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.     

An analytical design approach for self-powered active lateral secondary suspensions for railway vehicles

In this paper, an analytical design approach for the development of self-powered active suspensions is investigated and is applied to optimise the control system design for an active lateral secondary suspension for railway vehicles. The conditions for energy balance are analysed and the relationship between the ride quality improvement and energy consumption is discussed in detail. The modal skyhook control is applied to analyse the energy consumption of this suspension by separating its dynamics into the lateral and yaw modes, and based on a simplified model, the average power consumption of actuators is computed in frequency domain by using the power spectral density of lateral alignment of track irregularities. Then the impact of control gains and actuators’ key parameters on the performance for both vibration suppressing and energy recovery/storage is analysed. Computer simulation is used to verify the obtained energy balance condition and to demonstrate that the improved ride comfort is achieved by this self-powered active suspension without any external power supply.     

Motorcycle suspension design using matrix inequalities and passivity constraints

This paper presents a design methodology for the suspension system of a novel aerodynamically efficient motorcycle. Since the machine’s layout and the rider’s seating position are unconventional, several aspects of the machine design, including the suspension, must be reviewed afresh. The design process is based on matrix inequalities that are used to optimise a road-grip objective function – others could be used equally well. The design problem is cast as the minimisation of an H ₂ cost with passivity constraints imposed on the suspension transference. The resulting bilinear matrix inequality problem is solved using a locally optimal iterative algorithm. The matrix inequality-type characterisation of positive real functions permits the optimisation of the suspension system over an entire class of passive admittances. Torsional springs, dampers and inerters are then used to construct networks corresponding to the optimal (positive real) admittances. Networks of first, second, third and fourth orders are considered, and an argument based on the compromise between complexity and improved grip is made for the most suitable suspension configuration. Finally, the effects of improved road grip on the stability of the vehicle’s lateral dynamics are analysed.     

车辆半主动悬架与助力转向集成控制的仿真研究

为协调车辆操纵稳定性和行驶平顺性,基于底盘系统动力学原理,建立了半主动悬架和电动助力转向的综合模型,对半主动悬架和电动助力转向系统进行集成控制.运用二次反馈法和PID策略分别对悬架的可调阻尼和转向系统的助力进行控制.仿真结果表明,在集成控制情况下,车辆的操纵稳定性和平顺性均优于悬架或转向单独控制的效果.     

Non-linear modelling and control of semi-active suspensions with variable damping

Electro-hydraulic dampers can provide variable damping force that is modulated by varying the command current; furthermore, they offer advantages such as lower power, rapid response, lower cost, and simple hardware. However, accurate characterisation of non-linear f–v properties in pre-yield and force saturation in post-yield is still required. Meanwhile, traditional linear or quarter vehicle models contain various non-linearities. The development of a multi-body dynamics model is very complex, and therefore, SIMPACK was used with suitable improvements for model development and numerical simulations. A semi-active suspension was built based on a belief–desire–intention (BDI)-agent model framework. Vehicle handling dynamics were analysed, and a co-simulation analysis was conducted in SIMPACK and MATLAB to evaluate the BDI-agent controller. The design effectively improved ride comfort, handling stability, and driving safety. A rapid control prototype was built based on dSPACE to conduct a real vehicle test. The test and simulation results were consistent, which verified the simulation.     

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.     

基于闭环力反馈原理的非线性液压主动阻尼悬架模型的研究及优化设计

本文在理论上建立了一套基于主动力反馈原理的新型主动阻尼悬架的设计和优化方法。首先提出了该主动阻尼悬架的实现模型，该模型是在传统的液力减振器的基础上，应用半主动控制的思想，结合力反馈的原理建立起来的内部液压反馈阻尼网络模型。理论优化分析和计算机仿真表明，通过该液阻网络模型，即可以实现电控的主动阻尼悬架的功能，它可以根据汽车行驶路况的好坏，自适应地调节悬架阻尼大小以实现主动阻尼悬架的最优控制。     

基于LQR控制的现代客车自适应空气悬架

长期在不良工况的道路上驾驶会降低驾驶员的乘坐舒适性。随着人们对乘坐舒适性需求不断提升,空气弹簧的优势尤为明显。文章提出了一种基于LQR控制策略的自适应空气悬架系统的创新设计方案,提出的LQR控制器采用粒子群算法进行优化。以客车空气悬架为研究对象,采用MATLAB软件对空气悬架系统的被动和自适应动力学模型进行了设计和仿真。仿真结果表明,自适应空气悬架系统在保证车辆稳定性的同时,降低了车辆在随机道路上的最大位移幅值,从而提高了车辆的平顺性。     

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.     

