Vehicle control synthesis using phase portraits of planar dynamics

ABSTRACT

Phase portraits provide control system designers strong graphical insight into nonlinear system dynamics. These plots readily display vehicle stability properties and map equilibrium point locations and movement to changing parameters and system inputs. This paper extends the usage of phase portraits in vehicle dynamics to control synthesis by illustrating the relationship between the boundaries of stable vehicle operation and the state derivative isoclines in the yaw rate–sideslip phase plane. Closed-loop phase portraits demonstrate the potential for augmenting a vehicle's open-loop dynamics through steering and braking. The paper concludes by applying phase portrait analysis to an envelope control algorithm for yaw stability and a sliding surface controller for stabilising a saddle point equilibrium in drifting.     

Nonlinear dynamics and stability analysis of vehicle plane motions

In this article, the problems of dynamics and stability for vehicle planar motion systems have been investigated. By introducing a so-called joint-point locus approach, equilibria of the system and their associated stability properties are given geometrically. With this method, it is discovered that the difference between the front and the rear steering angles plays a key role in vehicle system dynamics and that the topological structure of the phase portrait and the types of bifurcations are different from those published previously. In particular, the vehicle system could still be stabilized even when pushed to work in a certain severely nonlinear region, by applying extremely large steering angles. However, it is worth noticing that the attractive domain of the stable equilibrium is very narrow. These developments might prove to be important in active steering control design. Numerical experiments are carried out to illustrate the potentials of the proposed techniques.     

Nonlinear dynamics and stability analysis of vehicle plane motions

In this article, the problems of dynamics and stability for vehicle planar motion systems have been investigated. By introducing a so-called joint-point locus approach, equilibria of the system and their associated stability properties are given geometrically. With this method, it is discovered that the difference between the front and the rear steering angles plays a key role in vehicle system dynamics and that the topological structure of the phase portrait and the types of bifurcations are different from those published previously. In particular, the vehicle system could still be stabilized even when pushed to work in a certain severely nonlinear region, by applying extremely large steering angles. However, it is worth noticing that the attractive domain of the stable equilibrium is very narrow. These developments might prove to be important in active steering control design. Numerical experiments are carried out to illustrate the potentials of the proposed techniques.     

On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics

We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined, and the important case of multiple equilibrium states and their dependence on a parameter is discussed. It is argued that the analysis of nonlinear dynamic problems always should start with an analysis of the equilibrium states of the full nonlinear problem whereby great care must be taken in the choice of the numerical solvers. When the equilibrium states are known certain linearizations around one chosen state may be applied carefully in order to facilitate or speed up the numerical solution of the dynamical problem. It is argued, however, that certain problems cannot be linearized. The applications of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed.     

On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics

We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined, and the important case of multiple equilibrium states and their dependence on a parameter is discussed. It is argued that the analysis of nonlinear dynamic problems always should start with an analysis of the equilibrium states of the full nonlinear problem whereby great care must be taken in the choice of the numerical solvers. When the equilibrium states are known certain linearizations around one chosen state may be applied carefully in order to facilitate or speed up the numerical solution of the dynamical problem. It is argued, however, that certain problems cannot be linearized. The applications of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed.     

智能汽车轨迹跟踪与横摆稳定性协同控制

为了提高四轮独立驱动智能电动汽车在变曲率弯道下的轨迹跟踪精度和横摆稳定性,提出了一种模型预测控制与直接横摆力矩控制协同的综合控制方法。建立了横纵向耦合的车辆动力学模型,采用2阶龙格库塔离散法保证了离散模型的精度,并基于简化的2自由度动力学模型推导了车辆横摆稳定性约束,设计了非线性模型预测控制器;利用直接横摆力矩控制能够改变车辆横摆角速度和航向角的特点,考虑模型预测控制器的预测状态、控制量以及跟踪误差,设计了协同控制规则。仿真结果表明,协同控制方法解决了考虑横摆稳定性约束的模型预测控制器中存在的稳定性约束与控制精度相矛盾的问题,并补偿了模型预测控制器没有可行解时对横摆稳定性的约束,同时提高了智能汽车的轨迹跟踪精度和横摆稳定性。     

