车辆三自由度平面运动稳定性的非线性分析及控制策略评价
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摘要
车辆操纵稳定性分析与控制是涉及人身安全和公路利用率的重大科研课题,研究车辆在高速、冰雪雨霜等恶劣气候条件、紧急转向等工况下的转向失稳机理和评价车辆操纵稳定性控制策略的有效性非常重要。
因此,本论文在查阅大量国内外相关文献资料的基础上,通过对比分析现阶段关于车辆操纵稳定性分析及控制的研究,提出建立包括纵向速度在内的汽车操纵稳定性三自由度(纵向、侧向和横摆运动)非线性模型,用非线性分析方法对车辆系统的稳定性及相关的控制策略进行更加全面地研究。论文的主要内容是:
1.建立了汽车操纵稳定性三自由度(纵向、侧向和横摆运动)系统模型,分析了车辆的纵向加速度对车辆系统稳定条件的影响。
2.研究了三自由度车辆动力学系统的相空间特性,分析了不同前轮转角输入时,系统相轨线、状态变量以及车辆运动轨迹和前后轮胎侧向力的分布等动力学特性的变化;提出用遗传算法求解三自由度车辆动力学系统的平衡点,解决了传统解析算法和数值方法无法求解的问题;根据混沌动力学及分岔理论,分别用相轨线、庞加莱截面和功率谱密度揭示了车辆转向过程中出现的混沌运动。
3.提出了利用相空间搜索法和胞映射法的改进算法求解车辆三自由度平面运动的吸引域,得到了整个相空间范围内的吸引域;利用求解得到的车辆三自由度系统的不稳定平衡点,确定了车辆平面运动的r步吸引域。通过实例分析,即利用已有的赛车试验数据,对所得的理论分析结果进行了定性的验证。
4.基于吸引域的分析,分别研究直接橫摆力矩控制和四轮转向控制对车辆动力学系统吸引域的影响,分析这两种控制方式各自有效的作用区域,评价二者对车辆操作稳定性的控制效果。
The increase of traffic volume and vehicle speed, and the influence of atrocious weather such as ice, snow and rain make vehicle usually drive under the condition of high speed and emergency steer and lose its stability, which leads to many traffic accidents. On the other hand, the speed constrained by the current bend technique is the main bottleneck of increasing traffic volume and of highway utilization. Therefore, the analysis and control of vehicle handing stability are the important project for human safety and highway utilization. It is important to do the research on the mechanism of vehicle losing stability during ultimate conditions and the control strategy of increasing vehicle handing stability.
Vehicle dynamic characteristics change fundamentally with high speed during emergency conditions. It is necessary to know the vehicle dynamic characteristics, analyze vehicle stability and obtain the stability region before studying on vehicle stability control.
In the classic vehicle handling theory, the two degree of freedom (2DOF) vehicle dynamic model is established on the hypothesis of linear vehicle and tyre. This model contains two state variables, which are lateral velocity and yaw rate. It is suitable to analyze the stability during small steering angle and under low speed. But when vehicle running during large steering angle and with high speed, the tyre side slip angle is not in linear region anymore and the coupling of longitudinal motion and yaw motion make the longitudinal speed and acceleration change quickly. The linear hypothesis is not tenable.
Therefore, in order to study on the vehicle handling stability during emergency conditions, it is requisite to establish the nonlinear three degree of freedom (3DOF) vehicle dynamic model containing the longitudinal, lateral and yaw motion, and analyze the stability using nonlinear methods thoroughly. It is meaningful and important to study the vehicle handling stability and mechanism of vehicle losing stability.
Furthermore, with the development of chassis electronic, the basic forms of vehicle handling stability control have been conformed. Vehicle handling stability could be realized by direct yaw moment control, four-wheel steering control, driving force control, braking force control and active steering control. From the view of vehicle dynamics, the main purpose of these control strategy is to change the dynamic characteristics of vehicle mechanical system, increase the stable region during emergency conditions, and make vehicle dynamics meet the demand of driver handling under more conditions. Different control methods have different effective region.
