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CN115946707B - Tire force estimation method and system for full-wire control electric vehicle driven by four-wheel hub motor - Google Patents

Tire force estimation method and system for full-wire control electric vehicle driven by four-wheel hub motor Download PDF

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CN115946707B
CN115946707B CN202310237547.2A CN202310237547A CN115946707B CN 115946707 B CN115946707 B CN 115946707B CN 202310237547 A CN202310237547 A CN 202310237547A CN 115946707 B CN115946707 B CN 115946707B
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CN115946707A (en
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张雷
王震坡
丁晓林
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a tire force estimation method and a system for a four-wheel hub motor driven full-drive electric automobile, which relate to the technical field of vehicle safety control, and the method comprises the following steps: acquiring sensing signal parameters of an in-vehicle sensor; the sensing signal parameters comprise suspension height data, inertia measurement data, steering wheel angle data, vehicle signal data and motor data; respectively constructing a rolling dynamics model, a transverse vehicle model and a longitudinal vehicle model according to the sensing signal parameters; estimating vertical tire force according to a rolling dynamics model based on a strong tracking unscented Kalman filter; estimating longitudinal tire forces according to a longitudinal vehicle model based on a classical kalman filter; based on the strong tracking unscented Kalman filter, lateral tire forces are estimated from the lateral vehicle model, the vertical tire forces, and the longitudinal tire forces. The invention utilizes the low-cost vehicle-mounted sensor information, the state feedback information of the hub motor and the linear control motor system to realize the longitudinal, lateral and vertical tire force estimation of the tire.

Description

四轮毂电机驱动全线控电动汽车轮胎力估计方法及系统Tire force estimation method and system for four-wheel-hub motor driven fully controlled-by-wire electric vehicle

技术领域Technical Field

本发明涉及车辆安全控制技术领域，特别是涉及一种四轮毂电机驱动全线控电动汽车轮胎力估计方法及系统。The present invention relates to the technical field of vehicle safety control, and in particular to a tire force estimation method and system for a four-wheel-hub motor driven fully-controlled-by-wire electric vehicle.

背景技术Background Art

车辆纵向、侧向、垂向轮胎力学状态是车辆主动安全控制的主要控制变量，同时也是车辆综合稳定性评估的重要指标，它的准确获取直接关系车辆行驶稳定性与安全性。目前已有的现有技术如下：The longitudinal, lateral and vertical mechanical states of the vehicle tires are the main control variables for active safety control of the vehicle, and are also important indicators for comprehensive vehicle stability assessment. Its accurate acquisition is directly related to the driving stability and safety of the vehicle. The existing technologies are as follows:

（1）一种分布式电驱动车辆的前轮侧向力估算方法，首先采集车辆状态信号，利用车辆动力学方程实时估计轮胎的纵向力和垂向力；然后将估计的各轮的纵向力连同纵向加速度信号、侧向加速度信号、横摆角速度信号、方向盘转角信号传给车辆控制器中的卡尔曼侧向力观测器，得到两前轮的卡尔曼侧向力估计值和后轴侧向力估计值；最后利用各轮垂向力和前轮转角差对估计的侧向力进一步处理，得到最终的侧向力估计值。(1) A front wheel lateral force estimation method for a distributed electric drive vehicle first collects vehicle state signals and estimates the longitudinal force and vertical force of the tire in real time using the vehicle dynamics equation; then the estimated longitudinal force of each wheel together with the longitudinal acceleration signal, lateral acceleration signal, yaw angular velocity signal, and steering wheel angle signal are transmitted to the Kalman lateral force observer in the vehicle controller to obtain the Kalman lateral force estimation values of the two front wheels and the rear axle lateral force estimation value; finally, the estimated lateral force is further processed using the vertical force of each wheel and the front wheel steering angle difference to obtain the final lateral force estimation value.

（2）一种转向系统转向力矩及轮胎侧向力估计方法，包括以下步骤：1.采集车辆的纵向力和侧向力，根据车辆的七自由度模型，建立基于各个轮胎旋转中心以及质心的横摆力矩；2.利用干扰观测器对各轮胎旋转中心的横摆力矩进行计算得到各轮胎旋转中心的侧向力矩估计值；3.采用最小二乘法估计前后轮胎的侧向力之和；4.利用经验估计法分别计算前后轮的侧向力；5.将前后轮的侧向力转换为转向力矩并输出至助力电机中。(2) A method for estimating the steering torque and tire lateral force of a steering system, comprising the following steps: 1. collecting the longitudinal force and lateral force of the vehicle, and establishing the yaw moment based on the rotation center and the center of mass of each tire according to the seven-degree-of-freedom model of the vehicle; 2. using a disturbance observer to calculate the yaw moment of the rotation center of each tire to obtain an estimated value of the lateral moment of the rotation center of each tire; 3. using the least squares method to estimate the sum of the lateral forces of the front and rear tires; 4. using an empirical estimation method to calculate the lateral forces of the front and rear wheels respectively; 5. converting the lateral forces of the front and rear wheels into steering torque and outputting it to the power assist motor.

（3）一种四轮驱动电动汽车轮胎力软测量方法，包括以下步骤：第一步：获取汽车的纵向速度、质心侧偏角、纵向加速度、侧向加速度、前轮转角及轮胎纵向力；第二步：将获取的汽车的纵向速度、质心侧偏角、纵向加速度、侧向加速度、前轮转角及轮胎纵向力信息，输入给非线性车辆动力学模型，通过车辆动力学模型计算得到预估的纵向加速度和横向加速度；第三步：将获取的汽车的纵向速度、质心侧偏角、纵向加速度、横向加速度、前轮转角及轮胎纵向力信息和第二步预估的纵加速度、横向加速度信息一起输入给无迹卡尔曼滤波算法，获得基于模型的汽车轮胎力估计值。(3) A soft measurement method for tire force of a four-wheel drive electric vehicle, comprising the following steps: a first step: obtaining the longitudinal speed, center of mass sideslip angle, longitudinal acceleration, lateral acceleration, front wheel turning angle and tire longitudinal force of the vehicle; a second step: inputting the obtained information of the longitudinal speed, center of mass sideslip angle, longitudinal acceleration, lateral acceleration, front wheel turning angle and tire longitudinal force of the vehicle into a nonlinear vehicle dynamics model, and obtaining the estimated longitudinal acceleration and lateral acceleration through calculation of the vehicle dynamics model; a third step: inputting the obtained information of the longitudinal speed, center of mass sideslip angle, longitudinal acceleration, lateral acceleration, front wheel turning angle and tire longitudinal force of the vehicle together with the longitudinal acceleration and lateral acceleration information estimated in the second step into an unscented Kalman filter algorithm, and obtaining the model-based vehicle tire force estimation value.

（4）一种分布式驱动电动车的前轮侧向力估计方法，主要步骤为：1.依据各种传感器采集到的车辆状态信息，基于车辆动力学方程设计了滑模纵向力观测器对轮胎的纵向力进行实时估计；2.将估计的各轮纵向力以及纵向加速度信号、侧向加速度信号、横摆角速度信号等传输给滑模侧向力观测器，得到右前轮的侧向力估计值；3.通过滤波模块，对估计出的侧向力进一步优化处理，解决了侧向力估计值中出现的奇异问题，从而输出最终的两前轮侧向力估计值。(4) A method for estimating the lateral force of the front wheels of a distributed drive electric vehicle, the main steps of which are: 1. Based on the vehicle state information collected by various sensors, a sliding mode longitudinal force observer is designed based on the vehicle dynamics equation to estimate the longitudinal force of the tire in real time; 2. The estimated longitudinal force of each wheel as well as the longitudinal acceleration signal, lateral acceleration signal, yaw angular velocity signal, etc. are transmitted to the sliding mode lateral force observer to obtain the lateral force estimation value of the right front wheel; 3. Through the filtering module, the estimated lateral force is further optimized and processed to solve the singularity problem in the lateral force estimation value, thereby outputting the final lateral force estimation values of the two front wheels.

（5）分布式驱动电动汽车质心侧偏角与轮胎侧向力估计方法，该方法基于交互多模型算法-容积卡尔曼滤波对车辆质心侧偏角和轮胎侧向力进行实时估计，建立八自由度车辆模型，包括纵向运动、横向运动、横摆运动、侧倾运动以及四个轮胎的运动，非线性车辆模型考虑了车辆行驶过程中侧倾运动和载荷转移的影响；然后建立线性轮胎模型和非线性Dugoff轮胎模型作为交互多模型的模型集；最后对车辆质心侧偏角和轮胎侧向力进行估计。(5) A method for estimating the sideslip angle and tire lateral force of a distributed drive electric vehicle. This method estimates the sideslip angle and tire lateral force of the vehicle's center of mass in real time based on the interactive multi-model algorithm-volumetric Kalman filter. An eight-degree-of-freedom vehicle model is established, including longitudinal motion, lateral motion, yaw motion, roll motion, and the motion of the four tires. The nonlinear vehicle model takes into account the effects of roll motion and load transfer during vehicle driving. Then, a linear tire model and a nonlinear Dugoff tire model are established as the model set of the interactive multi-model. Finally, the vehicle's sideslip angle and tire lateral force are estimated.

（6）一种轮胎侧向力估算方法，包括以下步骤：1.设置一包括有轮心纵向速度传感器、路面附着系数传感器、轮胎垂向力传感器、轮胎侧偏角传感器、轮胎滑转率传感器和侧向力估计模块的轮胎侧向力估算系统；2.所述侧向力估计模块根据所采集的轮胎滑转率值、轮胎垂向力值、轮胎侧偏角和路面附着系数值，估算轮胎的准静态侧向力值；3.根据轮胎的动态侧向力与准静态侧向力的关系建立动态轮胎模型，所述侧向力估计模块根据采集的轮心纵向速度，并通过动态轮胎模型对所述步骤2估算的轮胎准静态侧向力值进行修正，得到动态轮胎侧向力值；4.将所述步骤3得到的动态轮胎侧向力值发送到整车控制器中，用于对车辆进行控制和监测。(6) A tire lateral force estimation method, comprising the following steps: 1. setting up a tire lateral force estimation system including a wheel center longitudinal velocity sensor, a road adhesion coefficient sensor, a tire vertical force sensor, a tire sideslip angle sensor, a tire slip rate sensor and a lateral force estimation module; 2. the lateral force estimation module estimates the quasi-static lateral force value of the tire according to the collected tire slip rate value, tire vertical force value, tire sideslip angle and road adhesion coefficient value; 3. establishing a dynamic tire model according to the relationship between the dynamic lateral force and the quasi-static lateral force of the tire, the lateral force estimation module corrects the quasi-static lateral force value of the tire estimated in step 2 according to the collected wheel center longitudinal velocity and through the dynamic tire model to obtain a dynamic tire lateral force value; 4. sending the dynamic tire lateral force value obtained in step 3 to the vehicle controller for controlling and monitoring the vehicle.

可以看出的是，目前车辆轮胎力估计方法大多基于特定的轮胎模型进行估算，而轮胎模型参数繁多，使得基于模型的估计方法呈现工况适应性差，精度低等问题；同时已有方案缺乏能够解耦估计车辆纵向、侧向和垂向轮胎力的高可靠估计方法。It can be seen that most of the current vehicle tire force estimation methods are based on specific tire models for estimation. However, the tire model has many parameters, which makes the model-based estimation method have problems such as poor adaptability to working conditions and low accuracy. At the same time, the existing solutions lack a highly reliable estimation method that can decouple the estimation of the vehicle's longitudinal, lateral and vertical tire forces.