Pivot point-based control for active rear-wheel steering in passenger vehicles

This paper presents a new application of active rear-wheel steering control to improve the lateral vehicle behaviour. In the state of the art, yaw or lateral velocity is used as control variable that means one degree of freedom being not directly controlled. A worse subjective impressions due to movements in the rear end of the vehicle during strong counter-steering are a consequence. To avoid this effect in urban surroundings, an innovative structure to control the pivot point distance of the vehicle is proposed. In this case the coupled elementary states yaw and lateral velocity can be influenced based on a higher level criteria. Analysis show that pivot point fixing provides a comprehensible reference behaviour. Solving the issue of singularity during disappearing yaw movement is the basis to design a performant modified feedforward input–output linearisation. An analytic stability analysis of the internal dynamics shows system immanent limitations which do not influence the target of improving the lateral vehicle dynamics in urban manoeuvres. Finally, the advantages of pivot-based control are highlighted by a comparison with state of the art rear axle control.     

Combined longitudinal and lateral control for automated vehicle guidance

This paper deals with the longitudinal and lateral control of an automotive vehicle within the framework of fully automated guidance. The automotive vehicle is a complex system characterised by highly nonlinear longitudinal and lateral coupled dynamics. Consequently, automated guidance must be simultaneously performed with longitudinal and lateral control. This work presents an automated steering strategy based on nonlinear model predictive control. A nonlinear longitudinal control strategy considering powertrain dynamics is also proposed to cope with the longitudinal speed tracking problem. Finally, a simultaneous longitudinal and lateral control strategy helps to improve the combined control performance. This whole control strategy is tested through simulations showing the effectiveness of the present approach.     

基于微分几何的四轮独立驱动车辆运动解耦控制研究

针对车辆在纵向运动和横摆运动时的强耦合关系给车辆动力学控制带来的困难，以四轮独立电驱动车辆作为研究对象，基于微分几何理论设计了车辆系统运动解耦控制方法，将非线性强耦合的四轮驱动车辆动力学系统解耦为纵向和横向两个相对独立运动控制子系统，并设计了鲁棒控制器，以提高抵抗车辆行驶时不确定外力如侧风的干扰能力。基于 Trucksim 软件建立四轮驱动车辆模型，并针对车辆解耦控制策略和抗干扰策略进行了仿真测试。结果表明，相比于无解耦控制的车辆，采用微分几何解耦控制的四轮独立驱动车辆纵向速度偏差降低了 82.1%，横摆角速度偏差降低了80.7%，且微风干扰下的抗干扰能力明显改善，车辆稳定性显著提升。为验证该运动解耦控制策略在实时系统中的控制效果，还进行了硬件在环试验，结果表明，硬件在环试验的结果与仿真结果一致。     

基于NMPC的智能汽车纵横向综合轨迹跟踪控制

本文中针对大曲率转弯工况下,智能汽车纵横向动力学特性的耦合和动力学约束导致轨迹跟踪精度和稳定性下降的问题,提出一种基于非线性模型预测控制(NMPC)的纵横向综合轨迹跟踪控制方法,通过NMPC和障碍函数法(BM)的有效结合,提高了跟踪精度,改善了行驶稳定性.首先建立四轮驱动-前轮转向智能汽车动力学模型和轨迹跟踪模型,采用...     

A curving ACC system with coordination control of longitudinal car-following and lateral stability

The paper presents a curving adaptive cruise control (ACC) system that is coordinated with a direct yaw-moment control (DYC) system and gives consideration to both longitudinal car-following capability and lateral stability on curved roads. A model including vehicle longitudinal and lateral dynamics is built first, which is as discrete as the predictive model of the system controller. Then, a cost function is determined to reflect the contradictions between vehicle longitudinal and lateral dynamics. Meanwhile, some I/O constraints are formulated with a driver permissible longitudinal car-following range and the road adhesion condition. After that, desired longitudinal acceleration and desired yaw moment are obtained by a linear matrix inequality based robust constrained state feedback method. Finally, driver-in-the-loop tests on a driving simulator are conducted and the results show that the developed control system provides significant benefits in weakening the impact of DYC on ACC longitudinal car-following capability while also improving lateral stability.     