Therefore, study on the influence of different control methods on the vehicle stable region using nonlinear dynamics could provide new academic guide for the design and evaluation of vehicle stability control strategies.
In a word, based on many references around the world, through the contrast and analysis of these researches on the vehicle handling stability analysis and control, the nonlinear 3DOF model containing longitudinal speed, lateral speed and yaw rate is established in the paper, and the stability analysis and control strategies evaluations of vehicle dynamic system are studied roundly by using nonlinear analysis methods. The main work contains the following contents:
1. Analysis of the influence of longitudinal acceleration on vehicle handling stability.
The nonlinear 3DOF model containing longitudinal speed, lateral speed and yaw rate is established, vehicle longitudinal speed is introduced to the system model, and in order to prove the influence of vehicle longitudinal motion on vehicle stability, the changes of stable conditions are analyzed using the stability theory of nonlinear dynamics.
This part of study validates the influence of longitudinal acceleration on vehicle handling stability from academic analysis and simulation experiments. This is the premise of studying the stability of vehicle 3DOF planar motion.
2. Dynamic analysis of vehicle 3DOF planar motion based on nonlinear dynamics.
(1) Based on the analysis of the limitation of phase plane portrait of 2DOF vehicle model, the necessity of phase space analysis of 3DOF model is proposed. Through analyzing the phase trajectories in the phase space, the state variables, vehicle route and the distribution of front and rear tyre force under different steering conditions, the reason of vehicle losing stability is expatiated.
(2) The method of using Genetic Algorithm to solve the equilibrium points of 3DOF vehicle model is proposed, which could solve the problem that conventional methods can not solve. The equilibrium points are solved with different front wheel steering angle, different longitudinal speed and different road adhesion coefficient, which deepen the analysis of phase space portrait.
(3) The chaos identification theory is used to analyze the chaos dynamics of 3DOF vehicle model. The phase trajectories, Poincarémap and Power Spectral Density exhibit the chaos motion, which deepen the understanding of 3DOF vehicle dynamic characteristic.
This part of study analyzes the vehicle handling stability from the view of dynamic, and analyzes the dynamic characteristic and motion characteristic under different conditions, which are used to analysis the reason of vehicle losing stability.
3. The solution of stable region of vehicle 3DOF planar motion based on Cell Mapping theory.
(1) The limitation of using Lyapunov function method to obtain the stable region of 3DOF vehicle planar motion is explained, and cell mapping method and phase space searching method are proposed, which are suitable for solving the region of attraction for 3DOF vehicle dynamic system. The region of attraction of 3DOF dynamic system is obtained finally.
(2) The unstable equilibrium points are used to obtain the boundary of stable region, and the controllable stable region is obtained finally. The experiment data of race car and ordinary vehicle is used to validate the region of attraction. Through the experiment analysis, the rationality of region of attraction of vehicle planar motion is validated.
The stable region obtained in this part of study will provide important theory basis for vehicle dynamic control, and this method of solving the stable region will provide method guide for the evaluation of vehicle dynamic control strategy.
4. The evaluation of vehicle dynamic control strategy based on region of attraction.
(1) According to the classic direct yaw moment control and four-wheel steering control theory, the state function of these two control system are established.
(2) The region of attraction of the control systems are obtained by phase space searching method and cell mapping method. Through the analysis of different parameters, the influence of different control method on the region of attraction of the vehicle dynamic system is studied in the whole phase space.
(3) Based on the analysis of the region of attraction, the changes of region of attraction for direct yaw moment control and four-wheel steering control are contrasted, the effective regions of each control method are analysis respectively, and the control effect of these two control methods is evaluated. The above studies provide academic basis for the synthetic evaluation of vehicle handling control strategy.
This part of study will provide new method and method guide for the evaluation of vehicle dynamic control strategy during vehicle steering with high speed.
In a word, the vehicle handling stability analysis of 3DOF planar motion based on nonlinear dynamics is the important part of vehicle lateral dynamic analysis, which provide important theory basis for the stability analysis and revealing the reason of vehicle losing stability. The vehicle control strategy evaluation method based on nonlinear dynamics analysis provide efficient evaluation method and theory guide for the engineering application of control strategy.
