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Article(id=1209871064692290096, tenantId=1146029695717560320, journalId=1189621681917173762, issueId=1209871062716781562, articleNumber=null, orderNo=null, doi=10.19620/j.cnki.1000-3703.20230950, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=null, receivedDateStr=null, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1766385340140, onlineDateStr=2025-12-22, pubDate=1727107200000, pubDateStr=2024-09-24, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1766385340140, onlineIssueDateStr=2025-12-22, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1766385340140, creator=13701087609, updateTime=1766385340140, updator=13701087609, issue=Issue{id=1209871062716781562, tenantId=1146029695717560320, journalId=1189621681917173762, year='2024', volume='', issue='9', pageStart='1', pageEnd='62', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1766385339669, creator=13701087609, updateTime=1766392185924, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1209899778067010242, tenantId=1146029695717560320, journalId=1189621681917173762, issueId=1209871062716781562, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1209899778067010243, tenantId=1146029695717560320, journalId=1189621681917173762, issueId=1209871062716781562, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=10, endPage=17, ext={EN=ArticleExt(id=1209871065803780663, articleId=1209871064692290096, tenantId=1146029695717560320, journalId=1189621681917173762, language=EN, title=A Model Predictive Tracking Control Study for Speed Trajectory of Autonomous Driving Trucks, columnId=null, journalTitle=Automobile Technology, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to prevent vehicle mass changes and road slope interfering with longitudinal speed of autonomous driving truck, this article utilizes an intelligent navigation system to obtain information including vehicle speed trajectory and road slope. Vehicle longitudinal dynamic model and Compressed Natural Gas (CNG) engine dynamic model are established, and a real-time Dynamic Programming (DP) speed trajectory tracking controller is designed based on the Model Predictive Control (MPC) framework. The simulation results under NEDC and WLTC operating conditions show that the controller can keep vehicle speed stable under conditions of truck mass change and road slope interference, and can optimize speed tracking error while reducing natural gas consumption.

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为避免车辆质量变化与道路坡度对自动驾驶载货汽车纵向车速控制的干扰，通过智能导航系统获取车辆速度轨迹及道路坡度信息，建立车辆纵向动力学模型和压缩天然气（CNG）发动机动力学模型，并基于模型预测控制（MPC）框架设计了一种实时的动态规划（DP）速度轨迹跟踪控制器。仿真结果表明，在新欧洲驾驶循环（NEDC）和全球统一轻型车辆测试循环（WLTC）工况下，该控制器在载货汽车质量变化和道路坡度干扰条件下能使车速保持稳定，并可在优化速度跟踪误差的同时降低发动机天然气消耗量。

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解方喜（1982—），男，教授，博士，主要研究方向为先进控制理论应用，。
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参数 取值 参数 取值
车辆质量M/kg 1 500 主减速比i0 4.05
空气密度ρ/kg·m-3 1.205 一挡速比i1 6.67
车辆迎风面积Af /m2 4 二挡速比i2 4.10
空气阻力系数cd 0.5 三挡速比i3 2.42
滚动阻力系数β 0.011 四挡速比i4 1.52
轮胎半径r/m 0.287 五挡速比i5 1
传动效率ηt 0.96 六挡速比i6 0.78
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车辆模型参数

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参数 取值 参数 取值
车辆质量M/kg 1 500 主减速比i0 4.05
空气密度ρ/kg·m-3 1.205 一挡速比i1 6.67
车辆迎风面积Af /m2 4 二挡速比i2 4.10
空气阻力系数cd 0.5 三挡速比i3 2.42
滚动阻力系数β 0.011 四挡速比i4 1.52
轮胎半径r/m 0.287 五挡速比i5 1
传动效率ηt 0.96 六挡速比i6 0.78
), ArticleFig(id=1209899465025122584, tenantId=1146029695717560320, journalId=1189621681917173762, articleId=1209871064692290096, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
控制器 参数 取值
PID控制器 比例系数P 6 000
积分系数I 10
微分系数D 100
DP控制器、DP_FO控制器、DP_SF控制器、DP_FOSF控制器 最大驱动力 F t m a x/N 8 000
最大制动力 F b m a x/N -8 000
油耗权重系数ωf 1
误差权重系数ωv 0.005
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控制器参数

