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.     

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.     

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 H ₂ (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.     

基于遗传算法的车辆悬架系统等效物理参数识别

针对车辆悬架系统的功能及物理特性,以车轴的运动为系统输入,对复杂的整车行驶模型进行了合理简化。以某型专用越野车辆为例,建立了簧载质量的3自由度振动模型,推导了簧载质量任意位置处的加速度频响函数;利用汽车试验场道路测试数据,通过遗传算法编写VC程序进行了数据拟合,得到了悬架系统在不同路面工况下的等效物理参数。实际应用表明,拟合结果具有较高的可信度。     

Road roughness estimation based on discrete Kalman filter with unknown input

ABSTRACT

The road roughness acts as a disturbance input to the vehicle dynamics, and causes undesirable vibrations associated with the ride and handing characteristics. Furthermore, the accurate measurement of road roughness plays a key role in better understanding a vehicle dynamic behaviour and active suspension control systems. However, the direct measurement by laser profilometer or other distance sensors are not trivial due to technical and economic issues. This study proposes a new road roughness estimation method by using the discrete Kalman filter with unknown input (DKF-UI). This algorithm is built on a quarter-car model and uses the measurements of the wheel stroke (suspension deflection), and the acceleration of the sprung mass and unsprung mass. The estimation results are compared to the measurements by laser profilometer in-vehicle test.     

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.     

A new active variable stiffness suspension system using a nonlinear energy sink-based controller

This paper presents the active case of a variable stiffness suspension system. The central concept is based on a recently designed variable stiffness mechanism which consists of a horizontal control strut and a vertical strut. The horizontal strut is used to vary the load transfer ratio by actively controlling the location of the point of attachment of the vertical strut to the car body. The control algorithm, effected by a hydraulic actuator, uses the concept of nonlinear energy sink (NES) to effectively transfer the vibrational energy in the sprung mass to a control mass, thereby reducing the transfer of energy from road disturbance to the car body at a relatively lower cost compared to the traditional active suspension using the skyhook concept. The analyses and simulation results show that a better performance can be achieved by subjecting the point of attachment of a suspension system, to the chassis, to the influence of a horizontal NES system.     

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.     

A 3D Brush-type Dynamic Tire Friction Model

The use of advanced dynamic friction models can improve the brush-type tire friction models. This paper presents a 3D dynamic brush model based on the LuGre friction model. The model describes the dynamics of longitudinal and lateral tire friction forces, as well as the self aligning torque dynamics. It has been originally derived in a distributed-parameter form, and then transformed to a simpler lumped-parameter form with only three internal states. Both uniform and non-uniform normal pressure distributions are considered. The model has analytical solution for steady-state conditions. The steady-state behavior is validated with respect to “magic” formula static model, which served as an “ideal” benchmark. The lumped model dynamic behavior is validated by comparing its time-responses with original distributed model responses. The model parameterization with respect to normal force and other tire/road parameters is considered as well.     

Active controller design for an electromagnetic energy-regenerative suspension

In this paper, with the parameters acquired from measured and tested data, a three-phase mathematical model is applied to the motor component of the developed electromagnetic suspension actuator. A main/inner-loop structure is used for its active control, and the constraints of the control current and energy flow states of actuator are analyzed by simplifying the inner-loop control system. Two different control modes, i.e., Consumptive Full Active (CFA) and Regenerative Semi Active (RSA) modes, which emphasize vibration control of sprung mass and vibration energy regeneration caused by road roughness, respectively, are proposed. Simulations are carried out using different road conditions, and the results demonstrate that the CFA mode can improve vehicle ride comfort by more than 30 percent, despite battery energy consumption; in RSA mode, the ride comfort can be improved by up to 10 percent with the battery charged by regenerated energy.     

