500 07.067
Fuzzy-PID17.14410.9800.530 028.825
MVO-Fuzzy-PID10.8857.5820.002 527.029
), ArticleFig(id=1322162673635152431, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, language=EN, label=Table 4, caption=

The respective fluctuation range of belt speed under actual belt speed and regulated belt speed

, figureFileSmall=null, figureFileBig=null, tableContent=
带速分类不同带速下各自的波动区间/(m/s)
1 m/s2 m/s3 m/s4 m/s5 m/s
实际带速0.960~1.0471.950~2.0522.942~3.0553.935~4.0484.917~5.076
调控带速0.981~1.0281.977~2.0222.979~3.0223.974~4.0164.973~5.026
), ArticleFig(id=1322162673731621424, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, language=CN, label=表4, caption=

实际带速和调控带速下各自的带速波动区间

, figureFileSmall=null, figureFileBig=null, tableContent=
带速分类不同带速下各自的波动区间/(m/s)
1 m/s2 m/s3 m/s4 m/s5 m/s
实际带速0.960~1.0471.950~2.0522.942~3.0553.935~4.0484.917~5.076
调控带速0.981~1.0281.977~2.0222.979~3.0223.974~4.0164.973~5.026
), ArticleFig(id=1322162673886810673, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, language=EN, label=Table 5, caption=

Comparison of the area of the velocity curve under the fixed coal flow rate at different stages

, figureFileSmall=null, figureFileBig=null, tableContent=
各阶段固定煤流量期望带速/(m/s)额定带速/(m/s)实际带速曲线面积调控带速曲线面积
9.024121120
17.244228230
4.0147873
22.054278280
12.634192188
), ArticleFig(id=1322162673987473970, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161859269083329, language=CN, label=表5, caption=

不同阶段固定煤流量下的带速曲线面积对比

, figureFileSmall=null, figureFileBig=null, tableContent=
各阶段固定煤流量期望带速/(m/s)额定带速/(m/s)实际带速曲线面积调控带速曲线面积
9.024121120
17.244228230
4.0147873
22.054278280
12.634192188
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基于多元宇宙优化算法的带式输送机智能控制系统研究
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张润华 , 孟巧荣 , 辛佳龙 , 张琛 , 马志坤
矿业研究与开发 | 矿山机电与矿业智能化 2025,45(9): 176-183
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矿业研究与开发 |矿山机电与矿业智能化 2025 , 45 (9) : 176 -183
基于多元宇宙优化算法的带式输送机智能控制系统研究
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张润华 , 孟巧荣 , 辛佳龙, 张琛, 马志坤
作者信息
  • 太原理工大学矿业工程学院，山西　太原　030024
通讯作者:
孟巧荣（1974—），女，山西朔州人，博士，副教授，主要从事原位改性采矿、智能开采方面的研究。E-mail:
作者简介:

张润华（1998—），男，山西太原人，硕士研究生，主要从事煤矿智能化方面的研究。E-mail:

Research on Intelligent Control System of Belt Conveyor Based on Multiverse Optimizer Algorithm
Runhua ZHANG , Qiaorong MENG , Jialong XIN, Chen ZHANG, Zhikun MA
Affiliations
  • College of Mining Engineering, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China
出版时间: 2025-09-25
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为实现龙泉煤矿4205工作面采区巷道带式输送机的煤流均衡控制及节能提效的目标，通过建立该带式输送机的数学模型，采用多元宇宙算法(MVO)优化模糊PID控制器，并基于MATLAB进行仿真与现场实际数据对比验证。结果表明：(1)相较于传统PID控制，MVO算法优化模糊PID控制使调节时间和超调量分别下降了46.4%和34.49个百分点，适应度值从初始迭代的1 022收敛至901.8，表明系统的响应速度、稳定性和抗干扰能力显著提升；(2)对比分析带式输送机上5个时间段300 s内带式输送机的实际带速与MVO-Fuzzy-PID的调控带速，验证调控带速能更准确地接近设定值；(3)从功率角度分析，MVO-Fuzzy-PID调控后所对应的电动机总功率显著降低。因此，MVO算法优化带速实现了节能控制与煤流量快速匹配。