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控制器 参数 取值
PID控制器 比例系数P 6 000
积分系数I 10
微分系数D 100
DP控制器、DP_FO控制器、DP_SF控制器、DP_FOSF控制器 最大驱动力 F t m a x/N 8 000
最大制动力 F b m a x/N -8 000
油耗权重系数ωf 1
误差权重系数ωv 0.005
), ArticleFig(id=1209899465264197921, tenantId=1146029695717560320, journalId=1189621681917173762, articleId=1209871064692290096, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
), ArticleFig(id=1209899465381638434, tenantId=1146029695717560320, journalId=1189621681917173762, articleId=1209871064692290096, language=CN, label=表3, caption=

NEDC无坡度工况验证

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车辆质量/kg 控制器 平均速度跟踪
误差/m·s-1		 累积天然气
消耗量/g
1 500 PID 0.70 466.98
DP 0.57 445.28
DP_FO 0.65 388.27
2 000 PID 0.79 515.11
DP 0.48 493.53
DP_FO 0.59 418.44
2 500 PID 0.87 567.30
DP 0.48 538.19
DP_FO 0.58 436.17
3 000 PID 0.96 624.76
DP 0.47 589.02
DP_FO 0.56 511.45
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NEDC无坡度工况误差值及累积天然气消耗量

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车辆质量/kg 控制器 平均速度跟踪
误差/m·s-1		 累积天然气
消耗量/g
1 500 PID 0.70 466.98
DP 0.57 445.28
DP_FO 0.65 388.27
2 000 PID 0.79 515.11
DP 0.48 493.53
DP_FO 0.59 418.44
2 500 PID 0.87 567.30
DP 0.48 538.19
DP_FO 0.58 436.17
3 000 PID 0.96 624.76
DP 0.47 589.02
DP_FO 0.56 511.45
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车辆质量/kg 控制器 平均速度跟踪
误差/m·s-1		 累积天然气消耗量/g
1 500 PID 0.94 1 199.72
DP 0.80 1 083.16
DP_FO 0.87 1 011.77
2 000 PID 1.15 1 426.76
DP 0.79 1 175.68
DP_FO 0.89 1 060.20
2 500 PID 1.36 1 682.56
DP 0.88 1 239.30
DP_FO 1.00 1 110.96
3 000 PID 1.60 1 953.38
DP 1.03 1 310.56
DP_FO 1.16 1 178.05
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WLTC无坡度工况误差值及累积天然气消耗量

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车辆质量/kg 控制器 平均速度跟踪
误差/m·s-1		 累积天然气消耗量/g
1 500 PID 0.94 1 199.72
DP 0.80 1 083.16
DP_FO 0.87 1 011.77
2 000 PID 1.15 1 426.76
DP 0.79 1 175.68
DP_FO 0.89 1 060.20
2 500 PID 1.36 1 682.56
DP 0.88 1 239.30
DP_FO 1.00 1 110.96
3 000 PID 1.60 1 953.38
DP 1.03 1 310.56
DP_FO 1.16 1 178.05
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车辆质量/kg 控制器 平均速度跟踪
误差/m·s-1		 累积天然气消耗量/g
1 500 PID 0.46 315.63
DP 0.45 297.69
DP_FO 0.49 248.19
DP_SF 0.42 294.32
DP_FOSF 0.47 245.09
2 000 PID 0.51 319.65
DP 0.36 312.52
DP_FO 0.42 246.33
DP_SF 0.32 309.58
DP_FOSF 0.39 241.06
2 500 PID 0.55 331.97
DP 0.32 328.62
DP_FO 0.40 248.59
DP_SF 0.27 325.93
DP_FOSF 0.35 244.99
3 000 PID 0.59 339.18
DP 0.31 338.24
DP_FO 0.39 266.10
DP_SF 0.24 334.43
DP_FOSF 0.35 261.94
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NEDC有坡度工况误差值及累积天然气消耗量

