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摘要: 针对传统模糊逻辑制动防抱死控制抗干扰能力较弱，在面对不同路面附着系数及理想滑移率时滑移率控制效果较差的问题，提出了一种区间二型模糊逻辑制动防抱死控制系统和方法；控制系统以滑移率误差为输入，利用区间二型模糊集合描述了滑移率误差及其变化率，并经模糊化、模糊推理、模糊降型、解模糊化4个步骤得到理想制动力矩输出；根据上、下隶属度函数确定的模糊变量隶属度计算模糊规则激活度区间，以增强系统的抗干扰能力，并保证滑移率精准跟踪；基于MATLAB/SIMULINK软件，针对搭载了提出的控制器与传统控制器的车辆，模拟了在不同路面附着条件下的防抱死控制性能，并搭建了防抱死硬件在环平台，进行了验证分析。研究结果表明：在区间二型模糊逻辑制动防抱死控制下，车辆在低附着系数路面下前、后轮滑移率误差均方分别下降了52.96%和57.36%，制动距离缩短了0.24 m，制动时间降低了0.04 s；在中附路面下前、后轮滑移率误差均方分别下降了65.15%和73.32%，制动距离缩短了0.36 m，制动时间降低了0.05 s；在高附着系数路面下前、后轮滑移率误差均方分别下降了47.20%和39.57%，制动距离缩短了0.19 m，制动时间降低了0.02 s。由此可见，相比于传统模糊逻辑制动防抱死控制，提出的区间二型模糊逻辑制动防抱死控制在不同制动条件下均能取得更好的滑移率控制效果。Abstract: To cope with the problem of weak anti-interference ability and poor slip ratio control effect when the traditional fuzzy logic anti-lock braking control facing different road surface adhesion coefficients and different ideal slip ratios, an interval type-2 fuzzy logic anti-lock braking control system and method were proposed. The slip ratio error was taken as input of the control system. The interval type-2 fuzzy sets were utilized to describe the slip ratio error and its change rate. Then the ideal braking torque output was obtained after the fuzzification, fuzzy inference, fuzzy type-reduction, and defuzzification. The fuzzy rule activation degree interval was calculated on the premise of fuzzy variables membership degree determined by the upper and lower membership functions. Through this process, the system's anti-interference ability was enhanced, and the accurate slip ratio tracking was ensured. Using the MATLAB/SIMULINK software, the vehicles equipped with the proposed controller and traditional controller were simulated for the anti-lock braking control performance under different road surface adhesion conditions, and the anti-lock hardware-in-the-loop platform was conducted for verification analysis. Research results show that under the interval type-2 fuzzy logic anti-lock braking control, the error mean squares of slip ratios for front and rear wheels of vehicles on the low adhesion coefficient road surface decrease by 52.96% and 57.36%, respectively, the braking distance reduces by 0.24 m, and the braking time declines by 0.04 s. On the middle adhesion coefficient road surface, the error mean squares of slip ratios decrease by 65.15% and 73.32%, respectively, the braking distance reduces by 0.36 m, and the braking time declines by 0.05 s. On the high adhesion coefficient road surface, the error mean squares of slip ratios decrease by 47.20% and 39.57%, respectively, the braking distance reduces by 0.19 m and the braking time declines by 0.02 s. It can be seen that compared with the traditional fuzzy logic anti-lock braking control, the proposed interval type-2 fuzzy logic anti-lock braking control achieves better slip ratio control effects under different braking conditions.