因此,本论文在查阅大量国内外相关文献资料的基础上,通过对比分析现阶段关于车辆操纵稳定性分析及控制的研究,提出建立包括纵向速度在内的汽车操纵稳定性三自由度(纵向、侧向和横摆运动)非线性模型,用非线性分析方法对车辆系统的稳定性及相关的控制策略进行更加全面地研究。论文的主要内容是:
1.建立了汽车操纵稳定性三自由度(纵向、侧向和横摆运动)系统模型,分析了车辆的纵向加速度对车辆系统稳定条件的影响。
2.研究了三自由度车辆动力学系统的相空间特性,分析了不同前轮转角输入时,系统相轨线、状态变量以及车辆运动轨迹和前后轮胎侧向力的分布等动力学特性的变化;提出用遗传算法求解三自由度车辆动力学系统的平衡点,解决了传统解析算法和数值方法无法求解的问题;根据混沌动力学及分岔理论,分别用相轨线、庞加莱截面和功率谱密度揭示了车辆转向过程中出现的混沌运动。
3.提出了利用相空间搜索法和胞映射法的改进算法求解车辆三自由度平面运动的吸引域,得到了整个相空间范围内的吸引域;利用求解得到的车辆三自由度系统的不稳定平衡点,确定了车辆平面运动的r步吸引域。通过实例分析,即利用已有的赛车试验数据,对所得的理论分析结果进行了定性的验证。
4.基于吸引域的分析,分别研究直接橫摆力矩控制和四轮转向控制对车辆动力学系统吸引域的影响,分析这两种控制方式各自有效的作用区域,评价二者对车辆操作稳定性的控制效果。
The increase of traffic volume and vehicle speed, and the influence of atrocious weather such as ice, snow and rain make vehicle usually drive under the condition of high speed and emergency steer and lose its stability, which leads to many traffic accidents. On the other hand, the speed constrained by the current bend technique is the main bottleneck of increasing traffic volume and of highway utilization. Therefore, the analysis and control of vehicle handing stability are the important project for human safety and highway utilization. It is important to do the research on the mechanism of vehicle losing stability during ultimate conditions and the control strategy of increasing vehicle handing stability.
Vehicle dynamic characteristics change fundamentally with high speed during emergency conditions. It is necessary to know the vehicle dynamic characteristics, analyze vehicle stability and obtain the stability region before studying on vehicle stability control.
In the classic vehicle handling theory, the two degree of freedom (2DOF) vehicle dynamic model is established on the hypothesis of linear vehicle and tyre. This model contains two state variables, which are lateral velocity and yaw rate. It is suitable to analyze the stability during small steering angle and under low speed. But when vehicle running during large steering angle and with high speed, the tyre side slip angle is not in linear region anymore and the coupling of longitudinal motion and yaw motion make the longitudinal speed and acceleration change quickly. The linear hypothesis is not tenable.
Therefore, in order to study on the vehicle handling stability during emergency conditions, it is requisite to establish the nonlinear three degree of freedom (3DOF) vehicle dynamic model containing the longitudinal, lateral and yaw motion, and analyze the stability using nonlinear methods thoroughly. It is meaningful and important to study the vehicle handling stability and mechanism of vehicle losing stability.
Furthermore, with the development of chassis electronic, the basic forms of vehicle handling stability control have been conformed. Vehicle handling stability could be realized by direct yaw moment control, four-wheel steering control, driving force control, braking force control and active steering control. From the view of vehicle dynamics, the main purpose of these control strategy is to change the dynamic characteristics of vehicle mechanical system, increase the stable region during emergency conditions, and make vehicle dynamics meet the demand of driver handling under more conditions. Different control methods have different effective region.
Therefore, study on the influence of different control methods on the vehicle stable region using nonlinear dynamics could provide new academic guide for the design and evaluation of vehicle stability control strategies.