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车辆质量/kg 控制器 平均速度跟踪
误差/m·s-1		 累积天然气消耗量/g
1 500 PID 0.46 315.63
DP 0.45 297.69
DP_FO 0.49 248.19
DP_SF 0.42 294.32
DP_FOSF 0.47 245.09
2 000 PID 0.51 319.65
DP 0.36 312.52
DP_FO 0.42 246.33
DP_SF 0.32 309.58
DP_FOSF 0.39 241.06
2 500 PID 0.55 331.97
DP 0.32 328.62
DP_FO 0.40 248.59
DP_SF 0.27 325.93
DP_FOSF 0.35 244.99
3 000 PID 0.59 339.18
DP 0.31 338.24
DP_FO 0.39 266.10
DP_SF 0.24 334.43
DP_FOSF 0.35 261.94
), ArticleFig(id=1209899466010784056, tenantId=1146029695717560320, journalId=1189621681917173762, articleId=1209871064692290096, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
), ArticleFig(id=1209899466094670139, tenantId=1146029695717560320, journalId=1189621681917173762, articleId=1209871064692290096, language=CN, label=表7, caption=

WLTC有坡度工况验证

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车辆质量/kg 控制器 平均速度跟踪
误差/m·s-1		 累积天然气
消耗量/g
1 500 PID 0.88 918.25
DP 0.67 880.81
DP_FO 0.72 805.86
DP_SF 0.66 873.90
DP_FOSF 0.71 798.67
2 000 PID 0.97 954.21
DP 0.56 936.29
DP_FO 0.62 834.44
DP_SF 0.55 930.32
DP_FOSF 0.61 827.43
2 500 PID 1.09 1 005.02
DP 0.54 987.69
DP_FO 0.61 865.80
DP_SF 0.51 981.73
DP_FOSF 0.59 858.63
3 000 PID 1.22 1 091.65
DP 0.60 10 036.03
DP_FO 0.66 906.48
DP_SF 0.56 1 031.47
DP_FOSF 0.64 903.85
), ArticleFig(id=1209899466304385346, tenantId=1146029695717560320, journalId=1189621681917173762, articleId=1209871064692290096, language=CN, label=表8, caption=

WLTC有坡度工况各质量误差及累积天然气消耗量

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车辆质量/kg 控制器 平均速度跟踪
误差/m·s-1		 累积天然气
消耗量/g
1 500 PID 0.88 918.25
DP 0.67 880.81
DP_FO 0.72 805.86
DP_SF 0.66 873.90
DP_FOSF 0.71 798.67
2 000 PID 0.97 954.21
DP 0.56 936.29
DP_FO 0.62 834.44
DP_SF 0.55 930.32
DP_FOSF 0.61 827.43
2 500 PID 1.09 1 005.02
DP 0.54 987.69
DP_FO 0.61 865.80
DP_SF 0.51 981.73
DP_FOSF 0.59 858.63
3 000 PID 1.22 1 091.65
DP 0.60 10 036.03
DP_FO 0.66 906.48
DP_SF 0.56 1 031.47
DP_FOSF 0.64 903.85
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自动驾驶载货汽车速度轨迹模型预测跟踪控制方法*
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赵靖华 1, 3 , 管清捷 1, 2 , 刘晓雪 1 , 解方喜 3
汽车技术 | 2024,(9): 10-17
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汽车技术 | 2024, (9): 10-17
自动驾驶载货汽车速度轨迹模型预测跟踪控制方法*
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赵靖华1, 3, 管清捷1, 2, 刘晓雪1, 解方喜3
作者信息
  • 1 吉林师范大学，四平 136000
  • 2 吉林警察学院，长春 130123
  • 3 吉林大学，汽车底盘集成与仿生全国重点实验室，长春 130022

通讯作者:

解方喜（1982—），男，教授，博士，主要研究方向为先进控制理论应用，。
A Model Predictive Tracking Control Study for Speed Trajectory of Autonomous Driving Trucks
Jinghua Zhao1, 3, Qingjie Guan1, 2, Xiaoxue Liu1, Fangxi Xie3
Affiliations
  • 1 Jilin Normal University, Siping 136000
  • 2 Jilin Police College，Changchun 130123
  • 3 National Key Laboratory of Automotive Chassis Integration and Bionics, Jilin University, Changchun 130022
出版时间: 2024-09-24 doi: 10.19620/j.cnki.1000-3703.20230950
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摘要
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为避免车辆质量变化与道路坡度对自动驾驶载货汽车纵向车速控制的干扰，通过智能导航系统获取车辆速度轨迹及道路坡度信息，建立车辆纵向动力学模型和压缩天然气（CNG）发动机动力学模型，并基于模型预测控制（MPC）框架设计了一种实时的动态规划（DP）速度轨迹跟踪控制器。仿真结果表明，在新欧洲驾驶循环（NEDC）和全球统一轻型车辆测试循环（WLTC）工况下，该控制器在载货汽车质量变化和道路坡度干扰条件下能使车速保持稳定，并可在优化速度跟踪误差的同时降低发动机天然气消耗量。

自动驾驶  /  纵向车速控制  /  模型预测控制  /  实时动态规划  /  道路坡度

In order to prevent vehicle mass changes and road slope interfering with longitudinal speed of autonomous driving truck, this article utilizes an intelligent navigation system to obtain information including vehicle speed trajectory and road slope. Vehicle longitudinal dynamic model and Compressed Natural Gas (CNG) engine dynamic model are established, and a real-time Dynamic Programming (DP) speed trajectory tracking controller is designed based on the Model Predictive Control (MPC) framework. The simulation results under NEDC and WLTC operating conditions show that the controller can keep vehicle speed stable under conditions of truck mass change and road slope interference, and can optimize speed tracking error while reducing natural gas consumption.

