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Article(id=1311999762690310970, tenantId=1146029695717560320, journalId=1311385739772133495, issueId=1311999647825101743, articleNumber=null, orderNo=null, doi=10.6041/j.issn.1000-1298.2025.12.016, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1736438400000, receivedDateStr=2025-01-10, revisedDate=1737734400000, revisedDateStr=2025-01-25, acceptedDate=null, acceptedDateStr=null, onlineDate=1790734719202, onlineDateStr=2026-09-30, pubDate=1766592000000, pubDateStr=2025-12-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1790734719202, onlineIssueDateStr=2026-09-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1790734719202, creator=13701087609, updateTime=1790734719202, updator=13701087609, issue=Issue{id=1311999647825101743, tenantId=1146029695717560320, journalId=1311385739772133495, year='2025', volume='56', issue='12', pageStart='1', pageEnd='818', issueExtLink='null', onlineDate='null', pubDate='1766592000000', pubDateStr='2025-12-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1790734691815, creator='13701087609', updateTime=1790738411040, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1312015247465083866, tenantId=1146029695717560320, journalId=1311385739772133495, issueId=1311999647825101743, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1312015247465083867, tenantId=1146029695717560320, journalId=1311385739772133495, issueId=1311999647825101743, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=180, endPage=189, ext={EN=ArticleExt(id=1311999762883248955, articleId=1311999762690310970, tenantId=1146029695717560320, journalId=1311385739772133495, language=EN, title=Design and Test of Tractor Tillage Depth Control System Based on Optimal Draft-position Comprehensive Degree, columnId=1311999648647185329, journalTitle=Transactions of the Chinese Society for Agricultural Machinery, columnName=Special Column of Key Technologies for Intelligent Agricultural Power Equipment, runingTitle=null, highlight=null, articleAbstract=

Aiming at the problem that the artificial setting of comprehensive coefficient is difficult to adapt to the complex and changeable working environment of soil conditions in the process of tractor electro-hydraulic suspension tillage depth control, a tillage depth control method based on optimal draft-position comprehensive coefficient was proposed. Firstly, the test platform of tractor electro-hydraulic suspension draft-position integrated tillage depth control and loading system was built and the system was modeled by system identification method. Then aiming at the problem of uncertain parameters of the equivalent transfer function of the system, a global sliding mode control algorithm was designed, and an arc-tangent function was introduced to reduce the chattering of the system. The full factor sample test was designed, and the comprehensive operation evaluation index was established by compromise programming method. The expected draft-position comprehensive coefficient under different working conditions was obtained, and the optimal draft-position comprehensive model was established based on the least squares support vector machine optimized by particle swarm optimization algorithm (PSO-LSSVM). Finally, the effect of the control system was verified by using the built control system test platform. The results showed that the proposed algorithm achieved a rise time of 1.06 s without noticeable chattering. Compared with the fixed weight-depth control method with a comprehensive coefficient of 0.5, the proposed method reduced the depth deviation rate by 19.5% and 13.9% at target depths of 140 mm and 220 mm, respectively, while improving depth uniformity by 16.6% and 11.2%. This method can realize the adaptive adjustment of the comprehensive coefficient according to the soil specific resistance and tillage depth, and was more adaptable to the complex field operation environment, which provided a reference for the research of tillage depth control method.

, authors=Xiaoxu SUN, Huawei LÜ, Jin QIAN, Yue SONG, Zhixiong LU, authorsList=Xiaoxu SUN, Huawei LÜ, Jin QIAN, Yue SONG, Zhixiong LU, authorCompany=null, correspAuthors=Zhixiong LU, 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=1311999770663682970, articleId=1311999762690310970, tenantId=1146029695717560320, journalId=1311385739772133495, language=CN, title=基于最优力位综合度的拖拉机耕深控制系统设计与试验, columnId=1311999648798180275, journalTitle=农业机械学报, columnName=智能农业动力装备关键技术专栏, runingTitle=null, highlight=null, articleAbstract=

