极限工况下汽车转向失稳的非线性动力学特性与主动控制研究
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摘要
随着社会节奏的加快和高等级公路的发展,现代汽车的行驶速度越来越高,这给行车安全带来了极大的隐患,保持高速大转向即极限工况下汽车的转向稳定性是现代汽车发展所要面临的重要课题。通过主动前轮转向(Active Front Steering,AFS)、四轮转向(Fout Wheel Steering,4WS)和基于横摆力矩控制的稳定性控制系统(Electronic Stability Program,ESP)改善汽车的操纵稳定性代表了现代汽车主动安全技术的发展方向。本课题研究的重点之一就是极限工况下汽车转向失稳的非线性动力学特性分析。从车辆动力学的角度来讲,极限工况下汽车的转向行为与常规工况有很大的不同,轮胎力达到饱和,系统呈现强非线性特性,需要从非线性动力学的角度探索极限工况下汽车的转向特性,从而为汽车稳定性控制系统提供更为丰富的理论依据。
本文重点讨论极限工况下汽车转向失稳的非线性动力学特性,包括分岔与稳定性等;研究基于状态流形的极限工况下汽车转向失稳的动态机制;探讨稳态转向失稳的预报方法及应用;研究大变化工况下底盘稳定性的鲁棒控制等内容。
分析汽车转向动力学的基本问题,讨论了不足转向梯度、操纵图法等汽车稳态转向动力学特性的分析方法;分析了基于线性轮胎模型的汽车转向稳定性,并应用参数根轨迹的方法对汽车的转向稳定性与横摆阻尼特性进行了对比分析;在理论分析的基础上,进行了汽车操稳性的实车试验,验证了理论分析的结果,并通过试验指出了现有汽车转向动力学分析和评价方法的不足,直接应用于底盘稳定性控制比较困难,引出了下文研究的问题。
研究了汽车稳态转向失稳的静态分岔特性。综合考虑轮胎的非线性特性和解析分析的需要,应用多项式平方轮胎模型建立了包含侧倾运动和平面运动的四维(4-D)非线性汽车转向动力学系统;借助于非线性动力学中心流形理论将高维系统降为一维中心流形系统,理论推导和实例分析表明,汽车稳态转向时不会出现Hopf分岔极限环现象,但是随着车速和前轮转角的增加将发生鞍结分岔,发生鞍结分岔后稳定的平衡点消失,若不采取措施,汽车将最终失去控制。研究了通过状态反馈并借助主动前轮转向系统对分岔点进行镇定,结果表明,对分岔点进行镇定可以延缓分岔的发生,增加了汽车稳态转向的稳定性。
基于非线性动力学的分岔与状态流形理论研究了汽车稳态转向和非稳态转向失稳的动态机制,并用数值方法对极限工况下汽车转向的频率特性进行了分析和讨论。给出了描述汽车发生静态分岔后,转向失稳动态过程的状态流形演化图;提出了将稳态转向失稳的动态过程划分为发展阶段和失控阶段两个阶段的新思想,一方面方便了对转向失稳的动态机制的描述和理解,另一方面,通过这种划分思想将非线性分岔分析的结果直接应用于底盘稳定性控制,即根据质心侧偏角的状态响应来进行控制逻辑的设计和决策。在失稳的发展阶段状态运动缓慢,进入失控阶段,运动急剧加快,并在有限的时间内通向无穷远处,导致汽车失去控制。在非稳态转向操作中,即使转向角暂时超过分岔值,如果系统状态仍处于失稳的发展阶段,汽车并没完全失控,还可以通过主动转向等底盘主动安全系统来使汽车恢复到稳定的转向状态,一旦状态进入失控阶段,汽车将迅速失去控制,通过主动控制系统改善其稳定性比较困难。
研究了汽车稳态转向失稳的实时预报方法及在汽车稳定性控制中的应用。研究了基于奇异值分解法和μ-δ,参数空间中实时追踪最近分岔点的汽车稳态转向失稳的预报方法,提出了基于稳态转向失稳预报的汽车稳定性控制的新思路,直接将非线性分岔分析的结果应用于汽车的稳定性控制系统的实时决策,迈出了将非线性动力学应用到底盘稳定性控制的关键的一步。讨论了极限转向角的取值对主动转向控制性能的影响,结果表明,极限转向角取小于分岔参数值时基本不影响控制性能,而超过分岔参数值后,对控制性能的影响明显,且随着极限转向角值的增加控制性能下降。
研究了考虑模型参数不确定性和大变化工况下汽车转向稳定性的鲁棒控制问题。建立了多功能试验车的9-DOF非线性车辆模型,并通过实车试验对模型进行了测试,以作为控制方案仿真验证的平台,通过多次调整汽车结构参数使仿真结果向试验结果靠拢,并以此估计了相关的汽车结构参数;讨论了汽车稳定性控制系统的鲁棒设计方法,提出了基于线性变参数(LPV)方法的汽车稳定性鲁棒增益自调度控制方法,建立了关于轮胎侧偏刚度和车速的多胞控制模型,非线性仿真表明,该控制方案对车速、路面附着系数的变化具有较强的鲁棒性。
With the development of senior freeway and the increasing pace of our society, the increasing vehicle speed brings about great threat to our life safety. It is a crucial issue for the vehicle industry and academic research to control vehicle cornering stability in critical situations. It is has been recognized that to increase vehicle handling and stability by AFS (Active Front Steering), 4WS (Four Wheel Steering), ESP (Electronic Stability Program) etc. is the direction of the development of vehicle chassis control. This thesis focuses on the issue of increasing vehicle cornering stability in critical situations. The vehicle cornering dynamics in critical situations where the tyre force approaches saturation has great difference with that of in the general situations. It is a bad need to investigate vehicle cornering performance in critical situations througth nonlinear dynamics theory in order to provide more precise information to vehicle stability control system.
The motivation of this thesis is to investigate the nonlinear vehicle cornering dynamics in critical situations. This research consists of the bifurcation in steady-state cornering, the dynamic mechanism elaboration of vehicle cornering destabilization based on state manifold theory, the forecast of the vehicle steady-state cornering destabilization and the application in vehicle cornering stability control, the robust control of vehicle cornering stability facing great uncertainty parameters.