带式输送机  /  智能控制  /  多元宇宙优化算法  /  带速

In order to achieve the goals of balanced coal flow control, energy saving, and efficiency improvement for the belt conveyor in the mining area of the 4205 working face at Longquan Coal Mine, a mathematical model of the belt conveyor was established. The Multiverse Optimizer (MVO) algorithm was employed to optimize the fuzzy PID controller. Simulations were conducted based on MATLAB, and the results were compared and validated against actual field data. The results are as follows. Firstly, compared with the traditional PID control, the fuzzy PID control optimized by MVO algorithm reduces the adjustment time and overshoot by 46.4% and 34.49 percentage points respectively, and the fitness value converges from 1 022 of the initial iteration to 901.8, indicating that the response speed, stability and anti-interference ability of the system are significantly improved. Secondly, by comparing and analyzing the actual belt speed of the belt conveyor and the regulated belt speed of MVO-Fuzzy-PID within 300 s of five time periods on the belt conveyor, it is verified that the regulated belt speed can be closer to the set value more accurately. Thirdly, from the power point of view, the total power of the motor after MVO-Fuzzy-PID control is significantly reduced. Therefore, the MVO algorithm optimizes the belt speed to achieve energy-saving control and fast matching of coal flow.

Belt conveyor  /  Intelligent control  /  Multiverse optimizer algorithm  /  Belt speed
张润华, 孟巧荣, 辛佳龙, 张琛, 马志坤. 基于多元宇宙优化算法的带式输送机智能控制系统研究. 矿业研究与开发, 2025 , 45 (9) : 176 -183 .
Runhua ZHANG, Qiaorong MENG, Jialong XIN, Chen ZHANG, Zhikun MA. Research on Intelligent Control System of Belt Conveyor Based on Multiverse Optimizer Algorithm[J]. Mining Research and Development, 2025 , 45 (9) : 176 -183 .
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0　引言
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煤炭地下井工开采过程中，矿用带式输送机起着举足轻重的作用，其具有运送量大、运送距离长和运输效率高等特点。随着煤炭智能化开采的不断推进，矿用带式输送机的作用日益凸显，该设备的安全、高效、节能对整个运输体系及煤矿开采效益至关重要[1-4]。