针对拖拉机电液悬挂力位综合耕深控制过程中，人工设定力位综合度难以适应土壤条件复杂多变的作业环境问题，提出了一种基于最优力位综合度的耕深控制方法。搭建了拖拉机电液悬挂力位综合耕深控制与加载系统试验平台并采用系统辨识方法进行系统建模。针对系统等效传递函数参数不确定问题，设计了一种全局滑模控制算法，并引入反正切函数以降低系统抖振。设计全因子样本试验，采用折衷规划法建立综合作业评价指标，得到不同工况下的期望力位综合度并基于粒子群优化的最小二乘支持向量机（PSO-LSSVM）建立最优力位综合度模型。利用搭建的控制系统试验平台对控制系统效果进行了验证。结果表明，本文算法上升时间为1.06 s且无明显抖振；相比于固定力位综合度为0.5的耕深控制方法，本文方法在目标耕深140、220 mm的耕深偏差率分别减小19.5%和13.9%，耕深均匀性提高16.6%和11.2%。该方法可以根据土壤比阻和耕深实现力位综合度的自适应调节，面对复杂田间作业环境适应性更强，为耕深控制方法研究提供了参考。

, authors=孙晓旭, 吕华伟, 钱进, 宋悦, 鲁植雄, authorsList=孙晓旭, 吕华伟, 钱进, 宋悦, 鲁植雄, authorCompany=null, correspAuthors=鲁植雄, authorNote=

孙晓旭（1995—），男，博士生，主要从事车辆电子控制技术研究，E-mail：

, correspAuthorsNote=
鲁植雄（1962—），男，教授，博士生导师，主要从事车辆电子控制技术研究，E-mail：
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孙晓旭（1995—），男，博士生，主要从事车辆电子控制技术研究，E-mail：

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孙晓旭（1995—），男，博士生，主要从事车辆电子控制技术研究，E-mail：

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1. 电磁换向阀　2. 安全阀　3. 蓄能器　4. 压力传感器　5. 过滤器　6. 液位计　7. 液压泵　8. 电机　9. 比例溢流阀　10. 加载液压缸　11. 力传感器　12. 无源阻尼液压缸　13. 单向节流阀　14. 试验犁架

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Parameter identification results

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k/（N·mm-2）a0b2b1b0RMSE/mmR2
0.030.259 63.896 67.142 00.106 41.056 60.998 3
0.040.258 23.546 56.851 00.098 00.942 50.998 5
0.050.277 63.528 57.084 60.067 31.228 40.996 8
0.060.300 73.592 97.473 60.114 01.060 80.998 2
0.070.314 33.606 27.654 70.089 21.265 90.997 8
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参数辨识结果

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k/（N·mm-2）a0b2b1b0RMSE/mmR2
0.030.259 63.896 67.142 00.106 41.056 60.998 3
0.040.258 23.546 56.851 00.098 00.942 50.998 5
0.050.277 63.528 57.084 60.067 31.228 40.996 8
0.060.300 73.592 97.473 60.114 01.060 80.998 2
0.070.314 33.606 27.654 70.089 21.265 90.997 8
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Weight of each evaluation index under different working conditions

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犁耕作业w1w2w3
浅耕0.570.210.22
中耕0.270.180.55
深耕0.170.570.26
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不同工况下各评价指标权重

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犁耕作业w1w2w3
浅耕0.570.210.22
中耕0.270.180.55
深耕0.170.570.26
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基于最优力位综合度的拖拉机耕深控制系统设计与试验
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孙晓旭 , 吕华伟 , 钱进 , 宋悦 , 鲁植雄
农业机械学报 | 智能农业动力装备关键技术专栏 2025,56(12): 180-189
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农业机械学报 |智能农业动力装备关键技术专栏 2025 , 56 (12) : 180 -189
基于最优力位综合度的拖拉机耕深控制系统设计与试验
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孙晓旭 , 吕华伟, 钱进, 宋悦, 鲁植雄
作者信息
  • 南京农业大学工学院，南京　210031
通讯作者:
鲁植雄（1962—），男，教授，博士生导师，主要从事车辆电子控制技术研究，E-mail：
作者简介:

孙晓旭（1995—），男，博士生，主要从事车辆电子控制技术研究，E-mail：

Design and Test of Tractor Tillage Depth Control System Based on Optimal Draft-position Comprehensive Degree
Xiaoxu SUN , Huawei LÜ, Jin QIAN, Yue SONG, Zhixiong LU
Affiliations
  • College of Engineering, Nanjing Agricultural University, Nanjing 210031, China
出版时间: 2025-12-25 doi: 10.6041/j.issn.1000-1298.2025.12.016
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摘要
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针对拖拉机电液悬挂力位综合耕深控制过程中，人工设定力位综合度难以适应土壤条件复杂多变的作业环境问题，提出了一种基于最优力位综合度的耕深控制方法。搭建了拖拉机电液悬挂力位综合耕深控制与加载系统试验平台并采用系统辨识方法进行系统建模。针对系统等效传递函数参数不确定问题，设计了一种全局滑模控制算法，并引入反正切函数以降低系统抖振。设计全因子样本试验，采用折衷规划法建立综合作业评价指标，得到不同工况下的期望力位综合度并基于粒子群优化的最小二乘支持向量机（PSO-LSSVM）建立最优力位综合度模型。利用搭建的控制系统试验平台对控制系统效果进行了验证。结果表明，本文算法上升时间为1.06 s且无明显抖振；相比于固定力位综合度为0.5的耕深控制方法，本文方法在目标耕深140、220 mm的耕深偏差率分别减小19.5%和13.9%，耕深均匀性提高16.6%和11.2%。该方法可以根据土壤比阻和耕深实现力位综合度的自适应调节，面对复杂田间作业环境适应性更强，为耕深控制方法研究提供了参考。

耕深控制系统  /  最小二乘支持向量机  /  参数辨识  /  全局滑模控制  /  最优力位综合度

Aiming at the problem that the artificial setting of comprehensive coefficient is difficult to adapt to the complex and changeable working environment of soil conditions in the process of tractor electro-hydraulic suspension tillage depth control, a tillage depth control method based on optimal draft-position comprehensive coefficient was proposed. Firstly, the test platform of tractor electro-hydraulic suspension draft-position integrated tillage depth control and loading system was built and the system was modeled by system identification method. Then aiming at the problem of uncertain parameters of the equivalent transfer function of the system, a global sliding mode control algorithm was designed, and an arc-tangent function was introduced to reduce the chattering of the system. The full factor sample test was designed, and the comprehensive operation evaluation index was established by compromise programming method. The expected draft-position comprehensive coefficient under different working conditions was obtained, and the optimal draft-position comprehensive model was established based on the least squares support vector machine optimized by particle swarm optimization algorithm (PSO-LSSVM). Finally, the effect of the control system was verified by using the built control system test platform. The results showed that the proposed algorithm achieved a rise time of 1.06 s without noticeable chattering. Compared with the fixed weight-depth control method with a comprehensive coefficient of 0.5, the proposed method reduced the depth deviation rate by 19.5% and 13.9% at target depths of 140 mm and 220 mm, respectively, while improving depth uniformity by 16.6% and 11.2%. This method can realize the adaptive adjustment of the comprehensive coefficient according to the soil specific resistance and tillage depth, and was more adaptable to the complex field operation environment, which provided a reference for the research of tillage depth control method.