Autonomous driving  /  Longitudinal speed control  /  Model Predictive Control (MPC)  /  Real-time Dynamic Programming (DP)  /  Road slope
赵靖华, 管清捷, 刘晓雪, 解方喜. 自动驾驶载货汽车速度轨迹模型预测跟踪控制方法*. 汽车技术, 2024 , (9) : 10 -17 . DOI: 10.19620/j.cnki.1000-3703.20230950
Jinghua Zhao, Qingjie Guan, Xiaoxue Liu, Fangxi Xie. A Model Predictive Tracking Control Study for Speed Trajectory of Autonomous Driving Trucks[J]. Automobile Technology, 2024 , (9) : 10 -17 . DOI: 10.19620/j.cnki.1000-3703.20230950
正文
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1 前言
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自动驾驶载货汽车的纵向车速控制是实现车辆平稳行驶的核心问题之一[1]，载货汽车质量的变化和道路坡度等因素会对纵向车速控制造成干扰[2-3]，因此，增强纵向速度跟踪控制器的鲁棒性对纵向运动控制具有重要意义[4]。
目前，自动驾驶车辆的纵向速度控制方法分为模型控制和非模型控制两类[5]。非模型控制方法中的线性比例-积分-微分（Proportional Integral Derivative，PID）控制算法因结构简单且易于实施而广泛应用，但因车辆系统具有高度非线性和受环境干扰影响，满足需求的PID参数难以获得[6]。Wang等[7]基于动力学模型优化纵向速度控制，提出了车辆模型和比例内模控制器，避免了路况干扰，但未考虑车辆质量、道路坡度等多约束干扰问题。模型预测控制（Model Predictive Control，MPC）[8-9]方法通过模型预测和在线优化策略实现控制序列的精确控制，具有实时性，可广泛应用于车速估计跟踪[10-12]。Chen等[13]利用具有循环神经网络记忆细胞的MPC方法，提高了自动驾驶车辆的轨迹跟踪性能，但该方法难以找到合适的算法求解优化问题。Gong等[14]通过动态规划（Dynamic Programming，DP）[15]方法求解换挡和能量分配优化策略，减少了参数的重复计算，从而提高了求解效率。但DP方法需要提供全局信息，因而计算负担较重，且缺乏实时性[16]。
为解决上述问题，本文基于MPC方法设计了一种实时速度轨迹跟踪动态规划控制器，并在多种瞬态工况下讨论该控制器对车速跟踪误差及天然气消耗量优化的潜力。
2 模型建立
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2.1 车辆纵向动力学模型
本文根据配置以压缩天然气（Compressed Natural Gas，CNG）为燃料的4缸1.59 L发动机的某自动驾驶载货汽车参数，建立车辆纵向动力学模型[17-19]：
v ˙ = f 1 ( v , F t , F b ) = 1 M ( F t - F b - 1 2 ρ c d A f v 2 ) - c r g
式中：v为车速，M为车辆质量，Ft为车辆的驱动力，Fb为制动力，ρ为空气密度，cd为空气阻力系数，Af为迎风面积，cr=βcos(α(s))+sin(α(s))为坡度阻力引起的加速度，g为滚动阻力引起的加速度，β为滚动阻力系数，s为位移，α(s)为道路坡度。
在不考虑节能优化策略的情况下，引入六挡变速器模型，建模参数如表1所示。发动机扭矩Te与车辆驱动力Ft的关系为Te=Ftr/(ηi0ig)，发动机转速ωe与车速v的关系为ωe=30i0igv/(rπ)。
2.2 压缩天然气发动机模型及验证
本文基于CNG发动机基本参数及试验数据，根据文献[20]建立面向控制器设计的二阶发动机动力学模型，并进行验证。该模型由进气歧管压力、排气歧管压力及发动机功率模型构成，其额定转速为6 000 r/min，最大净功率为72 kW。假设进气歧管容积固定，流入的气体质量为Wc，流出的气体质量为Wcyl，根据质量守恒定律，进气歧管内的气体质量为Wim=Wc-Wcyl。
假设进气过程温度不变，根据理想气体状态方程pV=nRT（n为物质的量，R为气体常数），进气歧管压强为：
p ˙ i m = R T i m V i m ( W c - W c y l )
式中：Tim、Vim分别为进气歧管的温度和体积。
此时，进入气缸的空气量为：
W c y l = p i m R T i m ⋅ η v o l ( p i m , ω e ) ⋅ V d i s p ⋅ ω e 120
式中：Vdisp为发动机总排量，ηvol(pim, ωe)为发动机容积效率。
发动机转速和进气歧管压强建模函数为：
η v o l = c v o l 1 p i m + c v o l 2 ω e + c v o l 3
