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

SUMMARY

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 H ₂ method, and showing how H ₂ 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.     

H2 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 H₂ optimal control of systems with time-delayed disturbances and develop a computationally efficient approach for controller synthesis. We extend the Lyapunov-based H₂ norm computation to systems with time-delayed disturbances and then derive a concise formula to explicitly evaluate the sensitivity of the system H₂ norm with respect to controller gains. Thence, a set of necessary conditions for H₂ 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 H₂ 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.     

线性最优控制主动悬架系统的鲁棒稳定性研究

本文采用系统性能分析和Ｍｏｎｔｅ－Ｃａｒｌｏ方法，对线性最优控制主动悬架系统作了鲁棒稳定性研究。     

基于SIMULINK的车辆主动悬架LQG控制仿真研究

通过建立1／4车辆模型,应用最优控制理论进行了车辆主动悬架的LQG(Linear Quadratic Gaussian)控制器的设计,并在Matlab／Simulink环境中建立系统模型并进行仿真,将仿真结果与被动悬架仿真结果进行对比分析。仿真结果表明,具有LQG控制器的主动悬架对车辆行驶平顺性和乘坐舒适性的改善有良好的效果。     

基于Simulink的车辆主动悬架LQG控制器的设计

建立了二自由度1/4车体的数学模型,并利用线性最优化控制理论进行了汽车主动悬架的LQG控制器设计,并在Matlab/Simulink环境下进行仿真,结果表明具有LQG控制器的主动悬架对车辆行驶平稳性和乘坐舒适性有了很大的改善。     

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.     

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...     

Structured H2 Optimization of Vehicle Suspensions Based on Multi-Wheel Models

Summary Various control techniques, especially LQG optimal control, have been applied to the design of active and semi-active vehicle suspensions over the past several decades. However passive suspensions remain dominant in the automotive marketplace because they are simple, reliable, and inexpensive. The force generated by a passive suspension at a given wheel can depend only on the relative displacement and velocity at that wheel, and the suspension parameters for the left and right wheels are usually required to be equal. Therefore, a passive vehicle suspension can be viewed as a decentralized feedback controller with constraints to guarantee suspension symmetry. In this paper, we cast the optimization of passive vehicle suspensions as structure-constrained LQG/H2 optimal control problems. Correlated road random excitations are taken as the disturbance inputs; ride comfort, road handling, suspension travel, and vehicle-body attitude are included in the cost outputs. We derive a set of necessary conditions for optimality and then develop a gradient-based method to efficiently solve the structure-constrained H2 optimization problem. An eight-DOF four-wheel-vehicle model is studied as an example to illustrate application of the procedure, which is useful for design of both passive suspensions and active suspensions with controller-structure constraints.     

Inverse neuro-fuzzy MR damper model and its application in vibration control of vehicle suspension system

In this paper, a magneto-rheological (MR) damper-based semi-active controller for vehicle suspension is developed. This system consists of a linear quadratic Gauss (LQG) controller as the system controller and an adaptive neuro-fuzzy inference system (ANFIS) inverse model as the damper controller. First, a modified Bouc–Wen model is proposed to characterise the forward dynamic characteristics of the MR damper based on the experimental data. Then, an inverse MR damper model is built using ANFIS technique to determine the input current so as to gain the desired damping force. Finally, a quarter-car suspension model together with the MR damper is set up, and a semi-active controller composed of the LQG controller and the ANFIS inverse model is designed. Simulation results demonstrate that the desired force can be accurately tracked using the ANFIS technique and the semi-active controller can achieve competitive performance as that of active suspension.     

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...     

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。     

砂性地层盾构隧道壁后注浆浆液扩散室内试验

为了探明盾构隧道壁后注浆浆液扩散机理,基于对壁后注浆过程的分析,设计由试验模型箱、注浆系统、浆液配制系统、测试及数据处理系统组成的模型试验系统,试验前首先对水泥浆液的特性进行测试,然后通过该模型试验系统分别对3种不同级配的砂样地层（对应不同分维数）进行牛顿流体、宾汉姆流体、幂律流体的壁后注浆室内试验。根据试验结果分析注浆过程中浆液流速、土体密度及含水率的变化规律,并结合理论计算分析浆液的充填率λ,超挖系数和浆液压缩系数λ₁+λ₂,浆液损耗系数λ₃,浆液在土体中的渗透系数及压密系数m的变化规律。结果表明：盾构隧道壁后注浆过程中,水灰比大小对浆液的流速、渗透扩散时间影响较大,砂样分维数对地层可注入时间的影响较为明显;浆液的充填率λ与水灰比大小有关,浆液损耗系数λ₃ 与水灰比呈正相关关系,不同砂样的超挖系数和浆液压缩系数λ₁+λ₂ 的数值变化不大;浆液在砂样中的渗透系数及压密系数m与砂样的分维数呈负相关关系;3种不同的流体注浆结束后,管片周围土体的密度与土体所处的深度成反比,随着深度的增加,土体密度的变化率减小且纵向上的离散性降低;周围土体的含水率与土体所处的深度成正比,随着深度的变化,含水率的变化率亦减小且在纵向分布上趋于某一确定值。     

Linear Quadratic Gaussian Control of a Quarter-Car Suspension

This paper presents a method for designing linear multivariable controllers in the frequency-domain for an intelligent controlled suspension system for a quarter-car model. The design methodology uses singular value inequalities and optimal control theory. The vehicle system is augmented with additional dynamics in the form of an integrator to affect the loop shapes of the system. The measurements are assumed to be obtained in a noisy state, and the optimal control gain and the Kalman filter gain are derived using system dynamics and noise statistics. A combination of singular value analysis, eigenvalue analysis, time response, and power spectral densities of random response is used to describe the performance of the active suspension systems.     