国内外学者在带式输送机的智能化研究领域取得了大量成果。JI Jianhua等[5]提出一种带式输送机能耗模型，基于此模型分析了煤流量的节能控制策略，通过调控带速实现节能。NI Yunfeng等[6]建立带式输送机的数学模型，采用模糊控制算法进行控制，通过感应电机转速公式与模糊算法的结合实现了显著的节能效果。韩东升[7]研究了带式输送机的调速系统，将预见控制理论应用于调速系统，实现了加速约束的预见控制。牛祯祖[8]运用BP神经网络建立优化模型，在变频调速领域取得了良好效果，实现了远程调速和实时监测。彭洁[9]融合模糊控制和神经网络控制算法，创新性地提出了模糊神经网络算法用于带式输送机控制，仿真结果表明该方法取得了很好的控制效果。
控制系统输出量为皮带速度。因此，速度的优化控制是带式输送机智能化研究的关键[10]。研究表明，带式输送机速度控制的基本方法为PID控制，通过优化PID控制参数可实现带速的稳定、安全和智能运行。为实现带式输送机的智能化控制，提高其响应速度、稳定性和抗干扰能力，确保带速与采煤机截割能力的匹配，进而实现节能的目的，本文采用多元宇宙算法(MVO)优化模糊PID控制器，形成基于煤流量调节带速的智能化控制方案。该算法相比其他控制算法具有结构简单、寻优速度快和鲁棒性强等优点，能满足工作面带式输送机智能调速的要求。
1　带式输送机及控制系统数学模型
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针对龙泉煤矿4205工作面顺槽带式输送机控制系统，建立数学模型。该带式输送机采用变频驱动，控制系统包括电机系统、变频器系统和输送带的纯滞后系统[11]。图1为输送机驱动示意。
1.1　电机及数学模型
永磁直驱电机具有输出扭矩大、系统效率高、动态响应快、抗冲击振动能力强等优点[12]。然而，永磁直驱电机结构复杂，难以直接建立数学模型，因此本文在理想条件下进行建模。
其动态电压方程为：
式中：ua和ub分别为定子三相绕组中两相的电压；ia和ib为对应两相的电流；ea和eb为两相的反电势；R为每相绕组的内阻；L为定子的自感和互感（恒定值）；Iu为逆变器输出方波电流的峰值[13]；t为时间。
基于电机基本理论，可以推导出以下表达式：
式中：Te为电磁转矩；Ti为负载转矩；J为转子转动惯量；ω为角速度；dω/dt为转子机械角加速度；np为电机极对数；ke为反电势系数。本次建模中电动机转速单位为n/min，且n=30ω/π。
对式(1)、式(2)进行拉普拉斯变换，得到：
式中：s为拉普拉斯变换中的复变量，表示系统的频率响应；U(s)为电压函数；Ea(s)为反电势函数；i(s)为电流函数；Ls为定子励磁电感；Te(s)为电磁转矩函数；Ti(s)为负载转矩函数。
最后得到电机系统传递函数的结构框，如图2所示。
根据图2可以推导出电机转速n(s)与输入电压u(s)之间的传递函数G1(s):
本文研究的永磁同步电机参数见表1。
将表1数值代入式(4)，得到电机的传递函数为：
1.2　带式输送机的整体数学模型
带式输送机控制系统可等效为由电机系统G1(s)、变频器系统G2(s)和输送带纯滞后系统G3(s)三部分组成。变频器可通过调节永磁电机的频率和电压实现带式输送机的控制，其传递函数在常规工况下可简化为小惯性环节或比例环节。输送带可建模为一个纯滞后系统，用于缓冲电动机运行时产生的冲击。因此，带式输送机控制系统的整体传递函数G(s)为：
其中，
最终得到带式输送机控制系统的整体传递函数为：
2　多元宇宙算法优化模糊PID
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2.1　多元宇宙算法理论概述
多元宇宙优化算法（Multi-Verse Optimizer, MVO）是Seyedali Mirjalili等人于2015年提出的一种新型智能优化算法[14]。该算法基于宇宙学原理，将优化过程模拟为多个宇宙间的物质交换：高膨胀率宇宙中的物质(对应白洞)会向低膨胀率(对应黑洞)迁移。算法通过虫洞实现物质传输，其核心机制包含探索(全局搜索)和开采(局部优化)两个阶段，具体步骤如下。
（1）初始化。建立多元宇宙矩阵U:
式中：d为优化变量个数；m为宇宙数量（候选解），即种群规模。
（2）选择。设定的任意宇宙都有不同的膨胀率，每个宇宙都会利用白洞/黑洞轨道进行迁移，其迁移遵循轮盘赌机制，见式(9)。
式中：为第i个宇宙里第j个物体；Ui为第i个宇宙；N(Ui)为第i个宇宙的标准膨胀率；r1为在0和1的任意数；为遵循轮盘赌机制后选择的第k个宇宙的第j个物体。
（3）移动。在MVO算法中，膨胀率决定物质转移概率但不直接影响移动过程，物体通过向当前最优宇宙的最佳位置迁移实现局部优化和膨胀率改进，其位置更新遵循式(10)。