State observer-based sliding mode control for semi-active hydro-pneumatic suspension

This paper proposes an improved virtual reference model for semi-active suspension to coordinate the vehicle ride comfort and handling stability. The reference model combines the virtues of sky-hook with ground-hook control logic, and the hybrid coefficient is tuned according to the longitudinal and lateral acceleration so as to improve the vehicle stability especially in high-speed condition. Suspension state observer based on unscented Kalman filter is designed. A sliding mode controller (SMC) is developed to track the states of the reference model. The stability of the SMC strategy is proven by means of Lyapunov function taking into account the nonlinear damper characteristics and sprung mass variation of the vehicle. Finally, the performance of the controller is demonstrated under three typical working conditions: the random road excitation, speed bump road and sharp acceleration and braking. The simulation results indicated that, compared with the traditional passive suspension, the proposed control algorithm can offer a better coordination between vehicle ride comfort and handling stability. This approach provides a viable alternative to costlier active suspension control systems for commercial vehicles.     

分布式电驱动车辆力矩分配控制研究现状综述

分布式电驱动车辆具有控制灵活度高、传动链短、结构紧凑、传动效率高、空间布置利用率高等特点,独特的结构特点与驱动方式令其在充分挖掘车辆动力学控制潜力、增强车辆安全性、提升驱动效率、简化底盘结构等方面带来明显的技术革新,为高性能车辆控制技术提供硬件载体。然而,作为过驱动、多约束、车辆纵向-横向-垂向运动行为强非线性耦合系统,分布式电驱动车辆在车辆动力学控制、车辆行驶经济性控制、协同控制等方面仍面临理论与技术挑战。基于此,综合国内外前沿分布式电驱动车辆力矩分配控制策略研究,主要从控制框架、稳定性控制、能效控制、兼顾稳定性与经济性控制4个方面重点阐述当前发展现状,设计并对比分析应用案例,从不同角度对力矩分配的发展方向进行展望,旨在为先进分布式电驱动车辆高性能力矩分配控制器开发提供参考。     

分布式驱动电动汽车动力学集成控制研究进展及趋势

分布式驱动电动汽车具有四轮可独立控制和响应速度快等突出优势，对增强车辆操纵稳定性、安全性和经济性具有重要的意义。但车辆是一个非线性、强耦合的系统，需研究解决各个控制器相互耦合、过驱动系统复杂性和不确定性等核心问题，这依赖于多维 （纵向、横向和垂向） 集成控制模式和容错控制。对现有研究进行分类和总结，从传统单一维度控制到多维集成控制，综述分布式驱动电动汽车的关键技术和发展现状，重点归纳了汽车动力学集成控制的多层结构及其应用，特别是集成了纵向-横向-垂向动力学的综合控制。最后对分布式驱动电动汽车动力学控制系统所面临的挑战提出了一些建议。     

Full drive-by-wire dynamic control for four-wheel-steer all-wheel-drive vehicles

Most of the controllers introduced for four-wheel-steer (4WS) vehicles are derived with the assumption that the longitudinal speed of the vehicle is constant. However, in real applications, the longitudinal speed varies, and the longitudinal, lateral, and yaw dynamics are coupled. In this paper, the longitudinal dynamics of the vehicle as well as its lateral and yaw motions are controlled simultaneously. This way, the effect of driving/braking forces of the tires on the lateral and yaw motions of the vehicle are automatically included in the control laws. To address the dynamic parameter uncertainty of the vehicle, a chatter-free variable structure controller is introduced. Elimination of chatter is achieved by introducing a dynamically adaptive boundary layer thickness. It is shown via simulations that the proposed control approach performs more robustly than the controllers developed based on dynamic models, in which longitudinal speed is assumed to be constant, and only lateral speed and yaw rate are used as system states. Furthermore, this approach supports all-wheel-drive vehicles. Front-wheel-drive or rear-wheel-drive vehicles are also supported as special cases of an all-wheel-drive vehicle.     

