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摘要:
路面附着系数(TRFC)是影响汽车行驶稳定性与动力学控制的关键因素，而采用非线性模型的无迹卡尔曼滤波(UKF)-TRFC观测器在车辆起步或路面条件发生突变时收敛较慢，采用线性模型的强跟踪卡尔曼滤波(STKF)-TRFC观测器在较大侧向加速度工况下精度显著降低。因此，提出一种基于UKF和STKF融合的TRFC观测方法。建立面向控制的线性二自由度和非线性三自由度车辆模型、Dugoff轮胎模型；基于线性车辆模型并引入时变渐消因子，设计了STKF-TRFC观测器；基于非线性车辆模型和轮胎模型建立UKF-TRFC观测器；探索轮胎侧向线性区域与非线性区域之间的临界点，在临界区域利用渐消记忆加权最小二乘法对2种观测器结果进行融合。硬件在环仿真试验结果表明：所提方法对车速与路面条件变化表现出较强的鲁棒性与精确性，相比单一STKF-TRFC观测器和UKF-TRFC观测器，其平均绝对误差最高分别降低了94.9%和78.1%，其均方根误差最高分别降低了59.2%和56.9%。
Abstract:The tire-road friction coefficient (TRFC) is an essential factor affecting driving stability and dynamic control of the automobile. However, when the car is starting or the road conditions change suddenly, the unscented Kalman (UKF) based TRFC observer using a nonlinear model converges slowly; under conditions of large lateral acceleration, the accuracy of the strong tracking Kalman (STKF) based TRFC observer using a linear model significantly decreases Therefore, a TRFC observation method based on the fusion of UKF and STKF is proposed. The control-oriented two-degree of freedom linear and three-degree-of-freedom nonlinear vehicle models, the Dugoff tire model are established. A STKF-TRFC observer is designed based on a linear vehicle model and a time-varying fading factor, a UKF-TRFC observer is established based on a nonlinear vehicle model and tire model. The critical point between linear and nonlinear tire lateral dynamics is explored, and the fading memory weighted least squares method is used to fuse the two observers in the critical region. The hardware-in-the-loop simulation results show that the proposed fusion observation method exhibits strong robustness and accuracy against changes in vehicle speed and road conditions. Its root mean square error drops by up to 59.2% and 56.9%, respectively, and its mean absolute error drops by up to 94.9% and 78.1% when compared to the single STRK-TRFC or UKF-TRFC observer.
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图 6 定车速定路面附着系数HIL测试结果
Figure 6. HIL test results under constant speed and tire-road friction coefficient
图 7 变车速定路面附着系数HIL测试结果
Figure 7. HIL test results under variable speed and constant tire-road friction coefficient
图 8 定车速变路面附着系数HIL测试结果
Figure 8. HIL test results under constant speed and variable tire-road friction coefficient
图 9 变车速变路面附着系数HIL测试结果
Figure 9. HIL test results under variable speed and tire-road friction coefficient
表 1 仿真车辆模型参数
Table 1. Simulate vehicle model parameters
参数 数值 车身绕z轴转动惯量Iz/(kg·m2) 700 车辆质量m/kg 600 质心距离前轴的距离b/m 1 质心距离后轴的距离a/m 1.26 前后轴距l/m 2.26 车轮有效滚动半径re/m 0.37 质心高度hg/m 0.45 轮距wb/m 1.5 
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表 2 观测结果平均绝对误差统计
Table 2. Statistics of average absolute error of observation results
工况 平均绝对误差 误差对比/% STKF-TRFC UKF-TRFC 本文融合方法 本文融合方法与STKF-TRFC 本文融合方法与UKF-TRFC 定车速定路面 0.00313 0.00034 0.00016 −94.9 −52.9 变车速定路面 0.01351 0.00183 0.00169 −87.5 −7.7 定车速变路面 0.00659 0.00152 0.00062 −90.6 −59.2 变车速变路面 0.01751 0.00687 0.00303 −82.7 −55.9
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表 3 观测结果均方根误差统计
Table 3. Statistics of root mean square error of observation results
工况 均方根误差 误差对比/% STKF-TRFC UKF-TRFC 本文融合方法 本文融合方法与STKF-TRFC 本文融合方法与UKF-TRFC 定车速定路面 0.00475 0.00308 0.00261 −55.1 −15.3 变车速定路面 0.01721 0.00692 0.00674 −60.8 −2.7 定车速变路面 0.01574 0.01323 0.01234 −21.6 −6.7 变车速变路面 0.03085 0.02286 0.00985 −78.1 −56.9
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