发明内容Summary of the invention

为了克服现有技术的不足，本发明的目的是提供一种四轮毂电机驱动全线控电动汽车轮胎力估计方法及系统。In order to overcome the deficiencies of the prior art, an object of the present invention is to provide a tire force estimation method and system for a four-wheel-hub motor driven fully controlled-by-wire electric vehicle.

为实现上述目的，本发明提供了如下方案：To achieve the above object, the present invention provides the following solutions:

一种四轮毂电机驱动全线控电动汽车轮胎力估计方法，包括：A tire force estimation method for a four-wheel-hub motor driven fully controlled-by-wire electric vehicle, comprising:

获取车内传感器的传感信号参数；所述传感信号参数包括悬架高度数据、惯性测量数据、方向盘角度数据、车辆信号数据和电机数据；Acquire sensor signal parameters of in-vehicle sensors; the sensor signal parameters include suspension height data, inertial measurement data, steering wheel angle data, vehicle signal data and motor data;

根据所述传感信号参数分别构建滚动动力学模型、横向车辆模型和纵向车辆模型；Constructing a rolling dynamics model, a lateral vehicle model and a longitudinal vehicle model respectively according to the sensor signal parameters;

基于强跟踪无迹卡尔曼滤波器，根据所述滚动动力学模型估计垂直轮胎力；estimating vertical tire forces according to the rolling dynamics model based on a strong tracking unscented Kalman filter;

基于经典卡尔曼滤波器，根据所述纵向车辆模型估计纵向轮胎力；estimating longitudinal tire forces according to the longitudinal vehicle model based on a classical Kalman filter;

基于强跟踪无迹卡尔曼滤波器，根据所述横向车辆模型、所述垂直轮胎力和所述纵向轮胎力估计侧向轮胎力。Lateral tire forces are estimated based on the lateral vehicle model, the vertical tire forces, and the longitudinal tire forces based on a strong tracking unscented Kalman filter.

一种四轮毂电机驱动全线控电动汽车轮胎力估计系统，包括：A tire force estimation system for a four-wheel-hub motor driven fully controlled-by-wire electric vehicle, comprising:

参数获取模块，用于获取车内传感器的传感信号参数；所述传感信号参数包括悬架高度数据、惯性测量数据、方向盘角度数据、车辆信号数据和电机数据；A parameter acquisition module, used to acquire sensor signal parameters of in-vehicle sensors; the sensor signal parameters include suspension height data, inertial measurement data, steering wheel angle data, vehicle signal data and motor data;

模型构建模块，用于根据所述传感信号参数分别构建滚动动力学模型、横向车辆模型和纵向车辆模型；A model building module, used to build a rolling dynamics model, a lateral vehicle model and a longitudinal vehicle model according to the sensor signal parameters;

第一估计模块，用于基于强跟踪无迹卡尔曼滤波器，根据所述滚动动力学模型估计垂直轮胎力；A first estimation module, configured to estimate vertical tire forces according to the rolling dynamics model based on a strong tracking unscented Kalman filter;

第二估计模块，用于基于经典卡尔曼滤波器，根据所述纵向车辆模型估计纵向轮胎力；a second estimation module, configured to estimate longitudinal tire forces according to the longitudinal vehicle model based on a classical Kalman filter;

第三估计模块，用于基于强跟踪无迹卡尔曼滤波器，根据所述横向车辆模型、所述垂直轮胎力和所述纵向轮胎力估计侧向轮胎力。A third estimation module is configured to estimate lateral tire force according to the lateral vehicle model, the vertical tire force and the longitudinal tire force based on a strong tracking unscented Kalman filter.

根据本发明提供的具体实施例，本发明公开了以下技术效果：According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

本发明提供了一种四轮毂电机驱动全线控电动汽车轮胎力估计方法及系统，获取车内传感器的传感信号参数，包括悬架高度数据、惯性测量数据、方向盘角度数据、车辆信号数据和电机数据；分别根据传感信号参数构建滚动动力学模型、横向车辆模型和纵向车辆模型；基于强跟踪无迹卡尔曼滤波器，根据滚动动力学模型估计垂直轮胎力；基于经典卡尔曼滤波器，根据纵向车辆模型估计纵向轮胎力；基于强跟踪无迹卡尔曼滤波器，根据横向车辆模型、垂直轮胎力和纵向轮胎力估计侧向轮胎力。本发明利用低成本车载传感器信息，轮毂电机和线控制动系统状态反馈信息实现轮胎纵向、侧向和垂向轮胎估计力；使用强跟踪无迹卡尔曼滤波器估计轮胎侧向力和垂向力，较之传统的卡尔曼滤波器，在动态跟踪能力和收敛速度方面具有更好的性能；未使用参数繁多的轮胎模型进行轮胎力估计，估计算法精度高、鲁棒性好。The present invention provides a tire force estimation method and system for a four-wheel hub motor driven fully controlled-by-wire electric vehicle, which obtains sensor signal parameters of in-vehicle sensors, including suspension height data, inertial measurement data, steering wheel angle data, vehicle signal data and motor data; respectively constructs a rolling dynamics model, a lateral vehicle model and a longitudinal vehicle model according to the sensor signal parameters; estimates vertical tire force according to the rolling dynamics model based on a strong tracking unscented Kalman filter; estimates longitudinal tire force according to the longitudinal vehicle model based on a classic Kalman filter; estimates lateral tire force according to the lateral vehicle model, vertical tire force and longitudinal tire force based on a strong tracking unscented Kalman filter. The present invention utilizes low-cost on-board sensor information, wheel hub motors and wire control brake system state feedback information to realize tire longitudinal, lateral and vertical tire force estimation; uses a strong tracking unscented Kalman filter to estimate tire lateral force and vertical force, which has better performance in terms of dynamic tracking capability and convergence speed than traditional Kalman filters; does not use tire models with many parameters for tire force estimation, and the estimation algorithm has high accuracy and good robustness.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动性的前提下，还可以根据这些附图获得其他的附图。In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

图1为本发明提供的实施例中的方法流程图；FIG1 is a flow chart of a method in an embodiment of the present invention;

图2为本发明提供的实施例中的总体方案示意图；FIG2 is a schematic diagram of the overall scheme in an embodiment provided by the present invention;

图3为本发明提供的实施例中的车辆侧倾动力学模型中的四分之一悬挂模型示意图；FIG3 is a schematic diagram of a quarter suspension model in a vehicle roll dynamics model in an embodiment of the present invention;

图4为本发明提供的实施例中的车辆侧倾动力学模型中的车辆侧倾动力学示意图；FIG4 is a schematic diagram of vehicle roll dynamics in a vehicle roll dynamics model in an embodiment provided by the present invention;

图5为本发明提供的实施例中的三自由度车辆模型示意图；FIG5 is a schematic diagram of a three-degree-of-freedom vehicle model in an embodiment provided by the present invention;

图6为本发明提供的实施例中的纵向轮胎动力学模型示意图；FIG6 is a schematic diagram of a longitudinal tire dynamics model in an embodiment provided by the present invention;

图7为本发明提供的实施例中的纵向车辆动力学模型示意图。FIG. 7 is a schematic diagram of a longitudinal vehicle dynamics model in an embodiment provided by the present invention.

具体实施方式DETAILED DESCRIPTION

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

本发明的目的是提供一种四轮毂电机驱动全线控电动汽车轮胎力估计方法及系统，未使用参数繁多的轮胎模型进行轮胎力估计，估计算法精度高、鲁棒性好。The purpose of the present invention is to provide a tire force estimation method and system for a four-wheel hub motor driven fully controlled-by-wire electric vehicle, which does not use a tire model with numerous parameters for tire force estimation, and has a high estimation algorithm accuracy and good robustness.

为使本发明的上述目的、特征和优点能够更加明显易懂，下面结合附图和具体实施方式对本发明作进一步详细的说明。In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

如图1所示，本发明提供了一种四轮毂电机驱动全线控电动汽车轮胎力估计方法，包括：步骤100：获取车内传感器的传感信号参数；所述传感信号参数包括悬架高度数据、惯性测量数据、方向盘角度数据、车辆信号数据和电机数据。步骤200：根据所述传感信号参数分别构建滚动动力学模型、横向车辆模型和纵向车辆模型。步骤300：基于强跟踪无迹卡尔曼滤波器，根据所述滚动动力学模型估计垂直轮胎力。步骤400：基于经典卡尔曼滤波器，根据所述纵向车辆模型估计纵向轮胎力。步骤500：基于强跟踪无迹卡尔曼滤波器，根据所述横向车辆模型、所述垂直轮胎力和所述纵向轮胎力估计侧向轮胎力。As shown in FIG1 , the present invention provides a tire force estimation method for a four-wheel-hub motor driven fully controlled-by-wire electric vehicle, comprising: Step 100: Acquire sensor signal parameters of in-vehicle sensors; the sensor signal parameters include suspension height data, inertial measurement data, steering wheel angle data, vehicle signal data and motor data. Step 200: Construct a rolling dynamics model, a lateral vehicle model and a longitudinal vehicle model respectively according to the sensor signal parameters. Step 300: Estimate vertical tire force according to the rolling dynamics model based on a strong tracking unscented Kalman filter. Step 400: Estimate longitudinal tire force according to the longitudinal vehicle model based on a classical Kalman filter. Step 500: Estimate lateral tire force according to the lateral vehicle model, the vertical tire force and the longitudinal tire force based on a strong tracking unscented Kalman filter.

优选地，所述车内传感器包括：悬架高度传感器、惯性测量装置、轮毂电机、车辆信号传感器和方向盘角度传感器；所述悬架高度传感器用于测量悬架高度数据；所述惯性测量装置用于测量惯性测量数据；所述轮毂电机用于测量电机数据；所述车辆信号传感器用于测量车辆信号数据；所述方向盘角度传感器用于测量方向盘角度数据。Preferably, the in-vehicle sensors include: a suspension height sensor, an inertial measurement device, a wheel hub motor, a vehicle signal sensor and a steering wheel angle sensor; the suspension height sensor is used to measure suspension height data; the inertial measurement device is used to measure inertial measurement data; the wheel hub motor is used to measure motor data; the vehicle signal sensor is used to measure vehicle signal data; and the steering wheel angle sensor is used to measure steering wheel angle data.