In a word, based on many references around the world, through the contrast and analysis of these researches on the vehicle handling stability analysis and control, the nonlinear 3DOF model containing longitudinal speed, lateral speed and yaw rate is established in the paper, and the stability analysis and control strategies evaluations of vehicle dynamic system are studied roundly by using nonlinear analysis methods. The main work contains the following contents:
1. Analysis of the influence of longitudinal acceleration on vehicle handling stability.
The nonlinear 3DOF model containing longitudinal speed, lateral speed and yaw rate is established, vehicle longitudinal speed is introduced to the system model, and in order to prove the influence of vehicle longitudinal motion on vehicle stability, the changes of stable conditions are analyzed using the stability theory of nonlinear dynamics.
This part of study validates the influence of longitudinal acceleration on vehicle handling stability from academic analysis and simulation experiments. This is the premise of studying the stability of vehicle 3DOF planar motion.
2. Dynamic analysis of vehicle 3DOF planar motion based on nonlinear dynamics.
(1) Based on the analysis of the limitation of phase plane portrait of 2DOF vehicle model, the necessity of phase space analysis of 3DOF model is proposed. Through analyzing the phase trajectories in the phase space, the state variables, vehicle route and the distribution of front and rear tyre force under different steering conditions, the reason of vehicle losing stability is expatiated.
(2) The method of using Genetic Algorithm to solve the equilibrium points of 3DOF vehicle model is proposed, which could solve the problem that conventional methods can not solve. The equilibrium points are solved with different front wheel steering angle, different longitudinal speed and different road adhesion coefficient, which deepen the analysis of phase space portrait.
(3) The chaos identification theory is used to analyze the chaos dynamics of 3DOF vehicle model. The phase trajectories, Poincarémap and Power Spectral Density exhibit the chaos motion, which deepen the understanding of 3DOF vehicle dynamic characteristic.
This part of study analyzes the vehicle handling stability from the view of dynamic, and analyzes the dynamic characteristic and motion characteristic under different conditions, which are used to analysis the reason of vehicle losing stability.
3. The solution of stable region of vehicle 3DOF planar motion based on Cell Mapping theory.
(1) The limitation of using Lyapunov function method to obtain the stable region of 3DOF vehicle planar motion is explained, and cell mapping method and phase space searching method are proposed, which are suitable for solving the region of attraction for 3DOF vehicle dynamic system. The region of attraction of 3DOF dynamic system is obtained finally.
(2) The unstable equilibrium points are used to obtain the boundary of stable region, and the controllable stable region is obtained finally. The experiment data of race car and ordinary vehicle is used to validate the region of attraction. Through the experiment analysis, the rationality of region of attraction of vehicle planar motion is validated.
The stable region obtained in this part of study will provide important theory basis for vehicle dynamic control, and this method of solving the stable region will provide method guide for the evaluation of vehicle dynamic control strategy.
4. The evaluation of vehicle dynamic control strategy based on region of attraction.
(1) According to the classic direct yaw moment control and four-wheel steering control theory, the state function of these two control system are established.
(2) The region of attraction of the control systems are obtained by phase space searching method and cell mapping method. Through the analysis of different parameters, the influence of different control method on the region of attraction of the vehicle dynamic system is studied in the whole phase space.
(3) Based on the analysis of the region of attraction, the changes of region of attraction for direct yaw moment control and four-wheel steering control are contrasted, the effective regions of each control method are analysis respectively, and the control effect of these two control methods is evaluated. The above studies provide academic basis for the synthetic evaluation of vehicle handling control strategy.
This part of study will provide new method and method guide for the evaluation of vehicle dynamic control strategy during vehicle steering with high speed.
In a word, the vehicle handling stability analysis of 3DOF planar motion based on nonlinear dynamics is the important part of vehicle lateral dynamic analysis, which provide important theory basis for the stability analysis and revealing the reason of vehicle losing stability. The vehicle control strategy evaluation method based on nonlinear dynamics analysis provide efficient evaluation method and theory guide for the engineering application of control strategy.
引文
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