The fundaments of vehicle cornering dynamics have been studied broadly. The concepts and the principles of understeer gradient, handling diagram used to analyze and evaluate vehicle handling and stability performance have been discussed. The vehicle cornering stability is analyzed based on linear tyre model and conventional control theory, during which the yaw stability and damp properties have been compared and analyzed by root-locus theory. Vehicle handling and stability field test has been conducted to understand the vehicle cornering dynamics in advance.
The static bifurcation of steady-state cornering destabilization has been studied. Considering the need of nonlinear analysis and numerical computation, a 4-D nonlinear vehicle cornering dynamics system is formulated comprises of the roll and planar motions and a quadratic tyre model. Then the high dimensional system is simplified by central manifold theory to 1-D. It has been proved analytically that not Hopf bifurcation but saddle-node bifurcation phenomena may be appear during the steady-state cornering destabilization, which will lead the vehicle out of control ultimately. The bifurcation stabilization through state feedback control based on active front steering is studied. The results demonstrate that saddle-node bifurcation can be delayed to appear which enhances the vehicle steady-state cornering stability.
Based on the state manifold theory, the dynamic mechanism of vehicle steady-state and non-steady-state cornering has been explored and elaborated. The cornering property versus steering frequency has also been studied through numerical method. The state manifold diagrams which can describe the dynamic mechanism have been provided. A new ideal which divides vehicle destabilization into two stages, that is developing stage and out of control stage has been put forward in order to assist the elaboration of the issue. The results demonstrate that the state moves slowly at the developing stage but much rapidly the the state entres the out of control stage which will lead to infinity in limited time and bring the vehicle out of control. In the non-steady-state cornering operation, even if the steering angle goes beyond the bifurcation value, if the state is still in the developing stage, the vehicle is still in control which can be steered to keep stable by AFS. On the contrary, once the state entres the out of control stage, it is very difficulty to control by AFS.
The forecast of steady-state cornering destabilization methods and the application of which is studied. Two forecast methods consisting of singular value decomposition and tracking the closest bifurcation point in u-δ_f parametric space is analyzed and compared. A new cornering stability control scheme is put forward, which is based on the forecast of steady-state cornering destabilization. This idea joints the bifurcation analysis and the cornering stability control directly. The influence of critical steering angle set based on the forecast result on the control efficiency of AFS is discussed. The results demonstrate that little difference is found when the critical steering angle is set smaller than the forecast value, however, the control efficiency declines as the increasing set of the critical steering angle when it goes beyond the forecast value.