如图2所示，通过车内传感器及车辆信号参数作为输入，分别建立滚动动力学模型、横向车辆模型、纵向车辆模型，得到垂直轮胎力、纵向轮胎力、侧向轮胎力的表达式；再分别选取强跟踪无迹卡尔曼滤波器和经典卡尔曼滤波器针对轮胎力进行估算。所述滚动动力学模型的构建方法如下：As shown in Figure 2, by using the in-vehicle sensors and vehicle signal parameters as input, the rolling dynamics model, lateral vehicle model, and longitudinal vehicle model are established respectively, and the expressions of vertical tire force, longitudinal tire force, and lateral tire force are obtained; then the strong tracking unscented Kalman filter and the classical Kalman filter are selected to estimate the tire force. The construction method of the rolling dynamics model is as follows:

构建第一模型。具体地，四分之一主动悬架系统如图3所示。忽略有效轮胎滚动半径的变化，滚动动力学模型，即第一模型的表达式为：Construct the first model. Specifically, the quarter active suspension system is shown in FIG3. Ignoring the change of the effective tire rolling radius, the rolling dynamics model, that is, the expression of the first model is:

Figure SMS_1
Figure SMS_1

其中，

Figure SMS_2
和
Figure SMS_5
分别为簧上和簧下的垂直位移，上标i∈[L1，L2，R1，R2]，L1、L2、R1和R2分别代表左前、右前、左后和右后；
Figure SMS_9
为主动悬架的执行力；
Figure SMS_3
为每个车轮上的分布簧载质量；
Figure SMS_6
和
Figure SMS_8
分别为每个悬架的刚度和阻尼，可以从主动悬架控制器获得；g为重力加速度；
Figure SMS_10
为悬架不变形的高度；
Figure SMS_4
表示求一阶导数；
Figure SMS_7
表示求二阶倒数。in,
Figure SMS_2
and
Figure SMS_5
are the sprung and unsprung vertical displacements, respectively, superscript i∈[L1, L2, R1, R2], L1, L2, R1, and R2 represent the left front, right front, left rear, and right rear, respectively;
Figure SMS_9
For the execution of active suspension;
Figure SMS_3
is the distributed sprung mass at each wheel;
Figure SMS_6
and
Figure SMS_8
are the stiffness and damping of each suspension, respectively, which can be obtained from the active suspension controller; g is the gravitational acceleration;
Figure SMS_10
is the height at which the suspension does not deform;
Figure SMS_4
It means to find the first-order derivative;
Figure SMS_7
It means to find the second-order reciprocal.

对于主动悬架，可以通过悬架高度传感器测量簧上质量和簧下质量的垂直位移。即根据所述第一模型确定第二模型，所述第二模型的表达式为：For active suspension, the vertical displacement of the sprung mass and the unsprung mass can be measured by a suspension height sensor. That is, the second model is determined according to the first model, and the expression of the second model is:

Figure SMS_11
；其中，
Figure SMS_12
为悬挂高度传感器测量的簧上和簧下质量的相对垂直位移。
Figure SMS_11
;in,
Figure SMS_12
The relative vertical displacement of the sprung and unsprung masses as measured by the ride height sensor.

根据所述第二模型确定第三模型；具体地，轮胎垂直力

Figure SMS_13
由静载荷和动载荷组成。静态轮胎力是由分布在每个角落的簧下质量
Figure SMS_14
和簧上质量
Figure SMS_15
的重量引起的，而动载荷由车辆横向和纵向运动引起。因此，轮胎垂直力
Figure SMS_16
可以表示为下文第三模型的表达式，如下：Determine the third model based on the second model; specifically, the tire vertical force
Figure SMS_13
It consists of static and dynamic loads. The static tire force is the unsprung mass distributed at each corner.
Figure SMS_14
and sprung mass
Figure SMS_15
The vertical force on the tire is caused by the weight of the vehicle, while the dynamic load is caused by the lateral and longitudinal movement of the vehicle.
Figure SMS_16
It can be expressed as the expression of the third model below, as follows:

Figure SMS_17
Figure SMS_17

；其中，

Figure SMS_18
表示车轮定位参数对垂直力的影响；
Figure SMS_19
表示随机道路激励；
Figure SMS_20
为垂直轮胎力，
Figure SMS_21
表示轮胎垂向力为簧下质量与道路激励的函数。;in,
Figure SMS_18
Indicates the influence of wheel alignment parameters on vertical force;
Figure SMS_19
represents random road excitation;
Figure SMS_20
is the vertical tire force,
Figure SMS_21
It represents the tire vertical force as a function of the unsprung mass and the road excitation.

构建侧倾动力学模型。具体地，为了准确预测轮胎垂直力，建立了一个带有主动悬架系统的车辆侧倾动力学模型，如图4所示，建立以x点为原点的坐标系，CG表示簧载的重心，B表示同一轴上左右轮胎安装位置之间的距离；

Figure SMS_22
表示某一悬架的阻尼；
Figure SMS_23
表示某一悬架的刚度；
Figure SMS_24
表示某一悬架上悬挂高度传感器测量的簧上和簧下质量的相对垂直位移，O表示车辆的重心处。为简化车辆侧倾动力学模型，忽略簧下侧倾角和侧向风的影响，因此侧倾动力学模型的表达式为：Construct a roll dynamics model. Specifically, in order to accurately predict the tire vertical force, a vehicle roll dynamics model with an active suspension system is established, as shown in Figure 4. A coordinate system with point x as the origin is established, CG represents the center of gravity of the sprung load, and B represents the distance between the left and right tire installation positions on the same axis;
Figure SMS_22
Indicates the damping of a certain suspension;
Figure SMS_23
Indicates the stiffness of a certain suspension;
Figure SMS_24
represents the relative vertical displacement of the sprung and unsprung masses measured by the suspension height sensor on a certain suspension, and O represents the center of gravity of the vehicle. To simplify the vehicle roll dynamics model, the influence of the unsprung roll angle and the side wind are ignored, so the expression of the roll dynamics model is:

Figure SMS_25
；
Figure SMS_32
；其中，
Figure SMS_35
、
Figure SMS_28
和
Figure SMS_30
分别为车辆的侧倾角、簧载质量和横向加速度；
Figure SMS_34
表示从重心到侧倾中心的垂直距离；
Figure SMS_36
表示弹簧质量在重心处绕x轴的转动惯量；
Figure SMS_26
表示滚动角刚度，
Figure SMS_29
表示阻尼系数。式中：l为同一轴上左右悬架安装位置之间的距离，假设前后悬架安装位置相同。由于小角度下，
Figure SMS_31
和
Figure SMS_33
，上述侧倾运动模型可以简化为：
Figure SMS_27
。
Figure SMS_25
;
Figure SMS_32
;in,
Figure SMS_35
,
Figure SMS_28
and
Figure SMS_30
are the roll angle, sprung mass and lateral acceleration of the vehicle respectively;
Figure SMS_34
It indicates the vertical distance from the center of gravity to the roll center;
Figure SMS_36
represents the moment of inertia of the spring mass around the x-axis at the center of gravity;
Figure SMS_26
represents the rolling angle stiffness,
Figure SMS_29
represents the damping coefficient. Where: l is the distance between the left and right suspension installation positions on the same axis, assuming that the front and rear suspension installation positions are the same.
Figure SMS_31
and
Figure SMS_33
, the above roll motion model can be simplified as:
Figure SMS_27
.

根据所述侧倾动力学模型确定第四模型；所述第四模型的表达式为：A fourth model is determined according to the roll dynamics model; the expression of the fourth model is:

Figure SMS_37
。
Figure SMS_37
.

根据所述第四模型确定第五模型。具体地，每个车轮上悬架系统的压缩都会导致车辆侧倾运动。因此，车辆侧倾状态与每个悬架的运动学之间的关系可以表达为第五模型，第五模型的表达式如下：The fifth model is determined based on the fourth model. Specifically, the compression of the suspension system on each wheel will cause the vehicle to roll. Therefore, the relationship between the vehicle roll state and the kinematics of each suspension can be expressed as a fifth model, and the expression of the fifth model is as follows:

Figure SMS_38
；其中，
Figure SMS_39
为悬架压缩量与车辆侧倾角之间的函数，
Figure SMS_40
为悬架压缩量。
Figure SMS_38
;in,
Figure SMS_39
is a function of the suspension compression and the vehicle roll angle,
Figure SMS_40
is the suspension compression.

综上可知，所述滚动动力学模型的表达式为：In summary, the expression of the rolling dynamics model is:

Figure SMS_41
Figure SMS_41

Figure SMS_42
。
Figure SMS_42
.

为了准确估计线性和非线性区域的横向轮胎力，建立一个简化的四轮横向车辆模型，如图5所示。其中，

Figure SMS_48
表示右后车轮纵向力，
Figure SMS_43
表示右后车轮的转矩，
Figure SMS_47
表示右后车轮的速度，
Figure SMS_49
表示右后车轮的偏转角，
Figure SMS_50
表示车辆的偏航角速度，
Figure SMS_51
表示左后车轮的转动周期转矩，
Figure SMS_54
表示左后车轮的速度，
Figure SMS_52
表示左后车轮的偏转角，
Figure SMS_56
表示左前车轮的转矩，
Figure SMS_45
表示左前车轮的速度，
Figure SMS_46
表示左前车轮的偏转角，
Figure SMS_53
表示右前车轮纵向力，
Figure SMS_58
表示右前车轮的转矩，
Figure SMS_55
表示右前车轮的速度，
Figure SMS_57
表示右前车轮的偏转角，图5中的x和y表示图5中建立的坐标系，
Figure SMS_44
表示车辆质心速度。基于此，横向车辆模型的构建方法为：In order to accurately estimate the lateral tire forces in the linear and nonlinear regions, a simplified four-wheel lateral vehicle model is established, as shown in Figure 5.
Figure SMS_48
represents the longitudinal force of the right rear wheel,
Figure SMS_43
represents the torque of the right rear wheel,
Figure SMS_47
represents the speed of the right rear wheel,
Figure SMS_49
represents the deflection angle of the right rear wheel,
Figure SMS_50
represents the vehicle's yaw rate,
Figure SMS_51
represents the rotation period torque of the left rear wheel,
Figure SMS_54
represents the speed of the left rear wheel,
Figure SMS_52
represents the deflection angle of the left rear wheel,
Figure SMS_56
represents the torque of the left front wheel,
Figure SMS_45
represents the speed of the left front wheel,
Figure SMS_46
represents the deflection angle of the left front wheel,
Figure SMS_53
represents the longitudinal force of the right front wheel,
Figure SMS_58
represents the torque of the right front wheel,
Figure SMS_55
represents the speed of the right front wheel,
Figure SMS_57
represents the deflection angle of the right front wheel, and x and y in FIG5 represent the coordinate system established in FIG5 ,
Figure SMS_44
Represents the vehicle center of mass velocity. Based on this, the construction method of the lateral vehicle model is:

构建三自由度车辆模型；所述三自由度车辆模型的表达式为：A three-degree-of-freedom vehicle model is constructed; the expression of the three-degree-of-freedom vehicle model is:

Figure SMS_59
Figure SMS_59

Figure SMS_60
Figure SMS_60

每个单独的横向轮胎力符合垂直力分布，可以由下式给出：Each individual lateral tire force conforms to the vertical force distribution and can be given by:

Figure SMS_61
。
Figure SMS_61
.

