Optimal Performance of Variable Component Suspensions

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.     

Optimal Performance of Variable Component Suspensions

SUMMARY

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.     

The Response of Active and Semi-active Suspensions to Realistic Feedback Signals

A simple vehicle model is presented incorporating passive, active, and semi-active suspensions. When the desired feedback variables are ideally available, the system response is well understood and excellent sprung mass isolation results. More often than not, the measured variables must be signal processed in some manner prior to their use in some control algorithm. This paper presents the expected response of a simple vehicle with an active and/or semi-active suspension, subject to non-ideal feedback information.     

The Response of Active and Semi-active Suspensions to Realistic Feedback Signals

SUMMARY

A simple vehicle model is presented incorporating passive, active, and semi-active suspensions. When the desired feedback variables are ideally available, the system response is well understood and excellent sprung mass isolation results. More often than not, the measured variables must be signal processed in some manner prior to their use in some control algorithm. This paper presents the expected response of a simple vehicle with an active and/or semi-active suspension, subject to non-ideal feedback information.     

汽车半主动悬架的模型参考自适应控制

在1／4车辆动力学模型的基础上，基于李雅普诺夫稳定性理论，以天棚阻尼半主动悬架为参考模型，设计了半主动悬架模型参考自适应控制器。自适应控制器包括可调前置控制器和状态反馈控制器两个部分。推导了自适应控制律与相应的约束条件。仿真结果表明：该控制器对于模型参数的不确定性具有良好的鲁棒特性。自适应控制器不仅明显降低了车身加速度，提高了平顺性，同时也使汽车的行驶安全性获得了改善，悬架动变形稍有增大。     

Active Damping in Road Vehicle Suspension Systems

Low order, linearized dynamic models of road vehicle suspension systems are analyzed to provide insight into the benefits of suspensions incorporating generalized velocity feedback compared with conventional passive suspensions. Damping forces from passive dampers are supplemented by forces generated by an active element requiring a power supply. A simple criterion is developed which indicates whether or not the introduction of activedamping forces will result in significant benefit for pneumatic tired vehicles.

An extended active suspension concept involving a high-gain load leveler as well as active damping is analyzed. The realization of active or semi-active damping forces through electrical or hydraulic means is briefly discussed.     

基于ILMI算法的车辆半主动悬架静态输出反馈控制

针对采用磁流变阻尼器的1/4汽车半主动悬架模型进行振动控制分析。利用迭代线性矩阵不等式(ILMI)算法在输出反馈控制中的求解优势,提出基于ILMI算法的半主动悬架静态输出反馈控制方法。仿真结果表明,结合合适的控制算法,采用磁流变阻尼器的半主动悬架系统有效地改善了汽车驾驶平顺性和乘坐舒适性。     

Skyhook and H8 Control of Semi-active Suspensions: Some Practical Aspects

Summary This paper deals with single-wheel suspension car model. We aim to prove the benefits of controlled semi-active suspensions compared to passive ones. The contribution relies on H 8 control design to improve comfort and road holding of the car under industrial specifications, and on control validation through simulation on an exact nonlinear model of the suspension. Note that we define semi-active suspensions as control systems incorporating a parallel spring and an electronically controlled damper. However, the type of damper used in automotive industry can only dissipate energy. No additional force can be generated using external energy. The control issue is then to change, in an accurate way, the damping (friction) coefficient in real-time. This is what we call semi-active suspension. For this purpose, two control methodologies, H 8 and Skyhook control approaches, are developed, using a linear model of the suspension, and compared in terms of performances using industrial specifications. The performance analysis is done using the control-oriented linear model first, and then using an exact nonlinear model of the suspension incorporating the nonlinear characteristics of the suspension spring and damper.     

Skyhook and H8 Control of Semi-active Suspensions: Some Practical Aspects

Summary This paper deals with single-wheel suspension car model. We aim to prove the benefits of controlled semi-active suspensions compared to passive ones. The contribution relies on H 8 control design to improve comfort and road holding of the car under industrial specifications, and on control validation through simulation on an exact nonlinear model of the suspension. Note that we define semi-active suspensions as control systems incorporating a parallel spring and an electronically controlled damper. However, the type of damper used in automotive industry can only dissipate energy. No additional force can be generated using external energy. The control issue is then to change, in an accurate way, the damping (friction) coefficient in real-time. This is what we call semi-active suspension. For this purpose, two control methodologies, H 8 and Skyhook control approaches, are developed, using a linear model of the suspension, and compared in terms of performances using industrial specifications. The performance analysis is done using the control-oriented linear model first, and then using an exact nonlinear model of the suspension incorporating the nonlinear characteristics of the suspension spring and damper.     