式中：Xj为当前最优宇宙的第j个物体；ubj和lbj分别为的最大值和最小值；r2,r3,r4均为在0和1内的的任意数；TDR(Travelling Distance Rate)为旅行距离率，随迭代减小，见式（11）；WEP （Wormhole Existence Probability）为虫洞存在概率，随迭代增加，见式（12）。
式中：c为当前迭代次数；C为最大迭代次数；p为开采度，即探测速度，其值越高，局部探测速度越快，用的时间越短[15]。
2.2　模糊控制器设计
针对带式输送机控制系统，以期望带速V1与实际带速V0的偏差e0及其变化率ec作为模糊控制器的输入，经糢糊化处理，模糊规则推理及解模糊化运算后输出比例系数Kp、积分系数Ki、微分系数Kd[16]。输入e0、ec和输出Kp、Ki、Kd的模糊子集均定义为{NB（负大），NM（负中），NS（负小），Z（零），PS（正小），PM（正中），PB（正大）}，对于e0、ec、Kp、Ki、Kd的量化论域统一取[－33]。
基于采区巷道的带式输送机的流量变化监测数据，结合工程人员的操作经验、专家知识库和PID相关理论，建立了模糊PID控制器所需的模糊控制规则（见表2）。其中数字1~7分别对应模糊子集{NB（负大），NM（负中），NS（负小），Z（零），PS（正小），PM（正中），PB（正大）}。
2.3　多元宇宙算法优化模糊PID控制器
2.3.1　控制器设计
采用MVO算法对模糊PID控制器的Kp、Ki、Kd参数和模糊规则进行智能化优化，可有效减小速度控制误差，提高其控制精度，实现更优的动态平衡性能。
2.3.2　性能指标及优化目标函数
在模糊PID控制器的基础上引入MVO算法优化，旨在获得与控制系统最佳匹配的参数组合，使响应误差趋近于0。与此同时控制效果体现为最大超调量MP、上升时间tr、峰值时间tp、调节时间ts等响应性能综合值最小，从而最终选定目标函数为ITAE（Integral of Time-weighted Absolute Error，时间加权绝对误差积分）。
ITAE通过将系统偏差的绝对值与时间t进行积分，能更全面地反映系统的稳定性和动态响应特性，其值越小，表明系统稳定性越强，动态响应速度越快。
2.3.3　优化模糊PID控制器的基本过程
采用多元宇宙算法（MVO）对带式输送机控制系统的模糊PID控制器的Kp、Ki、Kd参数和模糊逻辑规则进行优化，最终输出优化后的Kp、Ki、Kd参数和改进后的模糊逻辑规则[17]。具体的优化过程如下。
（1）初始化。最大迭代次数C=10,WEPmin=0.2,WEPmax=1,p=6。
（2）定义目标函数。计算每个宇宙的膨胀率获得最优宇宙，根据轮盘赌选择机制实现宇宙中的物质迁移。并将优化后的模糊控制规则和Kp、Ki、Kd参数赋予控制器。
（3）更新WEP（虫洞存在概率）和TDR（旅行距离率）参数，运用这两个参数并更新最优宇宙位置，并同步运行控制系统模型。若达到了预设的迭代次数和适应度阈值，则输出最优参数并终止算法，否则返回第二步。
多元宇宙算法(MVO)优化模糊PID控制器的流程如图3所示。
优化过程中输入e0、ec以及输出Kp在优化前后的模糊规则变化分别如图4、图5和图6所示。
3　仿真结果分析
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分别采用传统PID控制器、模糊PID控制器和多元宇宙算法优化模糊PID控制器对带式输送机控制系统进行控制效果对比，相应的性能指标对比结果见表3。
由表3可知，对比MVO-Fuzzy-PID和Fuzzy-PID的响应发生性能指标得出，MVO-Fuzzy-PID控制器作用后的上升时间从10.98 s下降到7.582 s，下降了31%，表明MVO优化后的控制系统响应速度提高了；调节时间从17.144 s下降到10.885 s，下降了36.5%，且超调量下降了0.527 5个百分点，表明系统的响应与期望值更加接近，其稳定性得到显著提升。相比之下，MVO-Fuzzy-PID的稳态误差更快趋于0，说明其控制系统的抗干扰能力更强。
图7 为3种PID控制器的阶跃响应曲线，图8为MVO算法的适应度值随迭代次数变化的ITAE演化曲线。
由图7可以看出，MVO-Fuzzy-PID较其他控制方法显著改善了系统响应指标，在控制精度和动态性能方面均取得显著提升，表现出更优异的综合控制效果。
如图8所示，适应度值(ITAE)表征带速误差的时间加权积分，其值等于系统响应曲线与设定值直线之间的面积总和。优化过程中，适应度值从最初迭代的1 022降至最终迭代的901.8，呈现明显的收敛趋势，并最后趋于稳定。ITAE值越小，表示系统的响应速度越快且误差越小，验证了控制系统综合性满足设计要求。
4　仿真结果与实际控制曲线对比
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为验证MVO-Fuzzy-PID控制系统对速度的调控特性，本文选取龙泉煤矿4205工作面顺槽的带式输送机为测试对象，对其在1 m/s、2 m/s、3 m/s、4 m/s和5 m/s的5个速度阶段（每阶段60 s，总计300 s）的实际运行数据与MVO-Fuzzy-PID控制后的数据进行对比分析（如图9所示）。