其中，m为车辆质量；

Figure SMS_72
为车辆的横向加速度；
Figure SMS_65
、
Figure SMS_69
和
Figure SMS_76
分别为前轮转向角、偏航加速度和绕z轴转动惯量；
Figure SMS_79
和
Figure SMS_78
分别为前胎面宽度和后胎面宽度；
Figure SMS_81
表示左前轮纵向力；
Figure SMS_70
表示左后轮纵向力；
Figure SMS_75
表示左前轮横向力；
Figure SMS_63
表示左后轮横向力；
Figure SMS_68
表示右前轮横向力；
Figure SMS_62
表示右前轮纵向力；
Figure SMS_66
表示右后轮纵向力；
Figure SMS_71
表示右后轮横向力；
Figure SMS_73
表示左前轮和左后轮的横向力之后；
Figure SMS_82
表示右前轮和右后轮的横向力之和；
Figure SMS_83
表示左前轮和左后轮的垂向力之和；
Figure SMS_80
表示右前轮和右后轮的垂向力之和；
Figure SMS_84
为垂直轮胎力；
Figure SMS_64
和
Figure SMS_67
分别表示从重心处到前轴和后轴的距离；
Figure SMS_74
表示求一阶导数；
Figure SMS_77
表示车辆的偏航角速度。Where, m is the vehicle mass;
Figure SMS_72
is the lateral acceleration of the vehicle;
Figure SMS_65
,
Figure SMS_69
and
Figure SMS_76
They are the front wheel steering angle, yaw acceleration and moment of inertia around the z-axis;
Figure SMS_79
and
Figure SMS_78
They are the front tread width and the rear tread width respectively;
Figure SMS_81
represents the longitudinal force of the left front wheel;
Figure SMS_70
represents the longitudinal force of the left rear wheel;
Figure SMS_75
represents the lateral force of the left front wheel;
Figure SMS_63
represents the lateral force of the left rear wheel;
Figure SMS_68
represents the lateral force of the right front wheel;
Figure SMS_62
represents the longitudinal force of the right front wheel;
Figure SMS_66
represents the longitudinal force of the right rear wheel;
Figure SMS_71
represents the lateral force of the right rear wheel;
Figure SMS_73
After indicating the lateral force of the left front wheel and the left rear wheel;
Figure SMS_82
It represents the sum of the lateral forces of the right front wheel and the right rear wheel;
Figure SMS_83
It represents the sum of the vertical forces of the left front wheel and the left rear wheel;
Figure SMS_80
It represents the sum of the vertical forces of the right front wheel and the right rear wheel;
Figure SMS_84
is the vertical tire force;
Figure SMS_64
and
Figure SMS_67
Respectively represent the distance from the center of gravity to the front axle and the rear axle;
Figure SMS_74
It means to find the first-order derivative;
Figure SMS_77
Indicates the vehicle's yaw rate.

构建线性化横向轮胎模型。具体地，为了描述车辆横向动力学与前轮转向角之间的关系，建立线性化横向轮胎模型，线性化横向轮胎模型的表达式为：Construct a linearized lateral tire model. Specifically, in order to describe the relationship between the vehicle lateral dynamics and the front wheel steering angle, a linearized lateral tire model is established. The expression of the linearized lateral tire model is:

Figure SMS_85
。
Figure SMS_85
.

对于前轮和后轮，轮胎侧偏角可由下式计算：For the front and rear wheels, the tire slip angle can be calculated as follows:

Figure SMS_86
。
Figure SMS_86
.

其中，

Figure SMS_87
和
Figure SMS_91
分别为每个车轴的侧偏刚度和轮胎侧偏角，上标
Figure SMS_94
表示前轴和后轴的侧偏刚度，
Figure SMS_88
表示前轴，
Figure SMS_92
表示后轴；
Figure SMS_93
和
Figure SMS_96
分别为车辆侧滑角和车辆纵向速度；
Figure SMS_89
为前轴或者后轴轮胎的横向力；
Figure SMS_90
表示前轴车轮的侧偏角；
Figure SMS_95
表示后轴车轮的侧偏角。in,
Figure SMS_87
and
Figure SMS_91
are the cornering stiffness and tire slip angle of each axle, respectively.
Figure SMS_94
represents the cornering stiffness of the front and rear axles,
Figure SMS_88
Represents the front axle,
Figure SMS_92
Rear axle;
Figure SMS_93
and
Figure SMS_96
are the vehicle sideslip angle and the vehicle longitudinal velocity respectively;
Figure SMS_89
is the lateral force of the front or rear axle tire;
Figure SMS_90
Indicates the side slip angle of the front axle wheel;
Figure SMS_95
Indicates the sideslip angle of the rear axle wheels.

根据所述三自由度车辆模型和所述线性化横向轮胎模型确定所述横向车辆模型。具体地，忽略纵向轮胎力，三自由度车辆模型可以简化为：The lateral vehicle model is determined according to the three-degree-of-freedom vehicle model and the linearized lateral tire model. Specifically, ignoring the longitudinal tire force, the three-degree-of-freedom vehicle model can be simplified as:

Figure SMS_97
Figure SMS_97

Figure SMS_98
Figure SMS_98

优选地，所述纵向车辆模型的构建过程如下：本实施例中，使用单轮模型，如图6所示来描述每个轮胎的动力学，其中，

Figure SMS_99
表示某一车轮的驱动扭矩，Fx表示某一轮胎的纵向力，Ff表示某一轮胎的滚动阻力，Fz表示某一轮胎的垂向力。基于此，构建轮胎动力学模型；所述轮胎动力学模型的表达式为：Preferably, the construction process of the longitudinal vehicle model is as follows: In this embodiment, a single wheel model is used to describe the dynamics of each tire as shown in FIG6 , wherein:
Figure SMS_99
represents the driving torque of a wheel, Fx represents the longitudinal force of a tire, Ff represents the rolling resistance of a tire, and Fz represents the vertical force of a tire. Based on this, a tire dynamics model is constructed; the expression of the tire dynamics model is:

Figure SMS_102
。其中，
Figure SMS_103
、
Figure SMS_106
、
Figure SMS_101
、
Figure SMS_104
、
Figure SMS_105
分别代表车轮的驱动扭矩、制动扭矩、滚动阻力、有效半径和转动惯量；
Figure SMS_107
代表轮胎的纵向力；
Figure SMS_100
表示车轮旋转角速度。
Figure SMS_102
.in,
Figure SMS_103
,
Figure SMS_106
,
Figure SMS_101
,
Figure SMS_104
,
Figure SMS_105
They represent the driving torque, braking torque, rolling resistance, effective radius and moment of inertia of the wheel respectively;
Figure SMS_107
Represents the longitudinal force of the tire;
Figure SMS_100
Indicates the wheel rotation angular velocity.

其中，轮胎滑移率定义为：

Figure SMS_108
。The tire slip ratio is defined as:
Figure SMS_108
.

构建纵向车辆动力学响应模型；为了描述纵向车辆动力学响应，如图7所示，基于此，所述纵向车辆动力学响应模型的表达式为：A longitudinal vehicle dynamics response model is constructed; in order to describe the longitudinal vehicle dynamics response, as shown in FIG7 , based on this, the expression of the longitudinal vehicle dynamics response model is:

Figure SMS_109
Figure SMS_109

Figure SMS_110
。
Figure SMS_110
.

其中，m为车辆质量；

Figure SMS_111
表示车辆的纵向加速度；
Figure SMS_116
表示整车总的滚动阻力；
Figure SMS_119
表示整车总的纵向力；上标i∈[L1，L2，R1，R2]，L1、L2、R1和R2分别代表左前、右前、左后和右后，上标
Figure SMS_113
表示前轴和后轴的侧偏刚度，
Figure SMS_115
表示前轴，
Figure SMS_121
表示后轴；
Figure SMS_125
为前轮转向角；g为重力加速度；
Figure SMS_112
、
Figure SMS_118
、
Figure SMS_120
、
Figure SMS_123
分别表示总的纵向驱动力、空气阻力、滚动阻力和坡度阻力；
Figure SMS_114
为气动阻力系数；A为迎风面积；
Figure SMS_117
为空气密度；f为滚动阻力系数；
Figure SMS_122
为道路坡度；
Figure SMS_124
为车辆纵向速度。Where, m is the vehicle mass;
Figure SMS_111
Indicates the longitudinal acceleration of the vehicle;
Figure SMS_116
Indicates the total rolling resistance of the vehicle;
Figure SMS_119
represents the total longitudinal force of the vehicle; superscript i∈[L1, L2, R1, R2], L1, L2, R1 and R2 represent the left front, right front, left rear and right rear, respectively, and superscript
Figure SMS_113
represents the cornering stiffness of the front and rear axles,
Figure SMS_115
Represents the front axle,
Figure SMS_121
Rear axle;
Figure SMS_125
is the front wheel steering angle; g is the acceleration due to gravity;
Figure SMS_112
,
Figure SMS_118
,
Figure SMS_120
,
Figure SMS_123
They represent the total longitudinal driving force, air resistance, rolling resistance and slope resistance respectively;
Figure SMS_114
is the aerodynamic drag coefficient; A is the windward area;
Figure SMS_117
is the air density; f is the rolling resistance coefficient;
Figure SMS_122
is the road slope;
Figure SMS_124
is the vehicle longitudinal velocity.

根据所述轮胎动力学模型和所述纵向车辆动力学响应模型确定所述纵向车辆模型。The longitudinal vehicle model is determined based on the tire dynamics model and the longitudinal vehicle dynamics response model.

值得注意的是：空气动力和滚动阻力可以通过现场车辆测试获得，而坡道阻力可以估计得到。另外，图7中，

Figure SMS_126
表示一个电动汽车轮胎总的纵向力；
Figure SMS_127
表示一个电动汽车轮胎总的滚动阻力；
Figure SMS_128
表示一个电动汽车轮胎总的垂向力；
Figure SMS_129
表示一个电动汽车轮胎总的驱动扭矩，La=a；Lb=b，R表示电动汽车轮胎的半径；Fw表示电动汽车的总的空气阻力，v表示电动汽车的行驶速度；
Figure SMS_130
表示电动汽车轮胎的转动角速度。It is worth noting that aerodynamic force and rolling resistance can be obtained through on-site vehicle testing, while ramp resistance can be estimated. In addition, in Figure 7,
Figure SMS_126
Represents the total longitudinal force of an electric vehicle tire;
Figure SMS_127
Indicates the total rolling resistance of an electric vehicle tire;
Figure SMS_128
It represents the total vertical force of an electric vehicle tire;
Figure SMS_129
represents the total driving torque of an electric vehicle tire, La = a; Lb = b, R represents the radius of the electric vehicle tire; Fw represents the total air resistance of the electric vehicle, and v represents the driving speed of the electric vehicle;
Figure SMS_130
Represents the angular velocity of the electric vehicle tire.

悬架是一个典型的非线性系统，本实施例使用STUKF进行垂直轮胎力估计，以悬架高度传感器测量得到的悬架压缩量、压缩率作为观测变量，以系统悬架压缩量、压缩率及通过模型计算得到的垂向轮胎力的初始状态作为状态变量，进行数据融合从而得到接近真实值得垂向轮胎力估计值。具体地，基于强跟踪无迹卡尔曼滤波器，根据所述滚动动力学模型估计垂直轮胎力，包括：The suspension is a typical nonlinear system. In this embodiment, STUKF is used to estimate the vertical tire force. The suspension compression and compression rate measured by the suspension height sensor are used as observation variables. The system suspension compression and compression rate and the initial state of the vertical tire force calculated by the model are used as state variables. Data fusion is performed to obtain a vertical tire force estimation value close to the actual value. Specifically, based on the strong tracking unscented Kalman filter, the vertical tire force is estimated according to the rolling dynamics model, including:

获取悬架系统的非线性离散空间表达式；所述非线性离散空间表达式为：Obtain a nonlinear discrete spatial expression of the suspension system; the nonlinear discrete spatial expression is:

Figure SMS_131
。
Figure SMS_131
.