tillage depth control system  /  PSO-LSSVM  /  parameter identification  /  global sliding mode control  /  optimal draft-position comprehensive degree
孙晓旭, 吕华伟, 钱进, 宋悦, 鲁植雄. 基于最优力位综合度的拖拉机耕深控制系统设计与试验. 农业机械学报, 2025 , 56 (12) : 180 -189 . DOI: 10.6041/j.issn.1000-1298.2025.12.016
Xiaoxu SUN, Huawei LÜ, Jin QIAN, Yue SONG, Zhixiong LU. Design and Test of Tractor Tillage Depth Control System Based on Optimal Draft-position Comprehensive Degree[J]. Transactions of the Chinese Society for Agricultural Machinery, 2025 , 56 (12) : 180 -189 . DOI: 10.6041/j.issn.1000-1298.2025.12.016
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0　引言
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拖拉机作为众多农业机械中实现农机具驱动和牵引的重要装备，长期以来被广泛运用于一系列的农业生产作业过程[1]。其中电液悬挂系统是实现拖拉机田间作业过程中动力传递和作业深度控制的关键部件，其性能直接影响拖拉机整个作业机组的作业质量[2]。因此，研究性能稳定、生产效率高、作业质量好的拖拉机电液悬挂系统，受到农机行业的重视。但由于拖拉机作业环境的复杂性与多样性，拖拉机作业过程往往呈现出较强的非线性特点，从而给拖拉机电液悬挂控制系统设计带来巨大挑战[3-6]。随着智能化与精准化农业的不断发展，如何提高拖拉机电液悬挂控制系统的作业质量和作业效率，实现拖拉机耕作深度的自适应控制成为学者研究的热点问题之一[7-10]。
力位综合耕深控制方法相对于单一的力控制方法和位控制方法，可以更好地综合两种控制方法在维持耕深稳定性和发动机负荷稳定性方面的优势，能适应多种作业环境，因此具有更加长远的研究价值。SHAFAEI等[11]设计了拖拉机模糊耕深-牵引力控制系统，根据轮胎滑转和实际耕深制定模糊控制规则，并进行了田间试验验证，结果表明，相对于传统的力控制系统，拖拉机模糊耕深-牵引力控制系统的牵引效率和总能效分别提高20%和73%。商高高等[12]对开关切换法和加权系数法两种力位综合耕深控制方法进行了研究，建立了拖拉机电液悬挂力位综合控制数学模型并进行了仿真分析，结果表明，加权系数法具有更加长远的研究和应用意义。文献[13-15]设计了拖拉机力位综合耕深控制系统，进行了不同力位综合度下控制效果的对比分析，但都仅限于人工设定力位综合度，实际作业效果受到人为因素的影响。李明生[16]设计了一种变权重的力位综合控制方案，驾驶员首先设定一个初始力位综合度，再根据作业过程中土质变化适当增加或减小力控制权重。但该方案的初始力位综合度和力位综合度的调节，仍需要驾驶员根据经验完成。王素玉等[17]通过建立拖拉机变权重力位综合仿真模型，根据仿真结果得到了权重系数取值范围与土壤比阻的近似关系，并通过试验验证了变权重力位综合控制方法的优势。
综上所述，目前针对拖拉机力位综合控制，相关学者进行了大部分研究。但大都局限于人工设定力位综合度进行对比分析，力位综合度受到人为因素影响。针对复杂田间作业环境下力位综合度自适应的力位综合控制方法研究少有报道。因此，本文提出一种基于最优力位综合度的拖拉机耕深控制方法。首先，引入力-等效耕深系数和最优力位综合度模型，设计拖拉机最优力位综合度的耕深控制方法并搭建拖拉机电液悬挂耕深控制平台。其次，基于试验平台输入与输出响应间的关系，采用参数辨识方法对拖拉机电液悬挂耕深控制系统进行等效传递函数建模。然后，进行不同耕深、不同土壤比阻和不同力位综合度的3因素全因子样本试验，采用折衷规划法建立包含耕深均匀性、负荷稳定性和牵引效率的综合作业评价指标目标函数，并基于层次分析法对不同工况下作业评价指标进行权重判定。最后，将不同工况下的期望力位综合度作为样本数据，基于PSO-LSSVM建立最优力位综合度模型并进行试验验证。
1　拖拉机电液悬挂最优力位综合度耕深控制系统搭建
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1.1　最优力位综合度耕深控制原理
