H 2 optimal control of disturbance-delayed systems with application to vehicle suspensions

Optimal control of systems with time delays among disturbances, such as vehicle suspensions, is a relatively simple but long-standing problem in time-delayed control. We consider the exact H ₂ optimal control of systems with time-delayed disturbances and develop a computationally efficient approach for controller synthesis. We extend the Lyapunov-based H ₂ norm computation to systems with time-delayed disturbances and then derive a concise formula to explicitly evaluate the sensitivity of the system H ₂ norm with respect to controller gains. Thence, a set of necessary conditions for H ₂ optimal control of such systems using static output feedback are obtained in the form of algebraic equations. Gradient-based methods are adapted to optimize the controller gains. The method is also extended to reduced-order and decentralized control. As an application, a passive suspension system for an eight-DOF four-wheel vehicle is designed via structured H ₂ optimization. The results are compared with those of a design based on a Pade expansion for the time delays and a design obtained by neglecting the disturbance delays.     

基于变传动比的全轮线控转向车辆可拓H∞控制方法研究

为了解决传统固定转向传动比以及鲁棒H_∞控制方法无法很好地改善车辆稳定性的问题,提出全轮线控转向车辆的变传动比和可拓H_∞控制策略。首先,建立八自由度车辆动力学模型和轮胎模型。其次,以车辆方向盘转角和车速为输入信息,基于模糊控制方法设计全轮线控转向车辆的转向传动比,并计算出全轮线控转向车辆的前轮转角。然后,以横摆角速度偏差和偏差微分为特征值,基于可拓控制理论将车辆状态划分为3个区域：经典域、可拓域和非域;在经典域中,采用基于横摆角速度反馈的鲁棒H_∞控制方法,实时获取全轮线控转向车辆的后轮转角;在可拓域和非域中,结合可拓控制和H_∞控制策略,动态调整H_∞控制器的输出信号,在保证控制系统鲁棒性的前提下改善车辆的操纵稳定性。最后,基于MATLAB/Simulink仿真平台和自主研制的全轮线控转向特种消防救援车辆,通过正弦转向、单移线、阶跃转向、双移线等典型工况对所提控制方法进行验证,并以平均绝对误差和均方根误差为评价指标,与无控制和H_∞控制方法进行对比分析。仿真和试验测试结果表明：①变传动比控制方法不仅可以提高车辆低速时的转向灵敏度,也能改善车辆高速时的稳定性;②相比传统鲁棒H_∞控制,可拓H_∞控制策略提高了全轮线控转向车辆的操纵稳定性,改善了车辆全轮线控转向控制系统的鲁棒性。     

Designing H∞/GH 2 static-output feedback controller for vehicle suspensions using linear matrix inequalities and genetic algorithms

This paper presents an approach to design the H_∞/GH ₂ static-output feedback controller for vehicle suspensions by using linear matrix inequalities (LMIs) and genetic algorithms (GAs). Three main performance requirements for an advanced vehicle suspension are considered in this paper. Among these requirements, the ride-comfort performance is optimized by minimizing the H_∞ norm of the transfer function from the road disturbance to the sprung mass acceleration, while the road-holding performance and the suspension deflection limitation are guaranteed by constraining the generalized H₂ (GH ₂) norms of the transfer functions from the road disturbance to the dynamic tyre load and the suspension deflection to be less than their hard limits, respectively. At the same time, the controller saturation problem is considered by constraining its peak response output to be less than a given limit using the GH ₂ norm as well. A four-degree-of-freedom half-car model with active suspension system is applied in this paper. Several kinds of H_∞/GH ₂ static-output feedback controllers, which use the available sprung mass velocities or the suspension deflections as feedback signals, are obtained by using the GAs to search for the possible control gain matrices and then resolving the LMIs together with the minimization optimization problem. These designed H_∞/GH ₂ static-output feedback controllers are validated by numerical simulations on both the bump and the random road responses which show that the designed H_∞/GH ₂ static-output feedback controllers can achieve similar or even better active suspension performances compared with the state-feedback control case in spite of their simplicities.     

Robust Stability Analysis of LQG-Controlled Active Suspension with Model Uncertainty Using Structured Singular Value, μ, Method

This paper presents a systematic approach toward robust stability analysis of LQG-con trolled active suspension systems. To perform this task, the paper starts with a brief background information on LQG control, its relation to H₂ method, and showing how H₂ could be formulated to become the frequency domain equivalent of LQG. Then unstructured and structured uncertainties of active suspension are formulated. The paper continues with the definition of maximum singular values and structured singular values of a transfer function matrix. Using these definitions, the robust stability of an active suspension system in the presence of assumed parameter variations are analyzed. These steps are illustrated by means of a numerical example of an active suspension system.     