其中，

Figure SMS_133
为所述滚动动力学模型的垂向状态演化函数，简称为
Figure SMS_135
；
Figure SMS_140
为所述滚动动力学模型的垂向观测函数，简称为
Figure SMS_134
；
Figure SMS_136
为垂向状态变量；
Figure SMS_139
为系统垂向输入；
Figure SMS_141
为垂向过程噪声；
Figure SMS_132
为垂向测量噪声，
Figure SMS_137
表示k-1时刻的垂向状态量；
Figure SMS_138
表示系统垂向测量。in,
Figure SMS_133
is the vertical state evolution function of the rolling dynamics model, referred to as
Figure SMS_135
;
Figure SMS_140
is the vertical observation function of the rolling dynamics model, referred to as
Figure SMS_134
;
Figure SMS_136
is the vertical state variable;
Figure SMS_139
It is the vertical input of the system;
Figure SMS_141
is the vertical process noise;
Figure SMS_132
is the vertical measurement noise,
Figure SMS_137
represents the vertical state quantity at time k-1;
Figure SMS_138
Indicates the vertical measurement of the system.

根据所述非线性离散空间表达式确定每个时间步长下的状态向量。具体地，对于单个悬架，假设弹簧和减尼器具有相同的压缩量和压缩率，可通过悬架高度传感器直接测量。为了提高计算效率，对每个拐角分别估计垂直轮胎力。输入向量

Figure SMS_142
为空。取系统状态下的压缩量、压缩率和轮胎垂直力等值，每个时间步长下的状态向量可表示为：The state vector at each time step is determined according to the nonlinear discrete space expression. Specifically, for a single suspension, the spring and damper are assumed to have the same compression amount and compression rate, which can be directly measured by the suspension height sensor. In order to improve the computational efficiency, the vertical tire force is estimated for each corner separately. The input vector
Figure SMS_142
Is empty. Taking the values of compression, compression rate and tire vertical force under the system state, the state vector at each time step can be expressed as:

Figure SMS_143
。
Figure SMS_143
.

其中，

Figure SMS_144
表示悬挂高度传感器测量的簧上和簧下质量的相对垂直位移；
Figure SMS_145
表示k时刻的垂向状态量1；
Figure SMS_146
表示k时刻的垂向状态量2；
Figure SMS_147
表示k时刻的垂向状态量3；
Figure SMS_148
表示转置。in,
Figure SMS_144
represents the relative vertical displacement of the sprung and unsprung masses as measured by the ride height sensor;
Figure SMS_145
represents the vertical state quantity 1 at time k;
Figure SMS_146
represents the vertical state quantity 2 at time k;
Figure SMS_147
represents the vertical state quantity 3 at time k;
Figure SMS_148
Indicates transpose.

根据所述非线性离散空间表达式确定垂直轮胎力估计的非线性函数。具体地，由于日常行驶中的道路激励相对较小，且非簧载质量的惯性力远小于垂直轮胎力，因此在这里忽略了道路激励的影响。所述垂直轮胎力估计的非线性函数的表达式为：The nonlinear function of the vertical tire force estimation is determined according to the nonlinear discrete space expression. Specifically, since the road excitation in daily driving is relatively small and the inertia force of the unsprung mass is much smaller than the vertical tire force, the influence of the road excitation is ignored here. The expression of the nonlinear function of the vertical tire force estimation is:

Figure SMS_149
Figure SMS_149

；其中，

Figure SMS_152
表示滚动动力学模型的第一垂向状态演化函数；
Figure SMS_153
表示滚动动力学模型的第二垂向状态演化函数；
Figure SMS_156
表示滚动动力学模型的第三垂向状态演化函数；
Figure SMS_151
为离散时间周期；g为重力加速度；
Figure SMS_155
表示k-1时刻的垂向状态量1；
Figure SMS_157
表示k-1时刻的垂向状态量2；
Figure SMS_158
表示第i轮悬架阻尼系数；
Figure SMS_150
表示车轮定位参数对垂直力的影响；
Figure SMS_154
表示第i轮簧下质量。;in,
Figure SMS_152
represents the first vertical state evolution function of the rolling dynamics model;
Figure SMS_153
represents the second vertical state evolution function of the rolling dynamics model;
Figure SMS_156
represents the third vertical state evolution function of the rolling dynamics model;
Figure SMS_151
is the discrete time period; g is the gravitational acceleration;
Figure SMS_155
represents the vertical state quantity 1 at time k-1;
Figure SMS_157
represents the vertical state quantity 2 at time k-1;
Figure SMS_158
represents the suspension damping coefficient of the i-th wheel;
Figure SMS_150
Indicates the influence of wheel alignment parameters on vertical force;
Figure SMS_154
represents the unsprung mass of the i-th wheel.

在时间步长k处的测量值

Figure SMS_159
，可以得出:
Figure SMS_160
。The measured value at time step k
Figure SMS_159
, we can conclude that:
Figure SMS_160
.

根据所述非线性离散空间表达式确定垂直轮胎力估计的观测函数。由于观测函数

Figure SMS_161
是线性的，可以得出所述垂直轮胎力估计的观测函数：The observation function of the vertical tire force estimation is determined according to the nonlinear discrete space expression.
Figure SMS_161
is linear, and the observation function of the vertical tire force estimation can be obtained:

Figure SMS_162
；
Figure SMS_162
;

其中，

Figure SMS_163
表示滚动动力学模型的第一垂向观测函数；
Figure SMS_164
表示滚动动力学模型的第二垂向观测函数。in,
Figure SMS_163
represents the first vertical observation function of the rolling dynamics model;
Figure SMS_164
Represents the second vertical observation function of the rolling dynamics model.

根据所述垂直轮胎力估计的非线性函数和所述垂直轮胎力估计的观测函数确定所述垂直轮胎力。The vertical tire force is determined based on a nonlinear function of the vertical tire force estimate and an observed function of the vertical tire force estimate.

优选地，所述基于经典卡尔曼滤波器，根据所述纵向车辆模型估计纵向轮胎力，包括：Preferably, the estimating the longitudinal tire force based on the longitudinal vehicle model based on a classical Kalman filter comprises:

构建离散的时变线性控制系统；所述时变线性控制系统的表达式为：A discrete time-varying linear control system is constructed; the expression of the time-varying linear control system is:

Figure SMS_165
。
Figure SMS_165
.

其中，

Figure SMS_167
为纵向状态向量；
Figure SMS_172
表示k-1时刻纵向状态变量；
Figure SMS_176
为纵向控制输入；
Figure SMS_168
为纵向测量值；
Figure SMS_170
和
Figure SMS_175
为白噪声；Aʹ和B均为状态转移矩阵；H=[0,1,0]为观测矩阵；
Figure SMS_179
为离散时间周期；车轮转速
Figure SMS_166
；所述纵向车辆模型的状态向量为：
Figure SMS_171
；
Figure SMS_174
表示k时刻的纵向状态向量1；
Figure SMS_178
表示k时刻的纵向状态向量2；
Figure SMS_169
表示k时刻的纵向状态向量3；
Figure SMS_173
表示转置；Aʹ、B的表达式分别为：
Figure SMS_177
；根据所述状态向量进行数据融合，得到所述纵向轮胎力。in,
Figure SMS_167
is the longitudinal state vector;
Figure SMS_172
represents the longitudinal state variable at time k-1;
Figure SMS_176
is the longitudinal control input;
Figure SMS_168
is the longitudinal measurement;
Figure SMS_170
and
Figure SMS_175
is white noise; Aʹ and B are both state transfer matrices; H=[0,1,0] is the observation matrix;
Figure SMS_179
is a discrete time period; wheel speed
Figure SMS_166
; The state vector of the longitudinal vehicle model is:
Figure SMS_171
;
Figure SMS_174
represents the longitudinal state vector 1 at time k;
Figure SMS_178
represents the longitudinal state vector 2 at time k;
Figure SMS_169
represents the longitudinal state vector 3 at time k;
Figure SMS_173
Indicates transposition; the expressions of Aʹ and B are:
Figure SMS_177
; Perform data fusion according to the state vector to obtain the longitudinal tire force.

进一步地，本实施例考虑到电机的输出转矩和车轮转速可以得到控制单元，采用广泛使用的经典卡尔曼滤波器进行纵向轮胎力估计，以轮速传感器测量得到的车轮转速作为观测变量，以车轮转矩作为输入变量，以车辆当前的车轮角速度、角加速度和计算得到的纵向力作为状态变量初值进行数据融合，从而得到接近真实值的纵向轮胎力估计值，具体步骤如下：Furthermore, this embodiment takes into account that the output torque of the motor and the wheel speed can be obtained by the control unit, adopts the widely used classic Kalman filter to estimate the longitudinal tire force, takes the wheel speed measured by the wheel speed sensor as the observation variable, takes the wheel torque as the input variable, and takes the current wheel angular velocity, angular acceleration and calculated longitudinal force of the vehicle as the initial value of the state variable for data fusion, thereby obtaining a longitudinal tire force estimation value close to the true value, and the specific steps are as follows:

考虑一个离散的时变线性控制系统为：Consider a discrete time-varying linear control system:

Figure SMS_180
；
Figure SMS_180
;

对于单个车轮，以车轮转矩为输入，以车轮的角速度、角加速度和纵向力为状态，状态向量可得：For a single wheel, with the wheel torque as input and the wheel angular velocity, angular acceleration and longitudinal force as states, the state vector can be obtained:

Figure SMS_181
。
Figure SMS_181
.

状态转移矩阵A和B可以表示为：The state transfer matrices A and B can be expressed as:

Figure SMS_182
。
Figure SMS_182
.

测量值

Figure SMS_183
为车轮转速，它等于轮内电机的转速:
Figure SMS_184
。Measurements
Figure SMS_183
is the wheel speed, which is equal to the speed of the in-wheel motor:
Figure SMS_184
.

优选地，基于强跟踪无迹卡尔曼滤波器，根据所述横向车辆模型、所述垂直轮胎力和所述纵向轮胎力估计侧向轮胎力，包括：Preferably, estimating the lateral tire force based on the lateral vehicle model, the vertical tire force and the longitudinal tire force based on a strong tracking unscented Kalman filter comprises:

构建轮胎侧向力估计的非线性离散空间方程；所述非线性离散空间方程的计算公式为：A nonlinear discrete space equation for estimating tire lateral force is constructed; the calculation formula of the nonlinear discrete space equation is:

Figure SMS_185
。
Figure SMS_185
.

其中，

Figure SMS_187
为所述横向车辆模型的状态演化函数，简称为
Figure SMS_190
，
Figure SMS_193
为所述横向车辆模型的观测函数，简称为
Figure SMS_188
；
Figure SMS_191
表示k时刻横向状态变量；
Figure SMS_194
表示k-1时刻横向状态变量；
Figure SMS_195
表示系统横向输入；
Figure SMS_186
表示系统横向过程噪声；
Figure SMS_189
表示系统横向测量；
Figure SMS_192
表示横向测量噪声。in,
Figure SMS_187
is the state evolution function of the lateral vehicle model, referred to as
Figure SMS_190
,
Figure SMS_193
is the observation function of the lateral vehicle model, referred to as
Figure SMS_188
;
Figure SMS_191
represents the lateral state variable at time k;
Figure SMS_194
represents the lateral state variable at time k-1;
Figure SMS_195
Indicates the lateral input of the system;
Figure SMS_186
represents the lateral process noise of the system;
Figure SMS_189
represents the lateral measurement of the system;
Figure SMS_192
represents the lateral measurement noise.