Linear Quadratic Gaussian Control of a Quarter-Car Suspension

This paper presents a method for designing linear multivariable controllers in the frequency-domain for an intelligent controlled suspension system for a quarter-car model. The design methodology uses singular value inequalities and optimal control theory. The vehicle system is augmented with additional dynamics in the form of an integrator to affect the loop shapes of the system. The measurements are assumed to be obtained in a noisy state, and the optimal control gain and the Kalman filter gain are derived using system dynamics and noise statistics. A combination of singular value analysis, eigenvalue analysis, time response, and power spectral densities of random response is used to describe the performance of the active suspension systems.     

Pole location control design of an active suspension system with uncertain parameters

This paper addresses the problem of robust control design for an active suspension quarter-car model by means of state feedback gains. Specifically, the design of controllers that assure robust pole location of the closed-loop system inside a circular region on the left-hand side of complex plane is investigated. Three sufficient conditions for the existence of a robust stabilizing state feedback gain are presented as linear matrix inequalities: (i) the quadratic stability based gain; (ii) a recently published condition that uses an augmented space and has been here modified to cope with the pole location specification; (iii) a condition that uses an extended number of equations and yields a parameter-dependent state feedback gain. Unlike other parameter-dependent strategies, neither extensive gridding nor approximations are needed. In the suspension model, the sprung mass, the damper coefficient and the spring constant are considered as uncertain parameters belonging to a known interval (polytope type uncertainty). It is shown that the parameter-dependent gain proposed allows one to impose the closed-loop system pole locations that in some situations cannot be obtained with constant feedback gains.     

Pole location control design of an active suspension system with uncertain parameters

This paper addresses the problem of robust control design for an active suspension quarter-car model by means of state feedback gains. Specifically, the design of controllers that assure robust pole location of the closed-loop system inside a circular region on the left-hand side of complex plane is investigated. Three sufficient conditions for the existence of a robust stabilizing state feedback gain are presented as linear matrix inequalities: (i) the quadratic stability based gain; (ii) a recently published condition that uses an augmented space and has been here modified to cope with the pole location specification; (iii) a condition that uses an extended number of equations and yields a parameter-dependent state feedback gain. Unlike other parameter-dependent strategies, neither extensive gridding nor approximations are needed. In the suspension model, the sprung mass, the damper coefficient and the spring constant are considered as uncertain parameters belonging to a known interval (polytope type uncertainty). It is shown that the parameter-dependent gain proposed allows one to impose the closed-loop system pole locations that in some situations cannot be obtained with constant feedback gains.     

先期振动对高聚物胶凝堆石料动变形特性的影响

先期振动对土石坝地震变形影响显著。通过开展不同先期动应力作用下的动三轴试验,研究了先期振动对未加固堆石料和高聚物胶凝堆石料动变形特性的影响。结果表明:先期振动对未加固堆石料和高聚物胶凝堆石料的弹性轴应变无明显影响,但显著降低了其塑性轴应变;未加固堆石料和高聚物胶凝堆石料的残余变形在先期振动影响下显著减小,与未经受先期振动的试样相比,先期动应力为40%围压的试样,最大残余剪应变降低幅度和最大残余体应变降低幅度的平均值分别为48.1%和42.0%;先期动应力为80%围压的试样,最大残余剪应变降低幅度和最大残余体应变降低幅度的平均值分别为80.9%和71.6%。先期动应力幅值越大,再次经历动应力时未加固堆石料和高聚物胶凝堆石料产生的残余变形越小,抵抗变形能力提高越明显。最大残余变形的降低幅度与固结比、围压及高聚物含量无关。随后修正了沈珠江动残余变形模型,修正后的残余变形模型可以反映高聚物对堆石料残余剪应变和残余体应变的影响。与未经受先期振动的试样相比,先期动应力为40%围压的高聚物胶凝堆石料(高聚物质量比R_p=2%)的改进残余变形模型参数c₁和c₄分别降低了27.7%和61.2%;先期动应力为80%围压的高聚物胶凝堆石料(R_p=2%)的改进残余变形模型参数c₁和c₄分别降低了68.8%和79.3%。     

基于改进稀疏正则化的扩展卡尔曼滤波损伤识别研究

基于传统扩展卡尔曼滤波方法（EKF）的损伤识别过程是一个典型的反问题求解，反问题的不适定性使EKF识别结果容易受噪声干扰，导致EKF算法收敛困难、识别精度下降。基于l₁正则化的EKF算法在一定程度上可以缓解此问题，但其不能获得足够准确的稀疏解。为此，提出了一种改进稀疏正则化的EKF方法。该方法采用Arctangent罚函数代替l₁范数以施加损伤稀疏性约束；通过伪测量技术将稀疏性约束嵌入到EKF中，获得施加约束方程后的递推解。采用3层剪切结构和悬臂梁2个试验算例验证了该方法的有效性。研究结果表明：即使在噪声干扰下，所提方法也可以准确识别出结构损伤；相比传统l₁正则化EKF方法，该方法需要的观测信息更少，能获得更准确的稀疏解。