式中：cvol1、cvol2、cvol3为拟合参数，取值分别为1.34、2.57、1.17。
设从排气歧管排出的废气质量为Wexh，进入排气歧管的气体质量为Wcyl，压缩天然气喷射量为Wfuel，则排气歧管内部的气体质量为Wem=Wcyl+Wfuel-Wexh。排气歧管压强动力学方程为：
p ˙ e x = R T e x V e x ( W c y l + W f u e l - W e x h )
式中：Tex、Vex分别为排气歧管的温度、体积。
因此，CNG发动机的功率模型为：
P E n g = 2 π ω e 60 [ T i - T p - T f ]
式中：PEng为发动机的需求功率，Ti、Tp、Tf分别为指示扭矩、泵气损失扭矩、摩擦扭矩。
本文选取CNG发动机的432个稳态工作点进行模型验证，结果如图1所示。通过对比稳态工作点的试验结果与仿真结果，该发动机模型精准度达到90.17%，满足系统测试需求。
3 车速轨迹跟踪控制方法
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本文根据速度轨迹目标及坡度信息，基于MPC的框架设计一种实时DP速度轨迹跟踪控制器，在优化车辆速度跟踪效果的同时，降低发动机天然气消耗量。
3.1 车速跟踪优化问题
针对自动驾驶载货汽车的速度轨迹跟踪问题，在MPC框架下，以速度v为状态量，驱动力Ft和制动力Fb为控制量，得到被控车辆模型的最优控制为：
m i n J = ∫ t t + T ω f ( S f u e l ) 2 + ω v ( v ( t ) - v ' ( t ) ) 2 d t s . t . v ˙ ( t ) = 1 M ( F t ( t ) - F b ( t ) - 1 2 ρ c d A f v 2 ( t ) ) - c r g v m i n ≤ v ( t ) ≤ v m a x 0 ≤ F t ( t ) ≤ F t m a x ,   0 ≤ F b ( t ) ≤ F b m a x
式中：J为优化目标；t为时间；T为预测时长；Sfuel为发动机天然气消耗量，根据发动机转速和扭矩查表获得；v(t)为目标速度；v′(t)为实际车速；vmax、vmin分别为最大、最小速度；ωf、ωv分别为油耗、误差权重系数； F t m a x、 F b m a x分别为最大驱动力、最大制动力。
3.2 DP算法求解速度轨迹跟踪问题
根据牛顿第二定律，最佳速度需找到各时刻车辆驱动力与制动力最优值，因此，可将速度轨迹跟踪视为车辆受力的在线优化分配问题。
本文采用DP算法，将速度轨迹跟踪问题分为优化计算与分配，有效简化速度轨迹跟踪问题的在线优化分配。该算法将速度轨迹跟踪优化过程分为顺序造表和逆序回溯2个部分，如图2所示。
根据不同的状态变量v，对车辆受力U划分网格，范围为-Fb~Ft，找寻代价函数（由速度轨迹跟踪误差和发动机天然气消耗组成）的最小值对应的U，并通过调整加权因子ωf和ωv权衡其性能。通过将智能网联系统中获取的信息输入递归完成顺序造表过程，到达递归出口之后，根据最小代价函数完成相应值的逆序回溯，找到速度跟踪问题的最优解。
4 仿真结果与分析
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为了分析载货汽车质量、坡度以及瞬态工况等因素对控制器跟踪误差和发动机天然气消耗量的影响，本文分别在新欧洲驾驶循环（New European Driving Cycle，NEDC）和全球统一轻型车辆测试循环（Worldwide Harmonized Light Vehicles Test Cycle，WLTC）工况下，观察有、无坡度信息的控制器控制效果，各控制器参数如表2所示。
本文使用5种控制器：
a. PID控制器。
b. DP控制器：采用实时DP算法进行优化求解。
c. DP_FO控制器：在DP算法基础上，将天然气消耗量优化项Sfuel引入代价函数。
d. DP_SF控制器：通过智能网联系统获取道路坡度信息，将其引入DP控制器，并在预测时域内滚动获取。
e. DP_FOSF控制器：在DP_SF方法基础上，使用代价函数考虑跟踪误差与发动机天然气消耗量，优化目标包含速度跟踪误差项ωv(v(t)-v′(t))2，并将天然气消耗量优化项ωf(Sfuel)2引入优化目标。
4.1 道路坡度α=0时，各工况验证分析
各工况测试车辆的质量分别为1 500 kg、2 000 kg、2 500 kg和3 000 kg。在道路无坡度时，使用PID控制器、DP控制器、DP_FO控制器即可完成跟踪任务。
4.1.1 NEDC无坡度工况验证
3种控制器在NEDC无坡度工况下的车速跟踪测试结果如表3所示。对比各质量车辆的工作区域，相较于PID控制器，DP控制器在速度目标提前获取的条件下，优化了控制器的制动力和驱动力，从而降低天然气消耗量；DP_FO控制器将天然气消耗量项引入优化目标，使发动机在较低的天然气消耗量区域工作，从而获得最低天然气消耗量。
各控制器平均速度跟踪误差和累积天然气消耗量对比结果如表4所示。鉴于DP控制器能够获得未来的速度信息，在平衡预测时域内整体控制效果后，将当前的控制力作用于被控车辆，由此减小跟踪误差。而DP_FO控制器在优化目标中引入天然气消耗量项，速度轨迹跟踪误差与天然气消耗量间的平衡效果优于其他控制器。因此，DP_FO控制器相比于DP控制器，平均速度跟踪误差提升16.39%，累计天然气消耗量降低17.80%。