State of the art survey: active and semi-active suspension control

This survey paper aims to provide some insight into the design of suspension control system within the context of existing literature and share observations on current hardware implementation of active and semi-active suspension systems. It reviews the performance envelop of active, semi-active, and passive suspensions with a focus on linear quadratic-based optimisation including a specific example. The paper further discusses various design aspects including other design techniques, the decoupling of load and road disturbances, the decoupling of pitch and heave modes, the use of an inerter as an additional design element, and the application of preview. Various production and near production suspension systems were examined and described according to the features they offer, including self-levelling, variable damping, variable geometry, and anti-roll damping and stiffness. The lessons learned from these analytical insights and related hardware implementations are valuable and can be applied towards future active or semi-active suspension design.     

Performance of Low-bandwidth, Semi-active Damping Concepts for Suspension Control

Active damping has been shown to offer increased suspension performance in terms of vehicle isolation, suspension packaging, and road-tire contact force. It can even approximate the performance of full state feedback control without requiring the difficult measurement of tire deflection. Many semi-active damping strategies have been introduced to approximate the response of active damping with the modulation of passive damping parameters. These strategies have typically required a relatively high bandwidth for actuator response. This paper investigates the simulation performance and “frequency response” of two concepts in low-bandwidth semi-active suspension control, one that sets a damping force directly and another that sets the damping resistance. The electronically controlled bandwidth of these actuators is approximately an order of magnitude less than other semi-active devices; high frequency control is handled mechanically. A quarter-car model is studied with the controlled damping replacing both passive and active damping of typical control schemes. Both low-bandwidth damping strategies perform remarkably well compared to both active and high-bandwidth, semi-active damping. In certain dynamic performances, the new semi-active strategies outperform active damping and what the author calls “nominal” semi-active damping.     

基于遗传算法和LQG控制的汽车半主动悬架结构和控制参数的集成优化研究

传统半主动悬架的设计是先设计其结构参数后设计其控制器参数，这样易造成系统失去全局最优性能。针对这一问题，本文提出一种基于遗传算法和LQG控制的集成优化半主动悬架结构参数和控制参数的方法，通过理论分析和仿真结果表明此方法与传统优化方法相比，对改善汽车行驶平顺性和提高汽车行驶安全性具有较优的效果。     

Performance of Low-bandwidth,Semi-active Damping Concepts for Suspension Control

Abstract

Active damping has been shown to offer increased suspension performance in terms of vehicle isolation, suspension packaging, and road-tire contact force. It can even approximate the performance of full state feedback control without requiring the difficult measurement of tire deflection. Many semi-active damping strategies have been introduced to approximate the response of active damping with the modulation of passive damping parameters. These strategies have typically required a relatively high bandwidth for actuator response. This paper investigates the simulation performance and “frequency response” of two concepts in low-bandwidth semi-active suspension control, one that sets a damping force directly and another that sets the damping resistance. The electronically controlled bandwidth of these actuators is approximately an order of magnitude less than other semi-active devices; high frequency control is handled mechanically. A quarter-car model is studied with the controlled damping replacing both passive and active damping of typical control schemes. Both low-bandwidth damping strategies perform remarkably well compared to both active and high-bandwidth, semi-active damping. In certain dynamic performances, the new semi-active strategies outperform active damping and what the author calls “nominal” semi-active damping.     