拖拉机耕深力位综合控制是一种将位置控制和牵引力控制特点进行综合应用的控制方法，结合了位置控制时耕深稳定性好和牵引力控制时负荷稳定性好的优点。当遇到路面起伏、土质波动地段，耕深力位综合控制方法既可以通过减小或增大耕深调节牵引阻力的变化，维持拖拉机负荷稳定性，又可以在一定程度上抑制耕深调节的幅度，从而保证一定的耕作质量。
拖拉机最优力位综合度耕深控制方法原理如图1所示。驾驶员通过操作面板设定耕深目标值Hset，作业开始前，拖拉机先进行预耕作业，通过位移传感器反馈的实际耕深H和牵引力传感器反馈的实际牵引阻力F，计算作业环境的初始力-等效耕深系数B0；开始作业后，力传感器反馈的实际工作阻力与初始力-等效耕深系数B0计算实时阻力的等效耕深；力传感器反馈的实际工作阻力与位移传感器反馈的实际耕深计算实时力-等效耕深系数B用来反馈作业土壤条件的变化；最优力位综合度模型则根据实时力-等效耕深系数B和位移传感器反馈的实际耕深输出此时最优力位综合度a；最后，耕深反馈计算模型利用最优力位综合度a和当前位移传感器与力传感器的反馈计算最终的耕深反馈值Hback并与驾驶员设定的耕深目标值Hset进行比较，计算实际耕深偏差输入到耕深控制器中进行耕深控制。
1.2　耕深控制与加载试验平台搭建
1.2.1　耕深控制台架结构与原理
拖拉机电液悬挂耕深控制台架整体结构如图2所示。台架整体结构由机械、液压、控制柜3部分组成[18]。
机械部分包括整体框架、三点悬挂杆件机构、试验犁架、提升液压缸和加载液压缸。其中整体框架为整个试验平台提供支撑；三点悬挂杆件机构为农机具的上下运动提供动力；试验犁架则模拟实际农具；提升液压缸作用在提升臂上，为农具的提升提供动力；加载液压缸作用在试验犁架上，用来模拟实际作业过程中的土壤阻力。
液压部分主要包括电机、液压泵、滤油器、电液比例溢流阀、电液比例换向阀、耕深控制阀和油管等。其中电机和液压泵为整个液压油路提供动力；2个电液比例溢流阀分别用来调节提升液压主油路和加载液压主油路压力；电液比例换向阀用来实现加载液压缸的前进与后退，从而控制加载力方向；耕深控制阀则用于控制提升液压系统流量，从而控制农具位置。
控制柜部分主要包括显示屏、控制器、操作手柄、比例放大器和相关转换电路板等。其中，显示屏与操作手柄通过CAN总线与控制器相连，显示屏用于整个控制系统的信号监测与显示；操作手柄用于设定目标耕深，选择工作模式。控制器为EPEC3610型控制器（EPEC Oy，芬兰），通过Codesys编程环境进行控制算法编写。根据传感器反馈信号，控制器根据控制算法计算控制量并输出给耕深控制阀；比例放大器用来放大信号给电磁比例溢流阀；相关转换电路板则负责台架信号连接过程中所需要的信号类型转换。
1.2.2　试验台模拟加载系统设计
拖拉机在田间进行犁耕作业时一般保持稳定的耕作速度，因此，影响犁耕阻力的因素主要有土壤比阻和耕深。根据前期进行的拖拉机犁耕阻力理论分析以及田间犁耕阻力测试试验将犁耕阻力划分为稳态阻力和动态阻力[18-19]。当耕深稳定，犁体在竖直方向不产生位移，此时受到的水平方向和竖直方向阻力与耕深成正比。将水平方向和竖直方向阻力合成，得到稳态阻力，即
式中
      Rx——水平方向阻力，N
      Rz——竖直方向阻力，N
      Rw——稳态阻力，N
      k——土壤比阻，N/mm2
      b——耕宽，mm      h——耕深，mm
      θ——稳态阻力与水平方向夹角，（°）
当耕深由于路面不平、车身俯仰等发生变化时，这种耕深的变化可以理解为相对于目标耕深的振动，此时会在犁体上产生竖直方向的动态阻力，满足
式中
      Rd——动态阻力，N      kd——系数
      vz——犁架提升速度，mm/s
综上，拖拉机在进行犁耕作业时，犁体受到的土壤阻力简化成与水平方向呈θ角的稳态阻力Rw和由耕深变化而产生的竖直方向动态阻力Rd。基于此，设计了一种双液压缸模拟加载方案。加载系统结构与原理如图3所示。
阻力模拟加载系统主要包括电机、液压泵、电液比例溢流阀、电磁换向阀、加载液压缸、无源阻尼液压缸、加载液压缸固定柱和拉压力传感器。加载液压缸和无源阻尼液压缸分别用来模拟试验犁架受到的稳态阻力和动态阻力，控制柜通过传感器反馈信号调节电液比例溢流阀进口压力以控制系统压力，实现对稳态阻力大小的控制，同时，在加载液压缸固定柱上设计滑槽，用来改变稳态阻力的加载方向。在阻尼液压缸和试验犁架连接处，设计脱钩，当试验犁架提升离开设定地面时，脱钩则自动打开。
2　基于粒子群优化算法的拖拉机电液悬挂系统参数辨识
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2.1　电液悬挂非线性系统等效传递函数