将侧向加速度、偏航加速度以及四个侧向轮胎力作为系统状态，获取状态向量；所述状态向量的计算公式为：The lateral acceleration, yaw acceleration and four lateral tire forces are taken as the system state to obtain the state vector; the calculation formula of the state vector is:

Figure SMS_196
；
Figure SMS_196
;

其中，

Figure SMS_197
表示k时刻的第1个横向状态变量，
Figure SMS_198
表示k时刻的第2个横向状态变量，
Figure SMS_199
表示k时刻的第3个横向状态变量，
Figure SMS_200
表示k时刻的第4个横向状态变量，
Figure SMS_201
表示k时刻的第5个横向状态变量，
Figure SMS_202
表示k时刻的第6个横向状态变量。in,
Figure SMS_197
represents the first lateral state variable at time k,
Figure SMS_198
represents the second lateral state variable at time k,
Figure SMS_199
represents the third lateral state variable at time k,
Figure SMS_200
represents the fourth lateral state variable at time k,
Figure SMS_201
represents the fifth lateral state variable at time k,
Figure SMS_202
Represents the sixth lateral state variable at time k.

获取系统横向输入；所述系统横向输入的计算公式为：Obtain the system horizontal input; the calculation formula of the system horizontal input is:

Figure SMS_203
。
Figure SMS_203
.

其中，

Figure SMS_207
表示k时刻前轮转角；
Figure SMS_213
表示左前轮横向力；
Figure SMS_215
表示右前轮横向力；
Figure SMS_204
表示左前轮垂向力；
Figure SMS_210
表示右前轮垂向力；
Figure SMS_211
表示左后轮垂向力；
Figure SMS_217
表示右后轮垂向力；
Figure SMS_205
表示系统横向输入量1；
Figure SMS_208
表示系统横向输入量2；
Figure SMS_212
表示系统横向输入量3；
Figure SMS_214
表示系统横向输入量4；
Figure SMS_206
表示系统横向输入量5；
Figure SMS_209
表示系统横向输入量6；
Figure SMS_216
表示系统横向输入量7。in,
Figure SMS_207
represents the front wheel turning angle at time k;
Figure SMS_213
represents the lateral force of the left front wheel;
Figure SMS_215
represents the lateral force of the right front wheel;
Figure SMS_204
represents the vertical force on the left front wheel;
Figure SMS_210
represents the vertical force on the right front wheel;
Figure SMS_211
represents the vertical force on the left rear wheel;
Figure SMS_217
represents the vertical force on the right rear wheel;
Figure SMS_205
Indicates the system lateral input 1;
Figure SMS_208
Indicates the system lateral input 2;
Figure SMS_212
Indicates the lateral input quantity of the system 3;
Figure SMS_214
Indicates the lateral input quantity of the system 4;
Figure SMS_206
Indicates the system lateral input quantity 5;
Figure SMS_209
Indicates the lateral input of the system 6;
Figure SMS_216
Indicates the system lateral input quantity 7.

根据所述非线性离散空间方程确定侧向轮胎力估计的非线性函数；所述侧向轮胎力估计的非线性函数的表达式为：The nonlinear function of lateral tire force estimation is determined according to the nonlinear discrete space equation; the expression of the nonlinear function of lateral tire force estimation is:

Figure SMS_218
Figure SMS_218

；其中，

Figure SMS_221
表示横向车辆模型的第一状态演化函数，
Figure SMS_223
表示横向车辆模型的第二状态演化函数，
Figure SMS_227
表示横向车辆模型的第三状态演化函数，
Figure SMS_222
表示横向车辆模型的第四状态演化函数，
Figure SMS_224
表示横向车辆模型的第五状态演化函数，
Figure SMS_226
表示横向车辆模型的第六状态演化函数；
Figure SMS_229
表示k-1时刻的第1个横向状态变量；
Figure SMS_219
表示k-1时刻的第2个横向状态变量；
Figure SMS_225
表示k-1时刻的第3个横向状态变量；
Figure SMS_228
表示k-1时刻的第4个横向状态变量；
Figure SMS_230
表示k-1时刻的第5个横向状态变量；
Figure SMS_220
表示k-1时刻的第6个横向状态变量。;in,
Figure SMS_221
represents the first state evolution function of the lateral vehicle model,
Figure SMS_223
represents the second state evolution function of the lateral vehicle model,
Figure SMS_227
represents the third state evolution function of the lateral vehicle model,
Figure SMS_222
represents the fourth state evolution function of the lateral vehicle model,
Figure SMS_224
represents the fifth state evolution function of the lateral vehicle model,
Figure SMS_226
represents the sixth state evolution function of the lateral vehicle model;
Figure SMS_229
represents the first lateral state variable at time k-1;
Figure SMS_219
represents the second lateral state variable at time k-1;
Figure SMS_225
represents the third lateral state variable at time k-1;
Figure SMS_228
represents the fourth lateral state variable at time k-1;
Figure SMS_230
represents the fifth lateral state variable at time k-1;
Figure SMS_220
represents the sixth lateral state variable at time k-1.

根据所述非线性离散空间方程确定侧向轮胎力估计的观测函数；所述侧向轮胎力估计的观测函数的表达式为：The observation function for estimating the lateral tire force is determined according to the nonlinear discrete space equation; the expression of the observation function for estimating the lateral tire force is:

Figure SMS_231
；其中，
Figure SMS_232
表示横向车辆模型的第一观测函数；
Figure SMS_233
表示横向车辆模型的第二观测函数。
Figure SMS_231
;in,
Figure SMS_232
A first observation function representing a lateral vehicle model;
Figure SMS_233
Represents the second observation function of the lateral vehicle model.

根据所述侧向轮胎力估计的观测函数和所述侧向轮胎力估计的非线性函数确定所述侧向轮胎力。The lateral tire force estimate is determined based on an observed function of the lateral tire force estimate and a nonlinear function of the lateral tire force estimate.

本实施例中，准确的侧向轮胎力估计对于车辆横向稳定性评估非常重要。本文的侧向轮胎力估计是以惯性测量装置、方向盘转角传感器测量计算得到的侧向加速度和偏航加速度作为观测变量，以前轮转向角、估算得到的纵向轮胎力和垂直轮胎力作为输入变量，以车辆当前的侧向加速度、偏航加速度以及四个计算得到的侧向轮胎力作为系统状态进行数据融合，从而得到接近真实值得侧向轮胎力估计值，具体步骤如下：In this embodiment, accurate lateral tire force estimation is very important for evaluating the lateral stability of the vehicle. The lateral tire force estimation in this paper uses the lateral acceleration and yaw acceleration measured and calculated by the inertial measurement device and the steering wheel angle sensor as observation variables, the front wheel steering angle, the estimated longitudinal tire force and the vertical tire force as input variables, and the current lateral acceleration, yaw acceleration and four calculated lateral tire forces of the vehicle as the system state for data fusion, so as to obtain a lateral tire force estimation value close to the actual value. The specific steps are as follows:

轮胎侧向力估计的非线性离散空间方程为：The nonlinear discrete space equation for tire lateral force estimation is:

Figure SMS_234
；
Figure SMS_234
;

取车辆的侧向加速度和偏航加速度以及四个侧向轮胎力作为系统状态，其状态向量可以表示为：Taking the lateral acceleration and yaw acceleration of the vehicle and the four lateral tire forces as the system state, its state vector can be expressed as:

Figure SMS_235
。
Figure SMS_235
.

系统横向输入具体为输入向量，由前轮转向角、纵向轮胎力和垂直轮胎力组成，可以表示为下式：The lateral input of the system is specifically an input vector, which is composed of the front wheel steering angle, longitudinal tire force and vertical tire force, and can be expressed as follows:

Figure SMS_236
；
Figure SMS_236
;

前轮转向角由转向角编码器测量，系统测量包括侧向加速度和偏航加速度，公式为：The front wheel steering angle is measured by the steering angle encoder. The system measures lateral acceleration and yaw acceleration. The formula is:

Figure SMS_237
。
Figure SMS_237
.

侧向轮胎力估计的非线性函数可以表示为：The nonlinear function of lateral tire force estimation can be expressed as:

Figure SMS_238
。
Figure SMS_238
.

观测函数

Figure SMS_239
可以表示为：Observation function
Figure SMS_239
It can be expressed as:

Figure SMS_240
。
Figure SMS_240
.

本实施例还提供了一种四轮毂电机驱动全线控电动汽车轮胎力估计系统，包括参数获取模块、模型构建模块、第一估计模块、第二估计模块和第三估计模块。The present embodiment also provides a tire force estimation system for a four-wheel-hub motor driven fully controlled-by-wire electric vehicle, comprising a parameter acquisition module, a model building module, a first estimation module, a second estimation module and a third estimation module.

参数获取模块，用于获取车内传感器的传感信号参数；所述传感信号参数包括悬架高度数据、惯性测量数据、方向盘角度数据、车辆信号数据和电机数据。模型构建模块，用于根据所述传感信号参数分别构建滚动动力学模型、横向车辆模型和纵向车辆模型。第一估计模块，用于基于强跟踪无迹卡尔曼滤波器，根据所述滚动动力学模型估计垂直轮胎力。第二估计模块，用于基于经典卡尔曼滤波器，根据所述纵向车辆模型估计纵向轮胎力。第三估计模块，用于基于强跟踪无迹卡尔曼滤波器，根据所述横向车辆模型、所述垂直轮胎力和所述纵向轮胎力估计侧向轮胎力。A parameter acquisition module is used to acquire sensor signal parameters of in-vehicle sensors; the sensor signal parameters include suspension height data, inertial measurement data, steering wheel angle data, vehicle signal data and motor data. A model construction module is used to respectively construct a rolling dynamics model, a lateral vehicle model and a longitudinal vehicle model according to the sensor signal parameters. A first estimation module is used to estimate the vertical tire force according to the rolling dynamics model based on a strong tracking unscented Kalman filter. A second estimation module is used to estimate the longitudinal tire force according to the longitudinal vehicle model based on a classical Kalman filter. A third estimation module is used to estimate the lateral tire force according to the lateral vehicle model, the vertical tire force and the longitudinal tire force based on a strong tracking unscented Kalman filter.

本发明的有益效果如下：The beneficial effects of the present invention are as follows:

（1）本发明利用低成本车载传感器信息，轮毂电机和线控制动系统状态反馈信息实现轮胎纵向、侧向和垂向轮胎估计力；(1) The present invention utilizes low-cost vehicle-mounted sensor information, wheel hub motor and wire control brake system status feedback information to achieve tire longitudinal, lateral and vertical tire force estimation;

（2）本发明使用强跟踪无迹卡尔曼滤波器估计轮胎侧向力和垂向力，较之传统的卡尔曼滤波器，在动态跟踪能力和收敛速度方面具有更好的性能；(2) The present invention uses a strong tracking unscented Kalman filter to estimate tire lateral force and vertical force, which has better performance in terms of dynamic tracking capability and convergence speed compared with the traditional Kalman filter;

（3）本发明未使用参数繁多的轮胎模型进行轮胎力估计，估计算法精度高、鲁棒性好。(3) The present invention does not use a tire model with numerous parameters to estimate tire force, and the estimation algorithm has high accuracy and good robustness.