Design and Evaluation of Robust Cooperative Adaptive Cruise Control Systems in Parameter Space

This paper is on the design of cooperative adaptive cruise control systems for automated driving of platoons of vehicles in the longitudinal direction. Longitudinal models of vehicles with simple dynamics, an uncertain first order time constant and vehicle to vehicle communication with a communication delay are used in the vehicle modeling. A robust parameter space approach is developed and applied to the design of the cooperative adaptive cruise control system. D-stability is chosen as the robust performance goal and the feedback PD controller is designed in controller parameter space to achieve this D-stability goal for a range of possible longitudinal dynamics time constants and different values of time gap. Preceding vehicle acceleration is sent to the ego vehicle using vehicle to vehicle communication and a feedforward controller is used in this inter-vehicle loop to improve performance. Simulation results of an eight vehicle platoon of heterogeneous vehicles are presented and evaluated to demonstrate the efficiency of the proposed design method. Also, the proposed method is compared with a benchmark controller and the feedback only controller. Time gap regulation and string stability are used to assess performance and the effect of the vehicle to vehicle communication frequency on control system performance is also investigated.     

车速控制系统自适应油门控制器设计

在分析非线性车辆纵向动力学模型及简化模型基础上，采用一种简化非线件模型设计自适应油门控制器，并应用李亚谱诺夫理论证明了传动系统存在动态过程时控制系统的稳定性。通过对基于简化线性和非线性模燃的自适应控制器的仿真研究，结果表明后者具有更好的收敛性。试验结果也进一步表明，基于非线性模型的自适应控制器可以通过自适应调节减小参数不确定造成的干扰，当传动系统存在动态过程时可以保证车速跟踪误差有界。     

Asymptotic sideslip angle and yaw rate decoupling control in four-wheel steering vehicles

This paper shows that, for a four-wheel steering vehicle, a proportional-integral (PI) active front steering control and a PI active rear steering control from the yaw rate error together with an additive feedforward reference signal for the vehicle sideslip angle can asymptotically decouple the lateral velocity and the yaw rate dynamics; that is the control can set arbitrary steady state values for lateral speed and yaw rate at any longitudinal speed. Moreover, the PI controls can suppress oscillatory behaviours by assigning real stable eigenvalues to a widely used linearised model of the vehicle steering dynamics for any value of longitudinal speed in understeering vehicles. In particular, the four PI control parameters are explicitly expressed in terms of the three real eigenvalues to be assigned. No lateral acceleration and no lateral speed measurements are required. The controlled system maintains the well-known advantages of both front and rear active steering controls: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres and improved manoeuvrability. In particular, zero lateral speed may be asymptotically achieved while controlling the yaw rate: in this case comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced. Also zero yaw rate can be asymptotically achieved: in this case additional stable manoeuvres are obtained in obstacle avoidance. Several simulations, including step references and moose tests, are carried out on a standard small SUV CarSim model to explore the robustness with respect to unmodelled effects such as combined lateral and longitudinal tyre forces, pitch, roll and driver dynamics. The simulations confirm the decoupling between the lateral velocity and the yaw rate and show the advantages obtained by the proposed control: reduced lateral speed or reduced yaw rate, suppressed oscillations and new stable manoeuvres.     

Nonlinear optimal integrated vehicle control using individual braking torque and steering angle with on-line control allocation by using state-dependent Riccati equation technique

This paper proposes the solution of state-dependent Riccati equation as a nonlinear optimal regulator to stabilise the motion dynamics of the vehicle model subjected to sudden disturbance inputs in the lateral direction. The proposed nonlinear regulator coordinates individually actuated wheel braking torque and steering wheel angle simultaneously in an optimal manner. Performance criteria are satisfied by solving the Riccati equation based on the given cost function subjected to the nonlinear vehicle dynamics. On-line control allocation in terms of optimal brake torque distribution enhanced by optimal wheel steering angle input is achieved. Furthermore, the proposed optimal nonlinear regulator is an active fault-tolerant control system against partial by-wire actuator failures while guaranteeing stability with good performance due to its capability to allocate the individual control inputs in an optimal way. The main aim is to stabilise the motion dynamics of the vehicle model during short-term emergency situations along the desired straight trajectory manageable by average drivers and to provide vehicle stability and handling predictability through the interaction of individual wheel braking and steering actuators. Simulation results are used to illustrate the effectiveness of the proposed methodology.