拖拉机电液悬挂耕深控制系统整个控制过程的信号转换主要分为4部分：①耕深控制阀接收电信号，根据电磁感应原理转换为电磁力推动阀芯运动，实现电信号与阀芯位移信号转换。②耕深控制阀阀芯位移改变阀口开度，从而引起通过阀流量变化，实现阀芯位移信号与阀流量转换。③经过耕深控制阀的液压油流入液压缸中，基于流量平衡和外负载平衡，从而推动液压缸活塞位移，实现流量与活塞位移信号转换。④活塞位移推动悬挂机构提升臂转动，经过连杆传递，实现活塞位移信号与耕深信号转换。同时电液悬挂耕深控制系统中的传感器将采集的信号反馈给控制器，实现闭环控制。以此为基础，建立电液悬挂系统传递函数形式为
式中
      Y（s）——液压缸位移拉氏变换
      U（s）——控制量拉氏变换
      a0——传递函数分子系数
      b0、b1、b2——传递函数分母系数
2.2　输出误差准则函数
等价准则是模型参数辨识的三大要素之一，通过误差准则判定模型结构，评判模型预报能力是一种客观可信的方法[20]。本研究通过构建系统的输出误差准则函数作为粒子群优化算法（PSO）迭代搜索的目标函数，从而寻找出满足与实际系统的响应输出误差最小的系统参数最优值。
根据式（3）得到系统预测输出为
式中
      、、、——系数预测值
则辨识后误差e（k）为
通过均方根误差构建误差准则函数J，得到
式中
      N——样本数量
2.3　基于台架试验的辨识数据获取
利用搭建的拖拉机耕深控制台架试验平台获取参数辨识所需要的系统输入输出数据。为充分观察不同输入信号下拖拉机电液悬挂系统的响应输出，设计阶跃信号作为试验台的信号输入，试验过程如图4所示。考虑所搭建的电液悬挂系统试验平台在不同外负载干扰下的响应不同，利用试验平台的加载系统，模拟不同土壤比阻对试验犁架进行加载。因此，本文辨识数据获取试验分别在土壤比阻0.03、0.04、0.05、0.06、0.07 N/mm2下进行，共获得5组样本数据，采样周期取25 ms，系统响应曲线如图5所示。
根据得到的等效传递函数以及台架辨识数据，采用PSO算法，基于建立的输出误差准则函数构建PSO寻优算法的目标函数，对等效传递函数中的系数进行寻优计算，求解a0、b0、b1和b2最优值。寻优过程中目标函数与待辨识系数迭代过程如图6所示（受篇幅限制，仅给出k取0.03 N/mm2结果）。将辨识后由传递函数输出得到的系统响应与原系统输出得到的响应曲线进行对比，以2条曲线的均方根误差（RMSE）和决定系数（R2）作为评价指标评价辨识结果精度，如表1所示。
3　基于反正切切换项的耕深全局滑模控制器设计
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3.1　系统状态空间方程
对式（3）进行变化，得到
式中
      y——液压缸位移
      u——控制量
选取系统状态变量
式中
      x1、x2、x3——液压缸位移、速度和加速度
得到系统状态方程为
3.2　控制器设计
设输入目标液压缸位移为r，则全局动态滑模面设计为
其中
式中
      c1、c2、λ——滑模面参数
      x10、x20、x30——液压缸位移、速度和加速度初值
      r0——输入目标液压缸位移初始值
根据前文不同工况下参数辨识结果，确定拖拉机电液悬挂等效传递函数系数范围。设a0变化范围为[0.25，0.32]；b0变化范围为[0.01，0.2]；b1变化范围为[6，8]；b2变化范围为[3.5，4]。取
根据系统状态方程，令
设计全局滑模控制率为
其中
式中
      uc——线性控制项
      uvss——切换项
      m——滑模参数
联立式（16）、（17）可得
为了降低抖振，采用反正切函数代替切换函数，设计控制率中切换项为
其中
式中
      ε——增益项
联立式（19）~（21）得
定义Lyapunov函数为
则
即
4　最优力位综合度模型建立
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4.1　基于传递函数的全因子样本试验方案
为分析不同力位综合度对拖拉机犁耕作业质量的影响，基于辨识得到的系统响应模型搭建拖拉机耕深控制仿真试验平台。选取耕深、土壤比阻和力位综合度作为试验变量。其中，根据拖拉机一般常用犁耕作业深度范围，取耕深分别为100、140、180、220、260、300 mm。根据不同土壤类型的实测比阻，取土壤比阻分别为0.03、0.04、0.05、0.06、0.07 N/mm2。力位综合度为位置控制所占权重，分别取0、0.1、0.2、0.3、0.4、0.5、0.6、0.7、0.8、0.9、1.0。采用全因子试验方法对多因素多水平组合工况进行试验，共计330组试验。