本说明书中各个实施例采用递进的方式描述，每个实施例重点说明的都是与其他实施例的不同之处，各个实施例之间相同相似部分互相参见即可。对于实施例公开的系统而言，由于其与实施例公开的方法相对应，所以描述的比较简单，相关之处参见方法部分说明即可。In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想；同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处。综上所述，本说明书内容不应理解为对本发明的限制。This article uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the method and core ideas of the present invention. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims (8)

1. The method for estimating the tire force of the four-wheel hub motor driven full-drive electric automobile is characterized by comprising the following steps of:
acquiring sensing signal parameters of an in-vehicle sensor; the sensing signal parameters comprise suspension height data, inertia measurement data, steering wheel angle data, vehicle signal data and motor data;
respectively constructing a rolling dynamics model, a transverse vehicle model and a longitudinal vehicle model according to the sensing signal parameters;
estimating vertical tire force according to the rolling dynamics model based on a strong tracking unscented Kalman filter; the construction method of the rolling dynamics model comprises the following steps:
constructing a first model: the expression of the first model is:
Figure QLYQS_1
；
wherein,
Figure QLYQS_2
and->
Figure QLYQS_6
The vertical displacements on and off the spring are respectively, and the superscripts i E [ L1, L2, R1, R2]L1, L2, R1 and R2 represent front left, front right, rear left and rear right, respectively;
Figure QLYQS_7
Is the actuating force of the active suspension;
Figure QLYQS_4
A distributed sprung mass on each wheel;
Figure QLYQS_8
And->
Figure QLYQS_9
Stiffness and damping for each suspension, respectively, obtained from an active suspension controller; g is gravity acceleration;
Figure QLYQS_10
the height of the suspension is not deformed;
Figure QLYQS_3
Representing a first derivative;
Figure QLYQS_5
Representing a second order reciprocal;
determining a second model according to the first model, wherein the expression of the second model is as follows:
Figure QLYQS_11
；
Wherein,
Figure QLYQS_12
relative vertical displacement of sprung and unsprung masses measured for suspension height sensor;
determining a third model according to the second model; the expression of the third model is:
Figure QLYQS_13
；
wherein,
Figure QLYQS_14
representing the influence of the wheel alignment parameters on the vertical force;
Figure QLYQS_15
Representing random road incentives;
Figure QLYQS_16
For vertical tyre force>
Figure QLYQS_17
Representing the tire vertical force as a function of unsprung mass and road excitation;
Figure QLYQS_18
Representing the unsprung mass at each corner;
constructing a roll dynamics model; the expression of the roll dynamics model is:
Figure QLYQS_19
；
Figure QLYQS_20
；
wherein,
Figure QLYQS_21
、
Figure QLYQS_22
and->
Figure QLYQS_23
The roll angle, sprung mass and lateral acceleration of the vehicle respectively;
Figure QLYQS_24
Representing the vertical distance from the center of gravity to the roll center;
Figure QLYQS_25
Indicating that the spring mass is wound at the centre of gravityxThe moment of inertia of the shaft;
Figure QLYQS_26
Representing roll angle stiffness, +.>
Figure QLYQS_27
Representing the damping coefficient;lrepresenting the distance between the mounting positions of the left and right suspensions on the same shaft;
determining a fourth model from the roll dynamics model; the expression of the fourth model is:
Figure QLYQS_28
；
determining a fifth model according to the fourth model; the expression of the fifth model is:
Figure QLYQS_29
；
wherein,
Figure QLYQS_30
as a function of the amount of suspension compression and the roll angle of the vehicle,/->
Figure QLYQS_31
Is the amount of suspension compression;
the expression of the rolling dynamics model is:
Figure QLYQS_32
Figure QLYQS_33
；
Estimating longitudinal tire forces from the longitudinal vehicle model based on a classical kalman filter;
based on a strong tracking unscented kalman filter, a lateral tire force is estimated from the lateral vehicle model, the vertical tire force, and the longitudinal tire force.
2. The four-wheel hub motor-driven all-drive-by-wire electric vehicle tire force estimation method according to claim 1, wherein the in-vehicle sensor includes: suspension height sensor, inertial measurement unit, in-wheel motor, vehicle signal sensor and steering wheel angle sensor; the suspension height sensor is used for measuring suspension height data; the inertial measurement device is used for measuring inertial measurement data; the hub motor is used for measuring motor data; the vehicle signal sensor is used for measuring vehicle signal data; the steering wheel angle sensor is used for measuring steering wheel angle data.
3. The four-wheel hub motor-driven all-drive-by-wire electric vehicle tire force estimation method according to claim 1, wherein the construction method of the lateral vehicle model is as follows:
constructing a three-degree-of-freedom vehicle model; the expression of the three-degree-of-freedom vehicle model is as follows:
Figure QLYQS_34
；
Figure QLYQS_35
；
Figure QLYQS_36
；
wherein m is the mass of the vehicle;
Figure QLYQS_54
Is the lateral acceleration of the vehicle;
Figure QLYQS_40
、
Figure QLYQS_44
And->
Figure QLYQS_53
The steering angle, yaw acceleration and moment of inertia around the z-axis of the front wheel are respectively;
Figure QLYQS_58
And->
Figure QLYQS_56
The front tread width and the rear tread width, respectively;
Figure QLYQS_57
Representing the left front wheel longitudinal force;
Figure QLYQS_45
representing the left rear wheel longitudinal force;
Figure QLYQS_50
Representing left front wheel lateral force;
Figure QLYQS_37
Representing left rear wheel lateral force;
Figure QLYQS_42
Representing the right front wheel lateral force;
Figure QLYQS_39
Represents the right rear wheel lateral force;
Figure QLYQS_41
Representing the right front wheel longitudinal force;
Figure QLYQS_46
Representing the right rear wheel longitudinal force;
Figure QLYQS_47
Representing the lateral forces of the left front wheel and the left rear wheel;
Figure QLYQS_49
Representing the sum of the lateral forces of the right front wheel and the right rear wheel;
Figure QLYQS_51
Representing the sum of the vertical forces of the left front wheel and the left rear wheel;
Figure QLYQS_52
Representing the sum of the vertical forces of the right front wheel and the right rear wheel;
Figure QLYQS_55
And->
Figure QLYQS_38
Representing distances from the center of gravity to the front and rear axes, respectively;
Figure QLYQS_43
Representing a first derivative;
Figure QLYQS_48
Representing a yaw rate of the vehicle;
constructing a linear transverse tire model; the expression of the linear transverse tire model is as follows:
Figure QLYQS_59
；/>
Figure QLYQS_60
；
wherein,
Figure QLYQS_63
and->
Figure QLYQS_65
The cornering stiffness and the tire cornering angle of each axle are respectively marked +.>
Figure QLYQS_69
Represents the cornering stiffness of the front and rear axle, < >>
Figure QLYQS_62
Representing the front axle->
Figure QLYQS_66
Representing the rear axle;
Figure QLYQS_68
And->
Figure QLYQS_70
The vehicle sideslip angle and the vehicle longitudinal speed respectively;
Figure QLYQS_61
A lateral force being the front axle or rear axle tire; / >
Figure QLYQS_64
Representing the slip angle of the front axle wheel;
Figure QLYQS_67
Representing the slip angle of the rear axle wheel;
determining the lateral vehicle model from the three degree of freedom vehicle model and the linearized lateral tire model; the expression of the lateral vehicle model is:
Figure QLYQS_71
；
Figure QLYQS_72
。
4. the four-wheel hub motor-driven all-drive-by-wire electric vehicle tire force estimation method according to claim 1, wherein the longitudinal vehicle model construction method is as follows:
building a tire dynamics model; the expression of the tire dynamics model is as follows:
Figure QLYQS_73
；
wherein,
Figure QLYQS_74
、
Figure QLYQS_75
、
Figure QLYQS_76
、
Figure QLYQS_77
、
Figure QLYQS_78
respectively representing the driving torque, braking torque, rolling resistance, effective radius and moment of inertia of the wheels;
Figure QLYQS_79
Representing the longitudinal force of the tire;
Figure QLYQS_80
Representing the rotational angular velocity of the wheel;
constructing a longitudinal vehicle dynamics response model; the expression of the longitudinal vehicle dynamics response model is:
Figure QLYQS_81
；
Figure QLYQS_82
；
wherein m is the mass of the vehicle;
Figure QLYQS_91
representing the longitudinal acceleration of the vehicle;
Figure QLYQS_84
Representing the total rolling resistance of the whole vehicle;
Figure QLYQS_87
Representing the total longitudinal force of the whole vehicle; superscript i.epsilon.L 1, L2, R1, R2]L1, L2, R1 and R2 represent left front, right front, left rear and right rear, respectively,/->
Figure QLYQS_94
Representing the left front wheel longitudinal force;
Figure QLYQS_96
Representing the left rear wheel longitudinal force;
Figure QLYQS_100
Representing left front wheel lateral force; / >
Figure QLYQS_102
Representing left rear wheel lateral force;
Figure QLYQS_92
Representing the right front wheel lateral force;
Figure QLYQS_95
Represents the right rear wheel lateral force; upper energizer->
Figure QLYQS_86
Represents the cornering stiffness of the front and rear axle, < >>
Figure QLYQS_89
Representing the front axle->
Figure QLYQS_83
Representing the rear axle;
Figure QLYQS_88
Steering angle for front wheel; g is gravity acceleration;
Figure QLYQS_93
、
Figure QLYQS_103
、
Figure QLYQS_97
、
Figure QLYQS_98
Respectively representing total longitudinal driving force, air resistance, rolling resistance and gradient resistance;
Figure QLYQS_99
Is the aerodynamic drag coefficient; a is the windward area;
Figure QLYQS_101
Is air density;fis the rolling resistance coefficient;
Figure QLYQS_85
Is road grade;
Figure QLYQS_90
Is the longitudinal speed of the vehicle; />
Determining the longitudinal vehicle model from the tire dynamics model and the longitudinal vehicle dynamics response model.
5. The method for estimating tire force of a four-wheel hub motor-driven all-drive-by-wire electric vehicle according to claim 1, wherein the estimating vertical tire force based on the rolling dynamics model based on a strong tracking unscented kalman filter comprises:
acquiring a nonlinear discrete space expression of a suspension system; the nonlinear discrete space expression is:
Figure QLYQS_104
；
wherein,
Figure QLYQS_107
is a vertical state evolution function of the rolling dynamics model, which is simply called +.>
Figure QLYQS_109
；
Figure QLYQS_112
For the vertical observation function of the rolling dynamics model, simply called +.>
Figure QLYQS_105
；
Figure QLYQS_110
Is a vertical state variable; / >
Figure QLYQS_113
Is a system vertical input;
Figure QLYQS_114
Is vertical process noise;
Figure QLYQS_106
For measuring noise vertically->
Figure QLYQS_108
Representing the vertical state quantity at the time of k-1;
Figure QLYQS_111
Representing a system vertical measurement;
determining a state vector at each time step according to the nonlinear discrete space expression; the expression of the state vector is:
Figure QLYQS_115
；
wherein,
Figure QLYQS_116
representing the relative vertical displacement of the sprung and unsprung masses measured by the suspension height sensor;
Figure QLYQS_117
A vertical state quantity 1 representing the time k;
Figure QLYQS_118
A vertical state quantity 2 representing the time k;
Figure QLYQS_119
A vertical state quantity 3 representing the time k;