An H2 Formulation for the Design of a Passive Vibration-Isolation System for Cars

Optimal design of an active suspension system for road vehicles can be solved using LQR techniques. Such a problem is equivalent, in the frequency domain, to determine the state feedback gain matrix that minimizes the H₂ norm of a suitable transfer matrix.

A passive suspension system can be seen as the physical realization of a suitable state feedback law whose gains are function of the system parameters. This law, and thus the characteristic elements of the passive suspension, can be determined as an approximation of the H₂ optimal solution. This methodology allows one to choose the best controller from a constrained subset (i.e., all possible passive suspensions of a particular form) of all possible controllers.     

Connected cruise control: modelling,delay effects,and nonlinear behaviour

Connected vehicle systems (CVS) are considered in this paper where vehicles exchange information using wireless vehicle-to-vehicle (V2V) communication. The concept of connected cruise control (CCC) is established that allows control design at the level of individual vehicles while exploiting V2V connectivity. Due to its high level of modularity the proposed design can be applied to large heterogeneous traffic systems. The dynamics of a simple CVS is analysed in detail while taking into account nonlinearities in the vehicle dynamics as well as in the controller. Time delays that arise due to intermittencies and packet drops in the communication channels are also incorporated. The results are summarised using stability charts which allow one to select control gains to maintain stability and ensure disturbance attenuation when the delay is below a critical value.     

An Optimal Self-Tuning Controller for an Active Suspension

An optimal self-tuning control algorithm is presented for vehicle suspension design. The controller, incorporating a weighting controller, state observer and parameter estimator, is designed according to linear optimal control (LQG) theory. Based on the updated estimates of vehicle parameters and states, and the adapted weighting parameters, the LQG controller provides the optimal set of gains over different operating conditions. The feasibility and effectiveness of the proposed self-tuning system was investigated and proved by simulation studies.     

基于脑电信号分析的不同年龄驾驶人疲劳特性

为研究不同年龄驾驶人驾驶过程中疲劳情况及疲劳累积速度,对比其疲劳产生与变化的差异性,获取不同年龄驾驶人的最优驾驶时间,设计自然驾驶试验,利用Physio生理多导仪采集脑电数据,并采用主观检测方法对驾驶人进行问询。应用MATLAB对采集到的脑电数据进行降噪处理,通过积分获取各时段α波、β波和θ波的平均功率谱密度,进而求得脑电指标R_（α/β）,R_（θ/β）,R_{（α+θ）/β}。利用SPSS将其与驾驶时间进行单因素方差分析,并通过敏感性判断,选取R_{（α+θ）/β}作为驾驶疲劳表征指标。对各年龄段驾驶人的R_{（α+θ）/β}进行均值化处理,并将其与驾驶时间进行线性拟合,分析驾驶人年龄对驾驶疲劳累积速度的影响。对驾驶过程中各时段的R_{（α+θ）/β}进行配对样本t检验,并结合主观问询结果确定不同年龄驾驶人的最优驾驶时间。研究结果表明：青年和中年驾驶人在0~1.5 h内疲劳累积速度相对缓慢,老年驾驶人较快;在1.5~3 h内,青年驾驶人疲劳累积速度最快,中年驾驶人最慢;老、中、青年驾驶人的最优驾驶时间分别为60~75,120~135,105~120 min;不同年龄驾驶人其驾驶经验、体力和精力及外界环境干扰是影响疲劳累积速度的重要因素;试验结果验证了采用R_{（α+θ）/β}作为驾驶疲劳表征指标的有效性,有助于为不同年龄驾驶人安全驾驶时长的确定提供科学依据。     

车辆悬架的最优自适应与自校正控制

本文研究了车辆主动悬架自适应与自校正控制的策略与算法。     

Optimal preview game theory approach to vehicle stability controller design

Dynamic game theory brings together different features that are keys to many situations in control design: optimisation behaviour, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In the presented methodology, vehicle stability is represented by a cooperative dynamic/difference game such that its two agents (players), namely the driver and the direct yaw controller (DYC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the DYC control algorithm is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degrees-of-freedom vehicle-handling performance model is put into discrete form to develop the game equations of motion. To evaluate the developed control algorithm, CarSim with its built-in nonlinear vehicle model along with the Pacejka tire model is used. The control algorithm is evaluated for a lane change manoeuvre, and the optimal set of steering angle and corrective yaw moment is calculated and fed to the test vehicle. Simulation results show that the optimal preview control algorithm can significantly reduce lateral velocity, yaw rate, and roll angle, which all contribute to enhancing vehicle stability.     