4.2　不同工况作业评价指标建立
将耕深均匀性、负荷稳定性和牵引效率作为不同工况下犁耕作业质量评价指标。
4.2.1　耕深均匀性
耕深均匀性即拖拉机犁耕作业时到达目标耕深以后耕深波动程度。耕深均匀性系数f4计算式为
4.2.2　负荷稳定性
负荷稳定性即拖拉机犁耕作业时到达稳定耕深以后牵引力波动程度。负荷稳定性系数f5计算式为
4.2.3　牵引效率
牵引效率表示拖拉机挂接农具在平整地块耕作时所需功率与系统输出有效功率之比，可以表示为
式中
      ηc——机械传动效率
      ηf——车轮滚动效率
      ηs——驱动车轮滑转效率
      ηT——牵引效率
传动效率由机组整体结构决定，而一定地面条件下，以常数近似表示滚动阻力；滑转效率则取决于车轮的滑转程度，牵引效率f6可表示为
式中
      s′——驱动轮滑转率
由于搭建的试验平台为室内台架，无法测量实际滑转率来计算拖拉机传动效率。因此，通过轮胎力与滑转率的关系，根据试验平台实时牵引阻力的变化来模拟滑转率。驱动轮滑转率与轮胎力变化关系为[21]
式中
      Ft——拖拉机牵引力，N
      Fz——轮胎垂直反力，N
      φ——地面附着系数
      C——轮胎纵向刚度，N/mm
4.2.4　综合评价指标
为探究不同工况下最优力位综合度，基于折衷规划法建立耕深均匀性、牵引力稳定性和牵引效率的综合评价指标，其计算式为
式中
      w1、w2、w3——各指标权重
为得到最优力位综合度，即综合评价指标最小，需合理确定综合评价指标中各个不同指标的权重。根据耕深h的范围可以将犁耕作业划分为浅耕（h<180 mm）、中耕（180≤h≤220 mm）和深耕（h>220 mm）3种作业工况。根据实际不同工况下作业需求以及大量田间试验总结，采用层次分析法，判定不同工况下各个不同指标的权重，用于综合评价指标建立。当进行浅耕作业时，由于此时耕深较浅从而犁耕阻力较小，因此犁耕作业主要以保证耕深均匀性为主；当进行中耕作业时，对耕深均匀性和负荷稳定性要求一般，主要以减小滑转，提高效率为主；当进行深耕作业时，此时犁耕阻力较大，主要以维持作业过程中的负荷稳定性为主。基于层次分析法，得到不同工况下各评价指标权重如表2所示。
4.3　基于PSO-LSSVM的最优力位综合度模型建立
最小二乘支持向量机（LSSVM）是一种基于统计理论的改进型支持向量机（SVM），相对于传统的SVM，LSSVM采用平方误差作为损失函数并使用等式进行约束，在解决多变量校准问题上更具优势。目前已经成功应用于函数逼近和模式识别等多个领域[22-24]。
在使用LSSVM对样本进行训练过程中，模型训练结果会受到正则化参数c和核函数宽带系数σ的影响[25]。因此，本文采用PSO算法对训练过程中的c和σ进行优化，从而保证最优力位综合度模型训练的准确性和快速性。基于PSO-LSSVM的最优力位综合度模型建立过程如图7所示。
根据所搭建的拖拉机耕深-牵引力综合控制全因子试验平台并基于建立的综合评价指标，得到不同工况期望力位综合度如图8所示。将不同工况与其对应的期望力位综合度作为LSSVM模型训练的样本数据，取耕深h和土壤比阻k作为模型训练的输入样本，期望力位综合度作为输出，并采用PSO算法对训练过程中的正则化参数c和核函数宽带系数σ进行优化，最终得到最优力位综合度模型训练结果如图9所示。
5　验证试验
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5.1　控制算法效果对比
为验证本文设计的基于反正切函数的全局滑模控制算法优势，将本文设计的全局滑模控制、符号函数的全局滑模控制以及PD控制进行对比。设定目标耕深为100 mm，对比3种不同控制算法下的系统响应。
不同控制算法耕深响应曲线和控制量输出如图10所示。对比于全局滑模控制，PD控制存在一定超调，最大超调量达到10%；其次，由于系统参数不断变化，PD控制无法实现稳定跟踪，始终保持在目标值附近上下波动且存在一定的稳态误差，而全局滑模控制不存在稳态误差，能实现目标耕深的稳定跟踪。
对比采用符号函数全局滑模控制与本文全局滑模控制可知，本文算法上升时间为1.06 s，相比于采用符号函数全局滑模控制算法快0.37 s。另外，从图10b可以发现，采用符号函数全局滑模控制算法输出的控制量存在明显抖振，本文算法则无明显抖振，说明本文算法抗干扰能力更强。综上，本文算法与PD控制算法以及采用符号函数全局滑模控制算法相比动态响应快，具有更好的系统适应性和鲁棒性。
5.2　耕深控制结果
为验证本文提出的最优力位综合度耕深控制方法的优势，利用搭建的拖拉机电液悬挂耕深控制系统试验平台进行了与固定力位综合度为0.5的控制方法的对比试验。通过试验平台加载系统，模拟土壤比阻0.03~0.07 N/mm2随机波动对试验犁架进行犁耕阻力加载。设定目标耕深为140 mm和220 mm，试验结果如图11所示。