Figure QLYQS_120
Representing a transpose;
determining a nonlinear function of the vertical tire force estimate from the nonlinear discrete spatial expression; the expression of the nonlinear function of the vertical tire force estimate is:
Figure QLYQS_121
；
wherein,
Figure QLYQS_122
a first vertical state evolution function representing a rolling dynamics model;
Figure QLYQS_126
A second vertical state evolution function representing a rolling dynamics model;
Figure QLYQS_127
A third vertical state evolution function representing a rolling dynamics model;
Figure QLYQS_123
Is a discrete time period; g is gravity acceleration;
Figure QLYQS_128
A vertical state quantity 1 at time k-1;
Figure QLYQS_129
A vertical state quantity 2 representing the time k-1;
Figure QLYQS_130
representing the damping coefficient of the ith wheel suspension;
Figure QLYQS_124
Representing the influence of the wheel alignment parameters on the vertical force;
Figure QLYQS_125
Representing the i-th wheel unsprung mass;
determining an observation function of the vertical tire force estimation according to the nonlinear discrete space expression; the expression of the observation function of the vertical tire force estimation is:
Figure QLYQS_131
；
wherein,
Figure QLYQS_132
a first vertical observation function representing a rolling dynamics model;
Figure QLYQS_133
A second vertical observation function representing a rolling dynamics model; />
The vertical tire force is determined from a nonlinear function of the vertical tire force estimate and an observation function of the vertical tire force estimate.
6. The four-wheel hub motor driven all-drive-by-wire electric vehicle tire force estimation method according to claim 4, wherein the estimating longitudinal tire force from the longitudinal vehicle model based on a classical kalman filter comprises:
constructing a discrete time-varying linear control system; the expression of the time-varying linear control system is as follows:
Figure QLYQS_134
；
wherein,
Figure QLYQS_137
is a longitudinal state vector;
Figure QLYQS_140
Representing a longitudinal state variable at time k-1;
Figure QLYQS_143
Is a longitudinal control input;
Figure QLYQS_136
Is a longitudinal measurement;
Figure QLYQS_141
And->
Figure QLYQS_146
White noise; a ʹ and B are both state transition matrices; h= [0,1,0]Is an observation matrix;
Figure QLYQS_147
Is a discrete time period; wheel speed->
Figure QLYQS_135
The method comprises the steps of carrying out a first treatment on the surface of the The state vector of the longitudinal vehicle model is: / >
Figure QLYQS_139
；
Figure QLYQS_142
A vertical state vector 1 representing time k;
Figure QLYQS_145
A vertical state vector 2 representing the time k;
Figure QLYQS_138
A vertical state vector 3 representing the time k;
Figure QLYQS_144
Representing a transpose; the expressions of A ʹ and B are respectively:
Figure QLYQS_148
；
and carrying out data fusion according to the state vector to obtain the longitudinal tire force.
7. The four-wheel hub motor-driven all-drive-by-wire electric vehicle tire force estimation method according to claim 3, wherein estimating lateral tire forces from the lateral vehicle model, the vertical tire forces, and the longitudinal tire forces based on a strong tracking unscented kalman filter, comprises:
constructing a nonlinear discrete space equation of the tire lateral force estimation; the calculation formula of the nonlinear discrete space equation is as follows:
Figure QLYQS_149
；
wherein,
Figure QLYQS_151
a state evolution function for said transversal vehicle model, abbreviated as +.>
Figure QLYQS_154
，
Figure QLYQS_159
For the observation function of the transverse vehicle model, simply called +.>
Figure QLYQS_152
；
Figure QLYQS_153
Representing a transverse state variable at time k;
Figure QLYQS_156
Represents the transverse state variable at time k-1;
Figure QLYQS_158
Representing a system lateral input;
Figure QLYQS_150
Representing system lateral process noise;
Figure QLYQS_155
Representing a system lateral measurement;
Figure QLYQS_157
Representing lateral measurement noise;
taking the lateral acceleration, the yaw acceleration and the four lateral tire forces as system states, and acquiring state vectors; the calculation formula of the state vector is as follows:
Figure QLYQS_160
；
Wherein,
Figure QLYQS_161
represents the 1 st lateral state variable,/-at time k>
Figure QLYQS_162
Represents the 2 nd lateral state variable at time k,/->
Figure QLYQS_163
Represents the 3 rd lateral state variable,/-at time k>
Figure QLYQS_164
Represents the 4 th lateral state variable,/-at time k>
Figure QLYQS_165
Represents the 5 th lateral state variable,/-at time k>
Figure QLYQS_166
A 6 th lateral state variable representing time k;
acquiring system transverse input; the calculation formula of the system transverse input is as follows:
Figure QLYQS_167
；
wherein,
Figure QLYQS_169
the front wheel rotation angle at the moment k is represented;
Figure QLYQS_175
Representing left front wheel lateral force;
Figure QLYQS_180
Representing the right front wheel lateral force;
Figure QLYQS_171
Representing left front wheel vertical force;
Figure QLYQS_174
Representing right front wheel vertical force;
Figure QLYQS_179
Representing left rear wheel vertical force;
Figure QLYQS_181
Representing right rear wheel vertical force;
Figure QLYQS_168
Representing a system lateral input 1;
Figure QLYQS_172
Representing a system lateral input quantity 2;
Figure QLYQS_176
Representing a system lateral input 3;
Figure QLYQS_178
Representing a system lateral input 4;
Figure QLYQS_170
Representing a system lateral input 5;
Figure QLYQS_173
Representing a system lateral input 6;
Figure QLYQS_177
Representing a system lateral input 7;
determining a nonlinear function of the lateral tire force estimate from the nonlinear discrete space equation; the expression of the nonlinear function of the lateral tire force estimation is:
Figure QLYQS_182
；
wherein,
Figure QLYQS_185
a first state evolution function representing a transversal vehicle model,/->
Figure QLYQS_189
Representing a second shape of the transverse vehicle model State evolution function (DOF)>
Figure QLYQS_193
A third state evolution function representing a transversal vehicle model,/->
Figure QLYQS_183
A fourth state evolution function representing a transversal vehicle model,/->
Figure QLYQS_187
A fifth state evolution function representing a transversal vehicle model,/->
Figure QLYQS_190
A sixth state evolution function representing a lateral vehicle model;
Figure QLYQS_194
Represents the 1 st lateral state variable at time k-1;
Figure QLYQS_186
Represents the 2 nd lateral state variable at time k-1;
Figure QLYQS_188
Represents the 3 rd lateral state variable at time k-1;
Figure QLYQS_191
Represents the 4 th lateral state variable at time k-1;
Figure QLYQS_192
represents the 5 th lateral state variable at time k-1;
Figure QLYQS_184
Represents the 6 th lateral state variable at time k-1;
determining an observation function of the lateral tire force estimation according to the nonlinear discrete space equation; the expression of the observation function of the lateral tire force estimation is:
Figure QLYQS_195
；
wherein,
Figure QLYQS_196
a first observation function representing a lateral vehicle model;
Figure QLYQS_197
A second observation function representing a lateral vehicle model;
the lateral tire force is determined from an observation function of the lateral tire force estimate and a nonlinear function of the lateral tire force estimate.
8. A four-wheel hub motor-driven all-drive-by-wire electric vehicle tire force estimation system, comprising:
the parameter acquisition module is used for acquiring sensing signal parameters of the in-vehicle sensor; the sensing signal parameters comprise suspension height data, inertia measurement data, steering wheel angle data, vehicle signal data and motor data;
The model construction module is used for respectively constructing a rolling dynamics model, a transverse vehicle model and a longitudinal vehicle model according to the sensing signal parameters; the construction method of the rolling dynamics model comprises the following steps:
constructing a first model: the expression of the first model is:
Figure QLYQS_198
；
wherein,
Figure QLYQS_201
and->
Figure QLYQS_204
The vertical displacements on and off the spring are respectively, and the superscripts i E [ L1, L2, R1, R2]，L1、L2, R1 and R2 represent front left, front right, rear left and rear right, respectively;
Figure QLYQS_206
Is the actuating force of the active suspension;
Figure QLYQS_200
A distributed sprung mass on each wheel;
Figure QLYQS_203
And->
Figure QLYQS_205
Stiffness and damping for each suspension, respectively, obtained from an active suspension controller; g is gravity acceleration;
Figure QLYQS_207
the height of the suspension is not deformed;
Figure QLYQS_199
Representing a first derivative;
Figure QLYQS_202
Representing a second order reciprocal;
determining a second model according to the first model, wherein the expression of the second model is as follows:
Figure QLYQS_208
；
wherein,
Figure QLYQS_209
relative vertical displacement of sprung and unsprung masses measured for suspension height sensor;
determining a third model according to the second model; the expression of the third model is:
Figure QLYQS_210
；
wherein,
Figure QLYQS_211
representing the influence of the wheel alignment parameters on the vertical force;
Figure QLYQS_212
Representing random road incentives;
Figure QLYQS_213
For vertical tyre force>
Figure QLYQS_214
Representing the tire vertical force as a function of unsprung mass and road excitation; / >
Figure QLYQS_215
Representing the unsprung mass at each corner;
constructing a roll dynamics model; the expression of the roll dynamics model is:
Figure QLYQS_216
；/>
Figure QLYQS_217
；
wherein,
Figure QLYQS_218
、
Figure QLYQS_219
and->
Figure QLYQS_220
The roll angle, sprung mass and lateral acceleration of the vehicle respectively;
Figure QLYQS_221
Representing the vertical distance from the center of gravity to the roll center;
Figure QLYQS_222
Indicating that the spring mass is wound at the centre of gravityxThe moment of inertia of the shaft;
Figure QLYQS_223
Representing roll angle stiffness, +.>
Figure QLYQS_224
Representing the damping coefficient;lrepresenting the distance between the mounting positions of the left and right suspensions on the same shaft;
determining a fourth model from the roll dynamics model; the expression of the fourth model is:
Figure QLYQS_225
；
determining a fifth model according to the fourth model; the expression of the fifth model is:
Figure QLYQS_226
；
wherein,
Figure QLYQS_227
as a function of the amount of suspension compression and the roll angle of the vehicle,/->
Figure QLYQS_228
Is the amount of suspension compression;
the expression of the rolling dynamics model is:
Figure QLYQS_229
Figure QLYQS_230
；
the first estimation module is used for estimating the vertical tire force according to the rolling dynamics model based on a strong tracking unscented Kalman filter;
a second estimation module for estimating longitudinal tire forces from the longitudinal vehicle model based on a classical kalman filter;
a third estimation module for estimating lateral tire forces from the lateral vehicle model, the vertical tire forces, and the longitudinal tire forces based on a strong tracking unscented kalman filter.
CN202310237547.2A 2023-03-14 2023-03-14 Tire force estimation method and system for full-wire control electric vehicle driven by four-wheel hub motor Active CN115946707B (en)

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