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

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.     

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.     

汽车主动悬架的最优预见控制

本文针对1/2车辆模型,应用最优预见控制理论对汽车主动悬架进行控制系统的设计和研究。计算机仿真结果表明,所提出的系统能有效改善汽车乘坐舒适性。     

Optimal Linear Preview Control of Active Vehicle Suspension

SUMMARY

The problem of linear preview control of vehicle suspension is considered as a continuous time stochastic optimal control problem. In the proposed approach minimal a priori information about the road irregularities is assumed and measurement errors are taken into account. It is shown that estimation and control issues can be decoupled. The problem formulation and the analytical solution are given in a general form and hence they apply to other problems in which the system disturbances are unknown a priori, even in a stochastic sense, but some preview information is possible.

The solution is applied to a two-degree-of-freedom (2-DOF) vehicle model. The effects of preview information on ride comfort, road holding, working space of the suspension and power requirements are examined in time and frequency domains. The results show that the greatest potential is for improving road holding properties. This effect could not have been observed in previous studies based on a 1-DOF vehicle model. It is also demonstrated that the presence of preview drastically reduces power requirements, thus relieving the performance versus actuator power dilemma.     

Optimal Linear Preview Control of Active Vehicle Suspension

The problem of linear preview control of vehicle suspension is considered as a continuous time stochastic optimal control problem. In the proposed approach minimal a priori information about the road irregularities is assumed and measurement errors are taken into account. It is shown that estimation and control issues can be decoupled. The problem formulation and the analytical solution are given in a general form and hence they apply to other problems in which the system disturbances are unknown a priori, even in a stochastic sense, but some preview information is possible.

The solution is applied to a two-degree-of-freedom (2-DOF) vehicle model. The effects of preview information on ride comfort, road holding, working space of the suspension and power requirements are examined in time and frequency domains. The results show that the greatest potential is for improving road holding properties. This effect could not have been observed in previous studies based on a 1-DOF vehicle model. It is also demonstrated that the presence of preview drastically reduces power requirements, thus relieving the performance versus actuator power dilemma.     

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.     

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.     

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.     

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。     

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.     

Semi-Active Control Laws - Optimal and Sub-Optimal

SUMMARY

This paper attempts to clarify the question of what the optimal semi-active suspension is that minimizes a deterministic quadratic performance index. The optimal control law is a time-varying solution that involves three related Riccati equations. The constant Riccati solution (the so-called “clipped optimal” solution) is not optimal, although its performance is generally quite close to that of the time-varying solution. As the time-varying solution cannot be practically implemented, several constant gain sub-optimal solutions are investigated. A new semi-active algorithm, called the “steepest gradient” algorithm, is developed and its performance is shown to be superior to that of the “clipped optimal” solution.     

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

SUMMARY

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.     

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.     

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。     

Extended Ground-Hook - New Concept of Semi-Active Control of Truck's Suspension

This paper deals with the novel control concept, so called ground-hook for active and mainly semi-active suspension of vehicles with the ultimate objective to minimize the tyre-road forces and thus the road damage. The basic ground-hook concept is extended to the several variants which enable to decrease criteria of road damage as well as to increase driver's comfort for a broad range of road unevennesses. Parameters of control law are determined by the parameter optimization for generally nonlinear model. The influence and interaction of the damping rate limits and time constants of variable shock absorbers are also taken into account. The influence of implementation of more complicated truck models is also discussed.     

Extended Ground-Hook - New Concept of Semi-Active Control of Truck's Suspension

SUMMARY

This paper deals with the novel control concept, so called ground-hook for active and mainly semi-active suspension of vehicles with the ultimate objective to minimize the tyre-road forces and thus the road damage. The basic ground-hook concept is extended to the several variants which enable to decrease criteria of road damage as well as to increase driver's comfort for a broad range of road unevennesses. Parameters of control law are determined by the parameter optimization for generally nonlinear model. The influence and interaction of the damping rate limits and time constants of variable shock absorbers are also taken into account. The influence of implementation of more complicated truck models is also discussed.     

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.