基于分数阶的空气弹簧建模及电动汽车主动悬架控制研究

doi:10.19562/j.chinasae.qcgc.2024.07.015

Abstract

Abstract:

Electrically controlled air suspension （ECAS） has the function of adjusting suspension stiffness and body height， which can effectively improve vehicle ride comfort and handling stability. Taking a passenger car ECAS as an example， the viscoelastic damping characteristics of rubber airbag are described by fractional theory， and the thermodynamic model is optimized considering the equivalent damping and hysteretic characteristics， which is in good agreement with the experimental data， and the precision of the optimized air spring model is verified. On this basis， considering the longitudinal and lateral dynamic characteristics of the vehicle and the Dugoff tire model， a 14-degree-of-freedom vehicle ECAS dynamic model is established， and a Model Predictive Control （MPC） active suspension control method is proposed， with measurable variables as the input of the controller， to realize the active control under straight and turning driving conditions. Simulation and vehicle bench test show that the fractional correction model can well reflect the variable stiffness characteristics of ECAS， and the active suspension control strategy based on MPC can adjust the air spring stiffness in real time， control the body posture， and effectively improve the ride comfort and stability of the electric vehicle. The research method in this paper provides a new idea for vehicle suspension system modeling and active control.

Key words: air suspension, thermodynamics, viscoelastic damping, fractional order, model predictive control

Guizhen Feng,Dongpeng Zhao,Shaohua Li. Research on Air Spring Modeling Based on Fractional Order and Electric Vehicle Active Suspension Control[J].Automotive Engineering, 2024, 46(7): 1282-1293.

Figures/Tables 23

参数	数值
初始容积 $V 0$ /m³	0.000 79
有效承载面积 $A e$ /m²	0.003 5
初始压力 $p 0$ /MPa	1.48
实验加载 $F$ /N	4 900

参数	数值
簧上质量 $m s$ /kg	1 730
质心至前轴距离 $a$ /mm	1 189
质心至后轴距离 $b$ /mm	1 548
绕 $x$ 轴转动惯量 $I x$ /（kg·m²）	700
绕 $y$ 轴转动惯量 $I y$ /（kg·m²）	3 480
绕 $z$ 轴转动惯量 $I z$ /（kg·m²）	3 710
前轮距 $t f ?$ /mm	1 644
后轮距 $t r ?$ /mm	1 635
质心高度 $h$ /mm	704
车轮质量 $m w ?$ /kg	64.5
轮毂电机质量 $m d ?$ /kg	31.5
轮胎刚度 $k t$ /（N·mm^-1）	218 900
减振器阻尼系数 $C s$ /（N·s·m^-1）	1 200

References 26

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参数			仿真	实验	相对误差
滞回曲线面积/（N·mm）	0.8 Hz	10 mm	12 930	13 913	7.6%
	0.8 Hz	12 mm	21 022	21 534	2.4%
	1.0 Hz	10 mm	17 924	19 152	6.8%
	1.0 Hz	12 mm	25 872	28 275	9.2%
滞回曲线刚度/（N·mm^-1）	0.8 Hz	10 mm	78.05	84.25	8.0%
	0.8 Hz	12 mm	73.94	80.18	8.4%
	1.0 Hz	10 mm	86.87	96.74	7.6%
	1.0 Hz	12 mm	72.72	73.48	1.1%

车辆响应		侧倾角加速度		空气弹簧力
车辆响应		未考虑分数阶	考虑分数阶	未考虑分数阶	考虑分数阶
60 km/h	RMS	0.094 8	0.093 5	534.6	570.1
	max	0.287	0.291	1 114	1 117
	min	-0.253	-0.286	-1 197	-1 205
75 km/h	RMS	0.137 2	0.129 6	604.7	641.9
	max	0.357	0.379	1 289	1 294
	min	-0.380	-0.410	-1 376	-1 386
90 km/h	RMS	0.189	0.177	685.0	752.1
	max	0.416	0.432	1 416	1 460
	min	-0.561	-0.573	-1 701	-1 716

车辆响应		俯仰角加速度		空气弹簧力
车辆响应		未考虑分数阶	分数阶	未考虑分数阶	分数阶
3 m/s²	RMS	0.162	0.149	410.2	452.6
	max	1.033	1.035	645.2	670.1
	min	-0.563	-0.560	-1 318	-1 319
2.5 m/s²	RMS	0.146	0.136	366.8	399.9
	max	0.899	0.901	543.7	591.2
	min	-0.521	-0.521	-1 238	-1 235
2 m/s²	RMS	0.116	0.108	281.7	309.1
	max	0.689	0.690	385.6	391.3
	min	-0.440	-0.443	-1 025	-1 042

参数类别	系统参数
系统控制输入	空气弹簧质量流量
系统可测输出	俯仰角加速度、侧倾角加速度、悬架动挠度、簧上质量加速度、簧下位移
不可测输出	轮胎动载荷
可测干扰	制动力矩、前轮转角
不可测干扰	路面激励

车辆响应			被动悬架	PID控制	MPC控制
前悬架动挠度/mm	未考虑分数阶	RMS	7.8	6.8	7.3
		max	9.6	8.6	0
		min	-28.3	-25.3	-15.7
	考虑分数阶	RMS	7.9	6.9	7.4
		max	10.0	8.8	0
		min	-28.9	-25.8	-23.6
后悬架动挠度/mm	未考虑分数阶	RMS	9.3	6.9	7.9
		max	41.2	30.8	16.7
		min	-10.4	-7.05	0
	考虑分数阶	RMS	9.7	7.2	9.2
		max	44.1	33.0	19.2
		min	-11.5	-8.2	0
俯仰角加速度/（rad·s^-2）	未考虑分数阶	RMS	0.135	0.114 5	0.082 97
		max	0.903 7	0.903 6	0.903 9
		min	-0.521 9	-0.464 5	-0.453 4
	考虑分数阶	RMS	0.120	0.101 7	0.062 28
		max	0.911 2	0.910 8	0.911 4
		min	-0.512 1	-0.457 3	-0.455 3

Research on Air Spring Modeling Based on Fractional Order and Electric Vehicle Active Suspension Control

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Figures/Tables 23

References 26

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车辆响应			被动悬架	PID控制	MPC 控制
前左悬架动挠度/mm	未考虑分数阶	RMS	14.0	10.9	7.8
	max	42.7	31.7	17.3
	min	-23.8	-19.8	-20.7
	考虑分数阶	RMS	16.5	12.8	10.7
	max	43.4	32.1	26.8
	min	-24	-19.9	-30.5
前右悬架动挠度/mm	未考虑分数阶	RMS	14.5	11.2	10.5
	max	40.9	30.5	26.8
	min	-24.2	-20.2	-21.0
	考虑分数阶	RMS	17.3	13.6	11.2
	max	41.9	31.1	30.8
	min	-24.6	-20.5	-24.8
侧倾角加速度/（rad·s^-2）	未考虑分数阶	RMS	0.145 0	0.105 5	0.054 7
	max	0.365 6	0.278 1	0.143 5
	min	-0.377 5	-0.239 6	-0.144 1
	考虑分数阶	RMS	0.125 8	0.089 3	0.049 39
	max	0.380 5	0.287 9	0.145 8
	min	-0.414 8	-0.254 6	-0.141 1

悬架动挠度	急减速工况		双移线工况
悬架动挠度	控制前	控制后	控制前	控制后
max/mm	3	2	9	9
min/mm	-10	-10	-6	-5
RMS/mm	3.73	3.67	3.72	3.59

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