Root mean square optimization criterion for vibration behaviour of linear quarter car using analytical methods

In this paper, a linear two-degree-of-freedom quarter car model is used to derive a number of analytical formulae describing the dynamic behaviour of passively suspended vehicles running on a harmonically bumped road. The linearity of the system allows us to analytically investigate the steady-state response characteristics. We derive analytical expressions for the root mean square (RMS) of the sprung mass absolute acceleration and relative displacement. This paper demonstrates the shortcomings of existing classical optimization methods. Hence we introduce a new optimization method based on minimizing the absolute acceleration RMS with respect to the relative displacement RMS. The RMS optimization method is applied for the symbolic derivation of analytical formulae featuring the best compromise among conflicting performance indices pertaining to the vehicle suspension system, i.e., sprung mass acceleration and working space. The proposed optimization technique is utilized to find the optimal damping and stiffness curves for the main suspension. The RMS optimal values are used to create design charts for suspension parameters, which are very useful particularly in the presence of physical constraints such as a limit on relative displacement. We introduce a numerical example to illustrate the optimality of the obtained solutions.     

Enhancing grey prediction fuzzy controller for active suspension systems

A grey prediction fuzzy controller (GPFC) was proposed to control an active suspension system and evaluate its control performance. The GPFC employed the grey prediction algorithm to predict the position output error of the sprung mass and the error change as input variables of the traditional fuzzy controller (TFC) in controlling the suspension system to suppress the vibration and the acceleration amplitudes of the sprung mass for improving the ride comfort of the TFC used; however, the TFC or GPFC was employed to control the suspension system, resulting in a large tire deflection so that the road-holding ability in the vehicle becomes worse than with the original passive control strategy. To overcome the problem, this work developed an enhancing grey prediction fuzzy controller (EGPFC) that not only had the original GPFC property but also introduced the tire dynamic effect into the controller design, also using the grey prediction algorithm to predict the next tire deflection error and the error change as input variables of another TFC, to control the suspension system for enhancing the road-holding capability of the vehicle. The EGPFC has better control performances in suppressing the vibration and the acceleration amplitudes of the sprung mass to improve the ride quality and in reducing the tire deflection to enhance the road-holding ability of the vehicle, than both TFC and GPFC, as confirmed by experimental results.     

Modelling and characteristic analysis of tri-axle trucks with hydraulically interconnected suspensions

In this paper, a new hydraulically interconnected suspension (HIS) system is proposed for the implementation of a resistance control for the pitch and bounce modes of tri-axle heavy trucks. A lumped-mass half-truck model is established using the free-body diagram method. The equations of motion of a mechanical and hydraulic coupled system are developed by incorporating the hydraulic strut forces into the mechanical subsystem as externally applied forces. The transfer matrix method (TMM) is used to evaluate the impedance matrix of the hydraulic subsystem consisting of models of fluid pipes, damper valves, accumulators, and three-way junctions. The TMM is further applied to find the quantitative relationships between the hydraulic strut forces and boundary flow of the mechanical–fluid interactive subsystem. The modal analysis method is employed to perform the vibration analysis between the trucks with the conventional suspension and the proposed HIS. Comparison analysis focuses on free vibration with identified eigenvalues and eigenvectors, isolation vibration capacity, and force vibration in terms of the power spectrum density responses. The obtained results show the effectiveness of the proposed HIS system in reducing the pitch motion of sprung mass and simultaneously maintaining the ride comfort. The pitch stiffness is increased while the bounce stiffness is slightly softened. The peak values of sprung mass and wheel hop motions are greatly reduced, and the vibration decay rate of sprung mass is also significantly increased.     

Enhancing grey prediction fuzzy controller for active suspension systems

A grey prediction fuzzy controller (GPFC) was proposed to control an active suspension system and evaluate its control performance. The GPFC employed the grey prediction algorithm to predict the position output error of the sprung mass and the error change as input variables of the traditional fuzzy controller (TFC) in controlling the suspension system to suppress the vibration and the acceleration amplitudes of the sprung mass for improving the ride comfort of the TFC used; however, the TFC or GPFC was employed to control the suspension system, resulting in a large tire deflection so that the road-holding ability in the vehicle becomes worse than with the original passive control strategy. To overcome the problem, this work developed an enhancing grey prediction fuzzy controller (EGPFC) that not only had the original GPFC property but also introduced the tire dynamic effect into the controller design, also using the grey prediction algorithm to predict the next tire deflection error and the error change as input variables of another TFC, to control the suspension system for enhancing the road-holding capability of the vehicle. The EGPFC has better control performances in suppressing the vibration and the acceleration amplitudes of the sprung mass to improve the ride quality and in reducing the tire deflection to enhance the road-holding ability of the vehicle, than both TFC and GPFC, as confirmed by experimental results.     