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图 1 整车纵向动力学模型和单轮动力学模型
Figure 1. Vehicle longitudinal dynamics model and single wheel dynamics model
图 3 区间二型模糊逻辑制动防抱死控制系统工作原理
Figure 3. Working principle of interval-2 fuzzy logic anti-lock braking control system
图 5 低附着系数路面车轮滑移率曲线
Figure 5. Slip ratio curves of wheels on low adhesion coefficient road surface
图 6 低附着系数路面车轮制动力矩曲线
Figure 6. Braking torque curves of wheels on low adhesion coefficient road surface
图 7 低附着系数路面车速与轮速曲线
Figure 7. Velocity curves of vehicle and wheels on low adhesion coefficient road surface
图 8 中附着系数路面车轮滑移率曲线
Figure 8. Slip ratio curves of wheels on middle adhesion coefficient road surface
图 9 中附着系数路面车轮制动力矩曲线
Figure 9. Braking torque curves of wheels on middle adhesion coefficient road surface
图 10 中附着系数路面车速与轮速曲线
Figure 10. Velocity curves of vehicle and wheels on middle adhesion coefficient road surface
图 11 高附着系数路面车轮滑移率曲线
Figure 11. Slip ratio curves of wheels on high adhesion coefficient road surface
图 12 高附着系数路面车轮制动力矩曲线
Figure 12. Braking torque curves of wheels on high adhesion coefficient road surface
图 13 高附着系数路面车速与轮速曲线
Figure 13. Velocity curves of vehicle and wheels on high adhesion coefficient road surface
图 15 低附着系数路面制动盘与飞轮转速曲线
Figure 15. Speed curves of braking disc and fly wheel on low adhesion coefficient road surface
图 16 低附着系数路面滑移率曲线
Figure 16. Slip ratio curves on low adhesion coefficient road surface
图 17 中附着系数路面制动盘与飞轮转速曲线
Figure 17. Speed curves of braking disc and fly wheel on middle adhesion coefficient road surface
图 18 中附着系数路面滑移率曲线
Figure 18. Slip ratio curves on middle adhesion coefficient road surface
表 1 Burckhardt轮胎模型典型路面参数
Table 1. Typical road surface parameters of Burckhardt tire model
路面类型 c1 c2 c3 μp λd 干沥青 1.30 24.00 0.52 1.20 0.16 湿沥青 0.85 33.80 0.35 0.80 0.13 干水泥 1.20 25.17 0.54 1.09 0.15 湿鹅卵石 0.40 33.72 0.10 0.34 0.14 雪 0.20 94.10 0.05 0.20 0.05 冰 0.05 306.40 0.01 0.05 0.03 
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表 2 区间二型模糊逻辑控制规则
Table 2. Control rules of interval type-2 fuzzy logic
Tb_i $\dot{e}$ NE ZE PO e NE PB PB PM ZE PM PM PS PO PS PS PS
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表 3 仿真参数
Table 3. Simulation parameters
参数 数值 参数 数值 M/kg 960 hg/m 0.48 A/m2 2.57 Ii/(kg·m2) 2.10 CD 0.30 r/m 0.29 la/m 1.53 lb/m 1.55
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表 4 低附着系数路面防抱死效果评价指标
Table 4. Evaluation indexes of anti-lock effect on low adhesion coefficient road surface
评价指标 控制器1 控制器2 制动距离/m 32.96 33.20 制动时间/s 6.22 6.26 平均充分减速度/(m·s-2) 2.00 1.98 前轮滑移率误差均方 1.27×10-2 2.70×10-2 后轮滑移率误差均方 2.84×10-2 6.66×10-2
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表 5 中附着系数路面防抱死效果评价指标
Table 5. Evaluation indexes of anti-lock effect on middle adhesion coefficient road surface
评价指标 控制器1 控制器2 制动距离/m 30.69 31.05 制动时间/s 3.58 3.63 平均充分减速度/(m·s-2) 5.05 4.95 前轮滑移率误差均方 9.79×10-3 2.81×10-3 后轮滑移率误差均方 9.39×10-3 3.52×10-2
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表 6 高附着系数路面防抱死效果评价指标
Table 6. Evaluation indexes of anti-lock effect on high adhesion coefficient road surface
评价指标 控制器1 控制器2 制动距离/m 28.18 28.37 制动时间/s 2.42 2.44 平均充分减速度/(m·s-2) 10.69 10.57 前轮滑移率误差均方 3.87×10-2 7.33×10-2 后轮滑移率误差均方 2.72×10-2 3.86×10-2
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