由图11可知，当设定目标耕深为140 mm时，随着土壤比阻的变化，采用固定力位综合度为0.5的耕深控制方法平均耕深为115 mm，与目标耕深偏差为25 mm，计算得到此时耕深均匀性系数为0.84，负荷稳定性系数为0.88；而采用本文最优力位综合度耕深控制方法的平均耕深为137 mm，与目标耕深偏差仅为3 mm，此时耕深均匀性系数为0.98，负荷稳定性系数为0.83。由此可知，目标耕深为140 mm时，采用本文最优力位综合度耕深控制方法耕深偏差率减小19.5%，耕深均匀性提高16.6%；当设定目标耕深为220 mm时，随着土壤比阻的变化，采用固定力位综合度为0.5的耕深控制方法平均耕深为176 mm，与目标耕深偏差为44 mm，此时耕深均匀性系数为0.80，负荷稳定性系数为0.84；而采用本文最优力位综合度耕深控制方法平均耕深为198 mm，与目标耕深偏差仅为22 mm，此时耕深均匀性系数为0.89，负荷稳定性系数为0.82。由此可知，当目标耕深为220 mm时，采用本文最优力位综合度耕深控制方法耕深偏差率减小13.9%，耕深均匀性提高11.2%。
对比试验结果可以发现，当目标耕深为140 mm时，由于此时耕深较浅，实际犁耕阻力较小，在此工况下，对负荷稳定性要求较低，因此，本文最优力位综合度模型输出的力位综合度较小，即更偏向于位置控制。所以采用本文方法的实际耕深与目标耕深间偏差更小且耕深均匀性更好。当目标耕深为220 mm时，耕深增大，实际犁耕阻力增大，当土壤比阻增大时，对负荷稳定性的要求提高，因此，为了保证一定的负荷稳定性，相比于浅耕工况，此时最优力位综合度模型输出的力位综合度增大，即力控制权重相对增加；而当土壤比阻减小时，力位综合度相对减小，即增加位置控制权重，因此，相对于固定力位综合度为0.5的耕深控制方法，耕深均匀性更好。
6　结论
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（1）针对拖拉机电液悬挂耕深控制系统特点，搭建了基于EPEC的控制系统平台，通过建立综合作业评价指标，根据全因子样本试验结果，得到力位综合度与土壤比阻和耕深间的关系。
（2）设计了一种基于全局滑模耕深控制算法，通过引入反正切函数设计滑模控制切换项并与PD控制和传统采用符号函数切换项的滑模控制算法进行对比，结果表明，相对于PD控制算法，本文算法可以实现目标耕深的稳定跟踪；相对于传统采用符号函数切换项的滑模控制算法，本文算法上升时间为1.06 s，提高0.37 s。并且系统无明显抖振，说明本文算法具有较好鲁棒性。
（3）在目标耕深140 mm和220 mm下分别进行了固定力位综合度为0.5和本文提出的最优力位综合度方法的耕深控制试验。结果表明，本文提出的最优力位综合度耕深控制方法可以根据土壤比阻和耕深实现力位综合度自适应调节，相对于固定力位综合度为0.5方法，2种目标耕深下，本文方法耕深偏差率分别减小19.5%和13.9%，耕深均匀性分别提高16.6%和11.2%。
基金
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  • 国家重点研发计划项目(2020YFD2001202)
  • 江苏省研究生科研创新计划项目(KYCX22_0716)
文献
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2025年第56卷第12期
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doi: 10.6041/j.issn.1000-1298.2025.12.016
  • 接收时间：2025-01-10
  • 首发时间：2026-09-30
  • 出版时间：2025-12-25
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  • 收稿日期：2025-01-10
  • 修回日期：2025-01-25
基金
国家重点研发计划项目(2020YFD2001202)
江苏省研究生科研创新计划项目(KYCX22_0716)
作者信息
    南京农业大学工学院，南京　210031

通讯作者:

鲁植雄（1962—），男，教授，博士生导师，主要从事车辆电子控制技术研究，E-mail：
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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