Semi-Active Suspension with Preview Using a Frequency-Shaped Performance Index

SUMMARY

The objective of this study is to develop a control law for a semi-active suspension for the purpose of ride quality improvement. The semi-active control law is determined by reproducing the control force of an optimally controlled active suspension while suppressing its damping coefficient variation. The performance index of the optimal control for the active suspension is modified to include frequency-shaping by use of Parseval's theorem, which allows us to de-emphasize the effects of particular variables over specific frequency bands.

Through the numerical simulations, it was found that the semi-active suspension may reduce the vertical acceleration of the driver's seat and the sprung mass motions significantly. The road-holding and tire deflections were not affected much.     

Constrained Optimal Control of Semi-Active Suspension Systems with Preview

Controllers for semi-active suspensions have to account for constraints on damper range, tire force and suspension travel. Two approaches to incorporate these constraints in the design of controllers to minimize peak values in the chassis acceleration are considered. It is assumed that information on the oncoming road elevations (preview) is available. In the soft constraint approach, the constraints on tire force and suspension travel are included in a quadratic performance index. Two clipped optimal control laws, which deal with preview in a different way, are presented. Simulation results with a 2-DOF vehicle model on some rounded pulses show that these laws do not work satisfactorily with respect to the constraints. Therefore, the control problem is reformulated as a constrained optimization problem with hard constraints on tire force and suspension travel. Simulations with the same model on the same rounded pulses show that the hard constraint approach handles the constraints more properly.     

Performance Index for a Preview Active Suspension Applied to a Quarter-Car Model

A simple and convenient matrix expression is derived for the performance index in the case of a linear vehicle model with two degrees of freedom and a preview active suspension, subject to a unit step road input and employing optimal control. The usual quadratic integral-type performance index is assumed and the effect of an additional form of constraint is described briefly. The effects of preview time on the performance index and the optimal feed-forward control are illustrated graphically for a particular example.     

Performance Index for a Preview Active Suspension Applied to a Quarter-Car Model

A simple and convenient matrix expression is derived for the performance index in the case of a linear vehicle model with two degrees of freedom and a preview active suspension, subject to a unit step road input and employing optimal control. The usual quadratic integral-type performance index is assumed and the effect of an additional form of constraint is described briefly. The effects of preview time on the performance index and the optimal feed-forward control are illustrated graphically for a particular example.     

Direct Computation of the Performance Index for an Optimally Controlled Active Suspension with Preview Applied to a Half-Car Model

A quadratic integral performance index is defined for a linear active preview-type suspension and a series of matrix expressions derived for its evaluation by means of MATLAB or some similar computer program in the case of a unit step input to the system. The computation, which is both fast and accurate compared to simulation, requires the solution of Lyapunov- and Riccati-type equations. Some examples of numerical computation are given and these show excellent agreement with published results. The conclusion features a useful computer program.     

汽车主动悬架最优控制：采用频域计权形式性能指标函数

本文从提高汽车的乘坐舒适性角度出发，研究了主动悬架的最优控制问题。根据坐位人体的振动响应特性构造了频域计权形式二交型性能指标函数。     

Performance Potential and Power Consumption of Slow-Active Suspension Systems with Preview

Two possible layouts of a slow-active suspension model are analysed. Optimal control laws for different actuator bandwidths and various amounts of road preview are generated, and estimates of power consumption are made. Higher bandwidth systems (10Hz) require less preview to obtain a given level of performance than those with a lower bandwidth (3Hz) but use more energy in doing so. Similar performance is available from the two systems considered, although the second uses considerably less energy to obtain that performance.     

Hydro-pneumatic Slow-active Suspension with Preview Control

In this work, the preview control problem is considered for fully active and hydro-pneumatic slow-active systems. Based on the quarter car model, linear optimal control theory is used to derive the control laws. The Pade approximation technique is used to represent the preview time resulting from a preview sensor mounted at the front bumper to measure the road irregularities ahead of the front wheels. The results for the slow-active system with preview showed that there is 15% improvement in ride comfort compared to slow-active without preview and 28.5% improvement over passive system at similar root mean square (r.m.s) dynamic tyre load and suspension working space. The performance gains are, however, lower by about 15% than those obtainable with the theoretically ideal, fully active system with preview. The power results for slow active with and without preview showed that a 2kW fixed displacement hydraulic pump is enough for full vehicle requirements.     