Preview Control Algorithms for the Active Suspension of an Off-Road Vehicle

The potential performance improvement using preview control for active vehicle suspension was first recognized in the late nineteen sixties. All work done since that time has been based on optimal control theory using simple vehicle models.

In this article, the performance of quarter vehicle preview controllers when applied to a real off-road vehicle is simulated using both two degree of freedom quarter and ten degree of freedom full vehicle models. The results, which are compared with non-preview active and conventional passive suspensions, confirm that preview control reduces vertical acceleration of the body centre of gravity, which results in improved ride quality. Further, reductions in pitch and roll motion result from smaller vertical displacements of the vehicle quarters. Coupling between quarters, through the vehicle body, appears to have a smoothing effect on the control.

As an alternative to optimal control theory based controllers, a simple ad hoc preview controller based on isolating the vehicle body from dynamic loads transmitted through the suspension is proposed. Simulation results show that such a controller outperforms the optimal control theory based controllers over small discrete disturbances but responds poorly to disturbances encountered from other than steady state.     

Nonlinear ACC in Simulation and Measurement

In this paper an adaptive cruise control (ACC) of a convoy consisting of two passenger cars is designed and tested. For the ACC only on board sensors in the following vehicle are used, communication within the convoy or between the controlled vehicle and electronic systems on the roadside is not assumed. A laser scanner is applied for range measurements, derived from the complete vision data of the area in front of the car. Since the scanner provides the range only, a Kalman Filter is used to estimate the velocity and acceleration of the car. For controller design the concept of flat outputs in connection with the exact state linearization is applied. Moreover, the exact state linearization is combined with a sliding mode control. The control parameters are obtained by an optimization algorithm using optimal tracking formulation. The optimization also guarantees individual vehicle stability as well as string stability of the convoy. It is shown how the convoy is responding to disturbances resulting from initial errors or from velocity steps by the leading vehicle at lower speed in simulation and experiment.     

Nonlinear ACC in Simulation and Measurement

In this paper an adaptive cruise control (ACC) of a convoy consisting of two passenger cars is designed and tested. For the ACC only on board sensors in the following vehicle are used, communication within the convoy or between the controlled vehicle and electronic systems on the roadside is not assumed. A laser scanner is applied for range measurements, derived from the complete vision data of the area in front of the car. Since the scanner provides the range only, a Kalman Filter is used to estimate the velocity and acceleration of the car. For controller design the concept of flat outputs in connection with the exact state linearization is applied. Moreover, the exact state linearization is combined with a sliding mode control. The control parameters are obtained by an optimization algorithm using optimal tracking formulation. The optimization also guarantees individual vehicle stability as well as string stability of the convoy. It is shown how the convoy is responding to disturbances resulting from initial errors or from velocity steps by the leading vehicle at lower speed in simulation and experiment.     

Improved optimal controller for start-up of amt trucks in consideration of driver’s intention

A linear-quadratic optimal controller is proposed for vehicle start-up, which is designed as a linear feedback form of the states and the measured (estimated) disturbances. The requirements of less friction loss and less driveline shock are represented by the weighting matrices of the cost function. The driver’s intension is also considered and the controller gains are adjusted on-line accordingly. The designed control strategy is tested on a complete powertrain simulation model. Through large amount of simulations, it is verified that the system is robust to the variations of driving conditions, such as variation of vehicle mass and road grade. It is also shown that the control performance is influenced greatly by the estimation error of engine torque and clutch torque, and the acceptable level of mean estimation error is about ±10%.     

基于路堤粗粒土填料力学特性的改进邓肯-张模型

为研究动力及含水率变化对路堤粗粒土填料力学特性的影响，制作了不同含水率w的路堤粗粒土填料试样，先对其施加一定荷载频率f的动应力，再进行静三轴压缩试验，分析不同试样静偏应力σ₀-应变ε₁曲线变化规律，之后结合Janbu公式探讨动偏应力σ_d、w及f与参数n、K的联系，建立初始变形模量E_i、极限偏应力(σ₀)_ult与各控制变量的拟合公式，提出考虑动力及含水率影响的路堤粗粒土填料改进邓肯-张模型，最后开展验证试验，对比分析该改进模型的有效性。研究结果表明：三轴试验中粗粒土试样在ε₁>0.5%时由弹性变形进入塑性变形阶段，不同控制因素下的σ₀-ε₁曲线在0.5%<ε₁<2.0%范围内出现明显差异，切线变形模量E_t在该范围内迅速降低，降低幅度达到58%～76%;当ε₁>2%时E_t变化逐渐减缓并...     