The robust control of vehicle cornering stability considering the parametric uncertainties is studied. 9-DOF nonlinear vehicle model which has been validated by vehicle field test is constructed as the test platform of the proposed control scheme. A robust gain-scheduling yaw moment control scheme is proposed in this paper based on LPV (Linear Parameter-Varying) modeling method. Numerical simulation on the 9-DOF nonlinear vehicle model demonstrates that the proposed control scheme has much better adaptability to the variation of the operating conditions.
本文重点讨论极限工况下汽车转向失稳的非线性动力学特性,包括分岔与稳定性等;研究基于状态流形的极限工况下汽车转向失稳的动态机制;探讨稳态转向失稳的预报方法及应用;研究大变化工况下底盘稳定性的鲁棒控制等内容。
分析汽车转向动力学的基本问题,讨论了不足转向梯度、操纵图法等汽车稳态转向动力学特性的分析方法;分析了基于线性轮胎模型的汽车转向稳定性,并应用参数根轨迹的方法对汽车的转向稳定性与横摆阻尼特性进行了对比分析;在理论分析的基础上,进行了汽车操稳性的实车试验,验证了理论分析的结果,并通过试验指出了现有汽车转向动力学分析和评价方法的不足,直接应用于底盘稳定性控制比较困难,引出了下文研究的问题。
研究了汽车稳态转向失稳的静态分岔特性。综合考虑轮胎的非线性特性和解析分析的需要,应用多项式平方轮胎模型建立了包含侧倾运动和平面运动的四维(4-D)非线性汽车转向动力学系统;借助于非线性动力学中心流形理论将高维系统降为一维中心流形系统,理论推导和实例分析表明,汽车稳态转向时不会出现Hopf分岔极限环现象,但是随着车速和前轮转角的增加将发生鞍结分岔,发生鞍结分岔后稳定的平衡点消失,若不采取措施,汽车将最终失去控制。研究了通过状态反馈并借助主动前轮转向系统对分岔点进行镇定,结果表明,对分岔点进行镇定可以延缓分岔的发生,增加了汽车稳态转向的稳定性。
基于非线性动力学的分岔与状态流形理论研究了汽车稳态转向和非稳态转向失稳的动态机制,并用数值方法对极限工况下汽车转向的频率特性进行了分析和讨论。给出了描述汽车发生静态分岔后,转向失稳动态过程的状态流形演化图;提出了将稳态转向失稳的动态过程划分为发展阶段和失控阶段两个阶段的新思想,一方面方便了对转向失稳的动态机制的描述和理解,另一方面,通过这种划分思想将非线性分岔分析的结果直接应用于底盘稳定性控制,即根据质心侧偏角的状态响应来进行控制逻辑的设计和决策。在失稳的发展阶段状态运动缓慢,进入失控阶段,运动急剧加快,并在有限的时间内通向无穷远处,导致汽车失去控制。在非稳态转向操作中,即使转向角暂时超过分岔值,如果系统状态仍处于失稳的发展阶段,汽车并没完全失控,还可以通过主动转向等底盘主动安全系统来使汽车恢复到稳定的转向状态,一旦状态进入失控阶段,汽车将迅速失去控制,通过主动控制系统改善其稳定性比较困难。
研究了汽车稳态转向失稳的实时预报方法及在汽车稳定性控制中的应用。研究了基于奇异值分解法和μ-δ,参数空间中实时追踪最近分岔点的汽车稳态转向失稳的预报方法,提出了基于稳态转向失稳预报的汽车稳定性控制的新思路,直接将非线性分岔分析的结果应用于汽车的稳定性控制系统的实时决策,迈出了将非线性动力学应用到底盘稳定性控制的关键的一步。讨论了极限转向角的取值对主动转向控制性能的影响,结果表明,极限转向角取小于分岔参数值时基本不影响控制性能,而超过分岔参数值后,对控制性能的影响明显,且随着极限转向角值的增加控制性能下降。
研究了考虑模型参数不确定性和大变化工况下汽车转向稳定性的鲁棒控制问题。建立了多功能试验车的9-DOF非线性车辆模型,并通过实车试验对模型进行了测试,以作为控制方案仿真验证的平台,通过多次调整汽车结构参数使仿真结果向试验结果靠拢,并以此估计了相关的汽车结构参数;讨论了汽车稳定性控制系统的鲁棒设计方法,提出了基于线性变参数(LPV)方法的汽车稳定性鲁棒增益自调度控制方法,建立了关于轮胎侧偏刚度和车速的多胞控制模型,非线性仿真表明,该控制方案对车速、路面附着系数的变化具有较强的鲁棒性。
With the development of senior freeway and the increasing pace of our society, the increasing vehicle speed brings about great threat to our life safety. It is a crucial issue for the vehicle industry and academic research to control vehicle cornering stability in critical situations. It is has been recognized that to increase vehicle handling and stability by AFS (Active Front Steering), 4WS (Four Wheel Steering), ESP (Electronic Stability Program) etc. is the direction of the development of vehicle chassis control. This thesis focuses on the issue of increasing vehicle cornering stability in critical situations. The vehicle cornering dynamics in critical situations where the tyre force approaches saturation has great difference with that of in the general situations. It is a bad need to investigate vehicle cornering performance in critical situations througth nonlinear dynamics theory in order to provide more precise information to vehicle stability control system.