Semi-active suspension systems for railway vehicles using magnetorheological dampers. Part I: system integration and modelling

In this paper, it is aimed to investigate semi-active suspension systems using magnetorheological (MR) fluid dampers for improving the ride quality of railway vehicles. A 17-degree-of-freedom (DOF) model of a full-scale railway vehicle integrated with the semi-active controlled MR fluid dampers in its secondary suspension system is proposed to cope with the lateral, yaw, and roll motions of the car body, trucks, and wheelsets. The governing equations combining the dynamics of the railway vehicle integrated with MR dampers in the suspension system and the dynamics of the rail track irregularities are developed and a linear quadratic Gaussian (LQG) control law using the acceleration feedback is adopted, in which the state variables are estimated from the measurable accelerations with a Kalman estimator. In order to evaluate the performances of the semi-active suspension systems based on MR dampers for railway vehicles, the random and periodical track irregularities are modelled with a uniform state-space formulation according to the testing data and incorporated into the governing equation of the railway vehicle integrated with the semi-active suspension system. Utilising the governing equations and the semi-active controller developed in this paper, the simulation and analysis are presented in Part II of this paper.     

基于微分几何理论的汽车半主动悬架非线性振动控制

针对汽车悬架系统的非线性特性,采用1／4汽车二自由度悬架模型分析半主动悬架控制。应用微分几何理论得到输出-干扰解耦方法,再经适当的坐标变换将该模型由非线性系统简化成一线性系统,并对此系统进行最优控制,然后通过非线性状态反馈实现对原系统的半主动控制。与被动悬架的仿真结果进行了比较,表明这种针对具有非线性特征的半主动悬架的非线性控制方法是可行的。通过功率谱分析,控制后系统的能量比被动悬架更趋于平均,悬架动态性能更稳定。     

Non-stationary random vibration analysis of three-dimensional train–bridge systems

The quarter car model has been used extensively to study the benefits of active, semi-active and passive suspensions. Despite the evident simplicity of the model, the insights obtained from this model have been found to have counterparts in half- and full-car suspension models. Among the most interesting results of the analysis of the quarter car are the relationships among certain transfer function and invariant points in the frequency response functions. These results are of great interest for the application of linear control techniques to the design of active suspensions and the optimisation of linearised passive suspensions. This paper attempts to show why some of the limitations implied by the model are less absolute than they at first seem.     

电动赛车半主动悬架系统仿真及实现

应用汽车动力学理论,以1/4汽车悬架模型为研究对象,用调节减振器的阻尼系数法,建立了二自由度电动赛车的半主动悬架最优控制模型,利用编制的路面谱作为激励输入进行了仿真,并与被动悬架性能进行了对比。结果表明,半主动悬架在车身垂直振动加速度、悬架动行程、轮胎形变量的改善度分别为31.3%、21.4%、12.6%,使车身的振动被控制在某个范围之内,大大提高电动赛车在行驶过程中的平顺性。     

Road Vehicle Suspension System Design - a review

Based mainly on English language literature, information relating to the design of automobile suspension systems for ride comfort and control of wheel load variations for frequencies below body structure resonances is reviewed. The information is interpreted in the context of vehicles which travel through a wide speed range on roads of markedly differing quality, which do so carrying different loads and which are required to possess good handling qualities.

Sections are devoted to describing road surfaces, modelling vehicles and setting up performance criteria, and to passive, active, semi-active and slow-active system types. Methods for deriving active system control laws are outlined. Strengths and weaknesses of the various systems are identified and their relative performance capabilities and equipment requirements are discussed. Attention is given to adaptation of the suspension or control system parameters to changing conditions. Remaining research needs are considered.     

Semi-active suspension systems for railway vehicles using magnetorheological dampers. Part II: simulation and analysis

In this paper, the semi-active suspension system for railway vehicles based on the controlled (MR) fluid dampers is investigated, and compared with the passive on and passive off suspension systems. The lateral, yaw, and roll accelerations of the car body, trucks, and wheelsets of a full-scale railway vehicle integrated with four MR dampers in the secondary suspension systems, which are in the closed and open loops respectively, are simulated under the random and periodical track irregularities using the established governing equations of the railway vehicle and the modelled track irregularities in Part I of this paper. The simulation results indicate that (1) the semi-active controlled MR damper-based suspension system for railway vehicles is effective and beneficial as compared with the passive on and passive off modes, and (2) while the car body accelerations of the railway vehicle integrated with semi-active controlled MR dampers can be significantly reduced relative to the passive on and passive off ones, the accelerations of the trucks and wheelsets could be increased to some extent. However, the increase in the accelerations of the trucks and wheelsets is insignificant.     

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.