4.1.2 WLTC无坡度工况验证分析
相同测试车辆条件下，3种控制器整体的平均速度跟踪误差和累积天然气消耗量对比结果如表5所示。DP_FO控制器相比于DP控制器，平均速度跟踪误差降低10.50%，累计天然气消耗量降低10.19%。
因此，在NEDC和WLTC无坡度工况下，随着载货汽车质量的增加，各控制器的天然气消耗量均有所增加。此外，整车质量相同条件下，DP_FO控制器的平均速度轨迹跟踪误差约为0.79 m/s，平均天然气消耗量为764.43 g，验证了DP_FO控制器的有效性和鲁棒性。
4.2 道路坡度α≠0时，各工况验证分析
各工况测试车辆质量分别为1 500 kg、2 000 kg、2 500 kg和3 000 kg。对于道路存在坡度的情况，本文使用5种控制器进行仿真验证。
4.2.1 NEDC有坡度工况验证
NEDC工况下，道路坡度信息如图3所示，对比该工况下5种控制器的车速跟踪结果。鉴于DP_SF控制器能够提前获取道路的坡度信息，并据此给出当前控制量，而DP_FOSF控制器在获取道路坡度信息的同时，将天然气消耗量项加入到优化目标中，经权衡后给出控制量。相较于DP控制器，DP_SF控制器平均速度跟踪误差降低16.47%，天然气消耗量降低1.01%；相较于DP_FO控制器，DP_FOSF控制器平均速度跟踪误差降低9.64%，天然气消耗量降低1.62%。
5种控制器整体的平均速度跟踪误差和累积天然气消耗量对比结果如表6所示。相比于DP控制器，DP_FOSF控制器的速度跟踪误差增加7.93%，但是其累积天然气消耗量降低了28.59%，在付出较低的跟踪误差代价下获得了较大的累积天然气消耗量改进效果。
4.2.2 WLTC有坡度工况验证
相同测试车辆条件下，WLTC工况下道路坡度信息如图4所示，5种控制器的车速跟踪测试对比结果如表7所示。相比于DP控制器工作的天然气消耗量区域，DP_SF控制器的平均速度跟踪误差降低4.67%，天然气消耗量降低0.62%；相比于DP_FO控制器工作的天然气消耗量区域，DP_FOSF控制器平均速度跟踪误差降低2.14%，天然气消耗量降低0.72%。
各控制器整体的平均速度跟踪误差和累积天然气消耗量对比结果如表8所示。相比于DP控制器工作的天然气消耗量区域，DP_FOSF控制器在付出较低的速度跟踪误差（误差增加6.79%）的情况下，最大累积天然气消耗量降低13.27%。
因此，道路存在坡度工况下，DP控制器、DP_FO控制器、DP_SF控制器、DP_FOSF控制器可使不同质量车辆有效减小跟踪误差，并且DP_FOSF控制器降低车辆天然气消耗量效果显著。NEDC和WLTC有坡度工况下，随着载货汽车质量增加，各控制器天然气消耗量均增加，但DP_FOSF控制器的平均速度轨迹跟踪误差始终保持在约0.52 m/s，天然气消耗量为547.71 g，证明了DP_FOSF控制器的有效性和鲁棒性。
综上所述，在NEDC和WLTC瞬态工况下的仿真验证结果表明：对于不同质量的载货汽车，本文提出的基于DP方法的控制器能够保持较为稳定的控制效果；在优化目标中考虑发动机天然气消耗量时，能够在较小的车速跟踪误差条件下，获得较大的累积天然气消耗量改进效果；在可获取坡度信息时，能够优化速度跟踪误差从而降低天然气消耗量；当同时引入发动机天然气消耗量和坡度预测信息时，控制器的整体效果达到最佳。
5 结束语
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本文在MPC框架下设计了基于DP方法的速度轨迹跟踪控制器，利用速度轨迹目标和坡度信息，同时优化车辆层面的速度跟踪效果和发动机天然气消耗量。后续工作将在保证算法实时性的同时进一步提高控制器的准确性，并在考虑系统约束时加入车辆的挡位信息和行驶稳定性，以实现更加安全高效的驾驶。
基金
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  • *国家自然科学基金项目(61773009)
  • 吉林省科技发展计划项目(20240601034RC)
文献
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2024年第卷第9期
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doi: 10.19620/j.cnki.1000-3703.20230950
  • 首发时间：2025-12-22
  • 出版时间：2024-09-24
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基金
*国家自然科学基金项目(61773009)
吉林省科技发展计划项目(20240601034RC)
作者信息
    1 吉林师范大学，四平 136000
    2 吉林警察学院，长春 130123
    3 吉林大学，汽车底盘集成与仿生全国重点实验室，长春 130022

通讯作者:

解方喜（1982—），男，教授，博士，主要研究方向为先进控制理论应用，。
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