The motivation of this thesis is to investigate the nonlinear vehicle cornering dynamics in critical situations. This research consists of the bifurcation in steady-state cornering, the dynamic mechanism elaboration of vehicle cornering destabilization based on state manifold theory, the forecast of the vehicle steady-state cornering destabilization and the application in vehicle cornering stability control, the robust control of vehicle cornering stability facing great uncertainty parameters.
The fundaments of vehicle cornering dynamics have been studied broadly. The concepts and the principles of understeer gradient, handling diagram used to analyze and evaluate vehicle handling and stability performance have been discussed. The vehicle cornering stability is analyzed based on linear tyre model and conventional control theory, during which the yaw stability and damp properties have been compared and analyzed by root-locus theory. Vehicle handling and stability field test has been conducted to understand the vehicle cornering dynamics in advance.
The static bifurcation of steady-state cornering destabilization has been studied. Considering the need of nonlinear analysis and numerical computation, a 4-D nonlinear vehicle cornering dynamics system is formulated comprises of the roll and planar motions and a quadratic tyre model. Then the high dimensional system is simplified by central manifold theory to 1-D. It has been proved analytically that not Hopf bifurcation but saddle-node bifurcation phenomena may be appear during the steady-state cornering destabilization, which will lead the vehicle out of control ultimately. The bifurcation stabilization through state feedback control based on active front steering is studied. The results demonstrate that saddle-node bifurcation can be delayed to appear which enhances the vehicle steady-state cornering stability.
Based on the state manifold theory, the dynamic mechanism of vehicle steady-state and non-steady-state cornering has been explored and elaborated. The cornering property versus steering frequency has also been studied through numerical method. The state manifold diagrams which can describe the dynamic mechanism have been provided. A new ideal which divides vehicle destabilization into two stages, that is developing stage and out of control stage has been put forward in order to assist the elaboration of the issue. The results demonstrate that the state moves slowly at the developing stage but much rapidly the the state entres the out of control stage which will lead to infinity in limited time and bring the vehicle out of control. In the non-steady-state cornering operation, even if the steering angle goes beyond the bifurcation value, if the state is still in the developing stage, the vehicle is still in control which can be steered to keep stable by AFS. On the contrary, once the state entres the out of control stage, it is very difficulty to control by AFS.
The forecast of steady-state cornering destabilization methods and the application of which is studied. Two forecast methods consisting of singular value decomposition and tracking the closest bifurcation point in u-δ_f parametric space is analyzed and compared. A new cornering stability control scheme is put forward, which is based on the forecast of steady-state cornering destabilization. This idea joints the bifurcation analysis and the cornering stability control directly. The influence of critical steering angle set based on the forecast result on the control efficiency of AFS is discussed. The results demonstrate that little difference is found when the critical steering angle is set smaller than the forecast value, however, the control efficiency declines as the increasing set of the critical steering angle when it goes beyond the forecast value.
The robust control of vehicle cornering stability considering the parametric uncertainties is studied. 9-DOF nonlinear vehicle model which has been validated by vehicle field test is constructed as the test platform of the proposed control scheme. A robust gain-scheduling yaw moment control scheme is proposed in this paper based on LPV (Linear Parameter-Varying) modeling method. Numerical simulation on the 9-DOF nonlinear vehicle model demonstrates that the proposed control scheme has much better adaptability to the variation of the operating conditions.
引文
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