由图9可以看出，MVO-Fuzzy-PID控制的调控带速（见电子版黄线）较实际带速（见电子版红线）具有更快的动态响应和更高的稳定性，能更精确地跟踪期望带速（见电子版蓝线）。实际带速和调控带速的5个波动区间见表4。由表4可以看出，MVO-Fuzzy-PID调控带速的波动范围较实际带速的波动范围明显收窄，表明优化控制系统能更准确地跟踪设定值，具有更优异的均衡效果。
在总功率与带速正相关的条件下，为最小化功率损耗，需使带速和煤流量实现最优匹配。针对5个固定煤流量运输阶段，通过计算实际带速曲线与横坐标轴的面积以及调控带速曲线与横坐标的面积，进行比较带速的变化，从而得出功率的使用情况[18]。在控制仿真总时间为300 s和额定带速为4 m/s的情况下，额定带速曲线面积为4×300=1 200，在MATLAB中使用相应的函数计算工具可得出调控带速和实际带速分别与横坐标时间的面积，结果见表5。
由表5可知，实际带速与调控带速的累计曲线面积分别为897和891，较额定曲线面积分别减少了303和309，表明调控带速比实际带速对应的电动机总功率减少得更多，故MVO算法优化控制使电机总功率损耗进一步降低，节能效果显著提升。
结合图9、表4和表5的数据可知，MVO-Fuzzy-PID控制带式输送机可以使控制时间内的带速反应更快、更稳定，且煤流量匹配度得以提升，单位能耗更低。
5　结论
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针对实际生产过程中带式输送机的皮带速度智能控制问题，本研究通过分析带式输送机的控制机理和建立数学模型，提出了一种基于多元宇宙算法的模糊PID控制器实现带速实时控制。MVO算法通过动态更新WEP和TDR两个参数，保证了最优宇宙的计算能力，使算法有更快的寻优速度。通过对比分析3种不同控制器的仿真情况，验证了MVO算法在控制系统中取得了较好的优化效果，主要结论如下。
（1）相较于Fuzzy-PID控制，MVO-Fuzzy-PID控制器将带式输送机系统的调节时间从17.144 s缩短至10.885 s，下降了36.5%，超调量下降了0.527 5个百分点，表明系统稳定性显著提升，同时增强了抗干扰能力，并提高了控制精度。
（2）MVO-Fuzzy-PID控制器的ITEA适应度值随着迭代次数的变化而不断收敛，从初始迭代的1 022到第10次迭代的901.8，即系统的响应速度越快且误差越小，表明了系统的综合性能得到显著改善。
（3）MVO-Fuzzy-PID调控带速的波动范围较实际带速明显收窄，表明调控带速能更准确快速地接近设定值。经过对比分析实际带速曲线和调控带速曲线的时间积分面积，MVO-Fuzzy-PID优化后的调控带速所对应的电动机总功率显著降低，表明MVO算法优化带速控制既实现了节能控制又可以快速响应煤流量的变化。
基金
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  • 国家自然科学基金资助项目(51974191)
  • 山西省省筹资助回国留学人员项目(2021-059)
  • 2023年山西省高等学校教学改革创新项目(J20230222)
  • 智能机器人湖北省重点实验室开放基金资助项目(HBIR 202310)
文献
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2025年第45卷第9期
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  • 接收时间：2024-10-14
  • 首发时间：2026-10-28
  • 出版时间：2025-09-25
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  • 收稿日期：2024-10-14
基金
国家自然科学基金资助项目(51974191)
山西省省筹资助回国留学人员项目(2021-059)
2023年山西省高等学校教学改革创新项目(J20230222)
智能机器人湖北省重点实验室开放基金资助项目(HBIR 202310)
作者信息
    太原理工大学矿业工程学院，山西　太原　030024

通讯作者:

孟巧荣（1974—），女，山西朔州人，博士，副教授，主要从事原位改性采矿、智能开采方面的研究。E-mail:
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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