Observer Design for Semi-Active Suspension Control

This paper presents an observer for automotive semi-active suspension control. Automotive suspensions are disturbance affected dynamic systems and semi-active suspensions can be represented as a bilinear model. An observer for semi-active suspensions is formulated such that the estimation error is independent of unknown external disturbance. The proposed observer uses easily accessible measurements such as accelerations and guarantees exponentially convergent state estimation for suspension deflections and velocities. Absolute sprung mass and unsprung mass velocities can be estimated using the proposed observer. Simulations and experimental rig tests show that all states of a semi-active suspension can be estimated only with acceleration measurements. The estimated states are used to improve ride quality in a semi-active suspension.     

Observer Design for Semi-Active Suspension Control

This paper presents an observer for automotive semi-active suspension control. Automotive suspensions are disturbance affected dynamic systems and semi-active suspensions can be represented as a bilinear model. An observer for semi-active suspensions is formulated such that the estimation error is independent of unknown external disturbance. The proposed observer uses easily accessible measurements such as accelerations and guarantees exponentially convergent state estimation for suspension deflections and velocities. Absolute sprung mass and unsprung mass velocities can be estimated using the proposed observer. Simulations and experimental rig tests show that all states of a semi-active suspension can be estimated only with acceleration measurements. The estimated states are used to improve ride quality in a semi-active suspension.     

Optimal Preview Control of Rear Suspension Using Nonlinear Neural Networks

SUMMARY

The performance of neural networks to be used for identification and optimal control of nonlinear vehicle suspensions is analyzed. It is shown that neuro-vehicle models can be efficiently trained to identify the dynamical characteristics of actual vehicle suspensions. After trained, this neuro-vehicle is used to train both front and rear suspension neuro-controllers under a nonlinear rear preview control scheme. To do that, a neuro-observer is trained to identify the inverse dynamics of the front suspension so that front road disturbances can be identified and used to improve the response of the rear suspension. The performance of the vehicle with neuro-control and with LQ control are compared.     

基于轴间预瞄的主动悬架研究

以某型汽车的1／2车辆模型为研究对象，提出了一种轴间预瞄控制的方法，并结合最优控制理论设计了车辆悬架的控制策略。通过模拟和仿真分析，验证了所提出的轴间预瞄比传统的轴距预瞄具有更好的控制效果。     

Optimal Preview Control of Rear Suspension Using Nonlinear Neural Networks

The performance of neural networks to be used for identification and optimal control of nonlinear vehicle suspensions is analyzed. It is shown that neuro-vehicle models can be efficiently trained to identify the dynamical characteristics of actual vehicle suspensions. After trained, this neuro-vehicle is used to train both front and rear suspension neuro-controllers under a nonlinear rear preview control scheme. To do that, a neuro-observer is trained to identify the inverse dynamics of the front suspension so that front road disturbances can be identified and used to improve the response of the rear suspension. The performance of the vehicle with neuro-control and with LQ control are compared.     

基于天棚控制的半主动悬架建模及稳定性分析

为探究时滞因素对开关天棚控制半主动悬架动态稳定特性的影响,以含时滞的开关天棚控制半主动悬架模型和时滞微分方程理论为基础,并运用Lyapunov稳定性理论,提出该悬架控制系统失稳临界时滞求解的理论分析和数值计算方法;利用数值解法求得不同被动基值阻尼和可切换阻尼减振器阻尼系数下悬架系统的失稳临界时滞量及全(非全)时滞渐进稳定域;最后,通过建立含时滞开关天棚控制半主动悬架系统仿真模型,分析得到时滞对半主动悬架动特性的影响规律。结果表明,当时滞量达到临界值时,悬架系统稳定性将严重恶化。本研究为含时滞开关天棚控制可切换阻尼半主动悬架控制系统的时滞补偿及其稳定性控制策略的制定奠定基础。     

Neuro-Fuzzy Control of a Tracked Vehicle Featuring Semi-Active Electro-Rheological Suspension Units

This paper presents vibration control of a tracked vehicle installed with electro-rheological suspension units (ERSU). As a first step, an in-arm type ERSU is designed, and its spring and damping characteristics are evaluated with respect to the intensity of electric fields. Subsequently, a 16 degree-of-freedom model for a tracked vehicle equipped with the proposed ERSU is established followed by the formulation of a neuro-fuzzy controller. This controller takes account for both ride quality and steering stability by adopting a weighting parameter between two performance requirements. The parameter is appropriately determined by employing a fuzzy algorithm associated with two fuzzy variables: the vertical speed of the body and the rotational angular speed of the wheel. Control performances to isolate unwanted vibration from bump and random road excitations are evaluated through computer simulations. In addition, maximum speed of the vehicle with 6 Watt power absorption is investigated with respect to the road roughness.     