倾斜坡顶黄土边坡垂直裂隙深度计算方法

垂直裂隙在黄土层中发育极为普遍,为研究黄土边坡坡顶垂直裂隙深度的问题,改进传统裂隙法中存在的缺陷,分别建立单裂隙与多裂隙滑动模型,并结合边坡滑动后垂直裂隙后壁形成的垂直张拉段土体自稳特点,采用极限平衡法对2种滑动模型进行受力分析,建立边坡极限状态方程;并进一步利用最优值法对方程进行求解,推导出黄土边坡倾斜坡顶垂直裂隙极...     

Optimal roll control of an articulated vehicle: theory and model validation

This paper investigates optimal roll control of an experimental articulated vehicle. The test vehicle and the mathematical model used to design the control strategies are presented. The vehicle model is validated against experimental data from the test vehicle in passive configuration. The initial controller design, performed by Sampson (Sampson, D.J.M. and Cebon, D., 2003a, Achievable roll stability of heavy road vehicles. Proc. Instn. Mech. Engrs, Part D, J. Automobile Engineering, 217(4), 269-287), is reviewed and adapted for the experimental vehicle. The effect of not controlling all the axles on the vehicle is investigated and a variable vehicle speed controller is designed by interpolating between constant speed controllers. Substantial reduction in normalized load transfer is achieved for a range of manoeuvres, both in steady-state and transient conditions.     

Robust control for 4WS vehicles considering a varying tire-road friction coefficient

A µ-synthesis for four-wheel steering (4WS) problems is proposed. Applying this method, model uncertainties can be taken into consideration, and a µ-synthesis robust controller is designed with optimized weighting functions to attenuate the external disturbances. In addition, an optimal controller is designed using the well-known optimal control theory. Two different versions of control laws are considered here. In evaluations of vehicle performance with the robust controller, the proposed controller performs adequately with different maneuvers (i.e., J-turn and Fishhook) and on different road conditions (i.e., icy, wet, and dry). The numerical simulation shows that the designed µ-synthesis robust controller can improve the performance of a closed-loop 4WS vehicle, and this controller has good maneuverability, sufficiently robust stability, and good performance robustness against serious disturbances.     

基于自然驾驶数据的分心驾驶行为识别方法

大量证据表明，驾驶人分心是导致交通事故的主要原因之一。当前基于侵入式（如脑电波等）或半侵入式（如视频等）检测驾驶人分心的方法，不仅对驾驶任务造成一定干扰，且受多种环境因素的制约，误报率较高。基于此，只考虑非侵入式车辆运动特征，提出一种基于深度学习的驾驶人分心状态识别方法：首先，从自然驾驶数据集中获得大量的跟驰片段，采用态势感知方法，提取典型的分心驾驶片段，并建立仅包含车辆运动学特征的分心判别指标集；其次，利用梯度提升决策树-递归特征消除算法（GBDT-RFE）和随机森林-递归特征消除算法（RF-RFE）对特征进行重要度排序，得到重要度较高的分心监测指标；最后，采用长短时记忆神经网络（LSTM-NN）实现分心驾驶的分类识别，并与支持向量机和AdaBoost的模型结果进行对比。研究结果表明：LSTM-NN在判别分心或正常状态时F₁分别为89%、91%，高于SVM和AdaBoost对应二分类结果；进行多分类任务时，判别分心情景的平均F₁较SVM和AdaBoost分别提升了12%和7%，不同类别分心识别的误报率在15%以下，说明LSTM-NN能够有效学习分心序列的前后信息，有利于准确估计驾驶人的状态。研究结果可为车辆分心预警系统和驾驶风险倾向性评估提供方法基础。     

On Control Laws for Vehicle Suspensions Accounting for Input Correlations

Input correlations involving time delays are common in active vehicle suspension system problems. One approach to control law derivation fur such systems is to restrict attention to slate feedback laws in the interests of practicality and it is then of interest to determine the law which is, in some sense, the best. Under assumptions which are common in this area. relating to input, system and cost Function forms, a new derivation of the expression for the cost, accounting for time delays, is given. The use of the expression in numerical procedures for determining effective control gains is discussed and an example for a half car planar vehicle model is described. By comparing results with existing ones which are truly optimal, an estimate is made of the loss of performance which results from the restriction of the control law form in this case. Some generalisation of the results is attempted and they are placed in a contemporary context at the conclusion.