Kinematic and dynamic analysis of the McPherson suspension with a planar quarter-car model

McPherson suspension modelling poses a challenging problem due to its nonlinear asymmetric behaviour. The paper proposes a planar quarter-car analytical model that not only considers vertical motion of the sprung mass (chassis) but also: (i) rotation and translation for the unsprung mass (wheel assembly), (ii) wheel mass and its inertia moment about the longitudinal axis, and (iii) tyre damping and lateral deflection. This kinematic–dynamic model offers a solution to two important shortcomings of the conventional quarter-car model: it accounts for geometry and for tyre modelling. The paper offers a systematic development of the planar model as well as the complete set of mathematical equations. This analytical model can be suitable for fast computation in hardware-in-the-loop applications. Furthermore, a reproducible Simulink implementation is given. The model has been compared with a realistic Adams/View simulation to analyse dynamic behaviour for the jounce and rebound motion of the wheel and two relevant kinematic parameters: camber angle and track width variation.     

Optimal Preview Control of a Two-dof Vehicle Model Using Stochastic Optimal Control Theory

An optimal preview control algorithm is applied to a two degree of freedom(dof) vehicle model travelling with constant velocity on a randomly profiled road. The road roughness is modelled as a homogeneous random process being the output of a linear first order filter to white noise. The input from the road irregularity is assumed to be measured at some distance in front of the vehicle and this measured infonnation is utilized by the active controller to prepare the system for the ensuing input. The preview control algorithm is obtained by minimizing a quadratic performance index and by describing the average behaviour of the system by the covariance matrix of the vehicle response state vector. Results are presented for full state feedback and significant improvements in sprung mass acceleration, suspension working space and road holding are observed.     

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.     

电流变智能半主动悬架模糊PID控制

对带有电流变液智能阻尼器的半主动汽车悬架系统设计了一种模糊PID控制器。将半主动悬架簧载质量的位移及其导数作为模糊控制器的输入，PID控制器的3个增益参数作为其输出，利用电流变液智能阻尼器的阻尼力可随电压变化的特性来使车身的振动降为最小。仿真实验给出了最优被动悬架、固定参数PID控制智能半主动悬架和模糊PID控制智能半主动悬架在不同路面激励情况下的响应曲线。     

半主动悬架磁流变液减振器研究

针对Passat B5轿车前悬架,开发了双筒滑阀式磁流变液减振器,提出了簧载质量的绝对速度及其与非簧载质量间的相对运动速度估计算法,利用实测悬架参数和磁流变液减振器的非线性阻尼力特性,建立了带磁流变液减振器的半主动悬架模型。沥青路面试验结果表明:相对于被动悬架,采用磁流变液半主动悬架后车辆平顺性改善大于10%。     

H8 Control Performance of a Full-Vehicle Suspension Featuring Magnetorheological Dampers

Summary This paper presents an investigation of the feedback control performance of a full-vehicle suspension system featuring magnetorheological (MR) dampers. A cylindrical MR damper is designed and manufactured by incorporating a Bingham model of aMR fluid which is commercially available. After evaluating the field-dependent damping characteristics of the MR damper, a full-vehicle suspension system installed with 4 independent MR dampers is constructed and its governing equations of motion which include vertical, pitch and roll motions are derived. A H 8 controller which has inherent robustness against system uncertainties is formulated by treating the sprung mass of the vehicle as uncertain parameter. This is accomplished by adopting the loop shaping design procedure. For the demonstration of a practical feasibility, control performance characteristics for vibration suppression of the proposed MR suspension system are evaluated under various road conditions through the hardware-in-the-loop simulation (HILS) methodology.