Neuro-Fuzzy Control of a Tracked Vehicle Featuring Semi-Active Electro-Rheological Suspension Units

This paper presents vibration control of a tracked vehicle installed with electro-rheological suspension units (ERSU). As a first step, an in-arm type ERSU is designed, and its spring and damping characteristics are evaluated with respect to the intensity of electric fields. Subsequently, a 16 degree-of-freedom model for a tracked vehicle equipped with the proposed ERSU is established followed by the formulation of a neuro-fuzzy controller. This controller takes account for both ride quality and steering stability by adopting a weighting parameter between two performance requirements. The parameter is appropriately determined by employing a fuzzy algorithm associated with two fuzzy variables: the vertical speed of the body and the rotational angular speed of the wheel. Control performances to isolate unwanted vibration from bump and random road excitations are evaluated through computer simulations. In addition, maximum speed of the vehicle with 6 Watt power absorption is investigated with respect to the road roughness.     

Development of Preview Active Suspension Control System and Performance Limit Analysis by Trajectory Optimization

The main role of the suspension system is to achieve ride comfort by reducing vibrations generated by the road roughness. The active damper is getting much attention due to its reduced cost and ability to enhance ride comfort especially when the road ahead is measurable by an environment sensor. In this study a preview active suspension control system was developed in order to improve ride comfort when the vehicle is passing over a speed bump. The control system consists of a feedback controller based on the skyhook logic and a feedforward controller for canceling out the road disturbance. The performance limit for the active suspension control system was computed via trajectory optimization to provide a measure against which to compare and validate the performance of the developed controller. The simulation results indicated that the controller of this study could enhance ride comfort significantly over the active suspension control system employing only the skyhook feedback control logic. Also the developed controller, by displaying similar control pattern as the trajectory optimization during significant time portions, proved that its control policy is legitimate.     

一种引入行驶状态识别的半主动悬架PID控制修正算法

基于车辆不同行驶状态（路面不平度和车速）下悬挂质量垂向加速度和悬架动挠度响应不相同的客观事实,针对半主动悬架PID控制器无自适应能力的局限,以悬挂质量垂向加速度和悬架动挠度响应作为车辆行驶状态的识别判据．建立起一种引入行驶状态识别的半主动悬架PID控制修正算法,进而以某型轿车为对象,采用MATLAB／Simulink建立起半主动悬架PID控制的仿真模型,针对不同行驶状态计算出PID控制算法修正前、后的车辆平顺性响应并加以对比,表明所提出的PID控制修正算法是有效的。     

基于ADAMS的某悬架系统运动特性分析及结构优化

根据多体动力学理论,运用ADAMS／car软件对某微型轿车悬架系统建立了模型并进行仿真分析;使用ADAMS／Insight以轮胎横向滑移量、主销偏距和四个车轮定位参数为设计目标对悬架的结构关键点进行了优化分析,使该悬架的运动学特性更符合理想设计值。     

The Development and Implementation of Adaptive Semi-Active Suspension Control*

Using adjustable shock absorbers within vehicle suspension systems, it is possible to improve ride comfort significantly when a control strategy is applied based on the so-called skyhook principle. However, the drawback is a poorly damped wheel-hop mode which makes the road holding ability worse. Using adaptive semi-active suspension control based on the tire load variations as introduced in this paper, the trade-off between road holding and ride comfort can be relaxed. Implementation of adaptive skyhook control requires the determination of a number of important and difficult to measure states of the vehicle. This can either be accomplished by several sensors and filters or by a state estimator in combination with less sensors and an internal model of the vehicle. Both methods are discussed. Finally some preliminary test results are discussed.