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。     

基于串联型模糊神经网络的汽车半主动悬架的研究

本文建立了五自由度汽车半主动悬架系统模型，提出一种用于汽车悬 半主动振动控制系统的模糊神经网络方法，对半主动悬架 计算机仿真和结果分析，并通过与被动悬架相比较，证明半主动悬架系统在减少振动，提高汽车平一方面要优于被动悬架。     

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.     

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.     

基于1/2车辆模型的主动悬挂滤波输出反馈控制研究

基于1 2车辆模型,在分析被动悬挂弹簧和阻尼系数对车辆舒适性影响的基础上,提出并深入研究滤波输出反馈控制策略。研究表明,在对悬挂弹簧和阻尼系数进行主动滤波的基础上,采用输出反馈控制,能大幅度衰减车辆在低于和高于车轮频率范围内的车体起伏和俯仰运动,提高车辆的乘坐舒适性。仿真结果演示了主动悬挂的性能并验证了结论。     

Control Algorithms for Active Cab Suspensions on Agricultural Tractors

This paper describes active agricultural tractor cab suspensions based on optimal control theory. Control algorithms based on time invariant state feedback and on adaptive control are developed and studied. The influence of different observers and measurement noise levels on the vibration damping capacity are studied as well as the power consumption for the suspensions.

The principle for the adaptive algorithm is based on the parameters in the penalty matrices being varied so that the resulting controller always strives to make optimum use of available travel space. The feedback and observer gains are also changed depending on the characteristics of the vehicle's frame movements.

The results show that it is possible to design an effective active suspension, but that the choice of feedback gains must be dependent on the surface characteristics to reach satisfactory vibration damping performance.     

New insights from fractional order skyhook damping control for railway vehicles

Active suspensions for railway vehicles have been a topic of research for a number of decades and while their applications in service operation are limited, it seems clear that they will in due course see widespread adoption. Railway suspension design is a problem of compromise on the non-trivial trade-off of ride quality versus track following (guidance), and the skyhook damping control approach has been paramount in illustrating the potential benefits. Since skyhook damping control, various advanced control studies appeared contributing to redefine the boundaries of the aforementioned trade-off. Yet there is no study on the impact of fractional order (FO) methods in the context of skyhook railway active suspensions and in particular related to skyhook damping control. This is the area to which this paper strongly contributes. We present findings from a current project on FO controllers for railway vehicles active suspensions, in particular work on the effect of FO methods in basic skyhook damping control schemes, i.e. pure and intuitively based skyhook. First, we present a brief review of conventional skyhook damping control and then proceed to a rigorous investigation of the impact of FO on the ride quality/track following trade-off. The relevant benefits from FO methods are appraised and new insights highlighted.     

Roll- and pitch-plane coupled hydro-pneumatic suspension

Passive fluidically coupled suspensions have been considered to offer a promising alternative solution to the challenging design of a vehicle suspension system. A theoretical foundation, however, has not been established for fluidically coupled suspension to facilitate its broad applications to various vehicles. The first part of this study investigates the fundamental issues related to feasibility and properties of the passive, full-vehicle interconnected, hydro-pneumatic suspension configurations using both analytical and simulation techniques. Layouts of various interconnected suspension configurations are illustrated based on two novel hydro-pneumatic suspension strut designs, both of which provide a compact design with a considerably large effective working area. A simplified measure, vehicle property index, is proposed to permit a preliminary evaluation of different interconnected suspension configurations using qualitative scaling of the bounce-, roll-, pitch- and warp-mode stiffness properties. Analytical formulations for the properties of unconnected and three selected X-coupled suspension configurations are derived, and simulation results are obtained to illustrate their relative stiffness and damping properties in the bounce, roll, pitch and warp modes. The superior design flexibility feature of the interconnected hydro-pneumatic suspension is also discussed through sensitivity analysis of a design parameter, namely the annular piston area of the strut. The results demonstrate that a full-vehicle interconnected hydro-pneumatic suspension could provide enhanced roll- and pitch-mode stiffness and damping, while retaining the soft bounce- and warp-mode properties. Such an interconnected suspension thus offers considerable potential in realising enhanced decoupling among the different suspension modes.     

Optimal Linear Active Suspensions with Multivariable Integral Control

In this paper, an optimal suspension system is derived for a quarter-car model using multivariable integral control. The suspension system features two parts. The first part is an integral control acting on suspension deflection to ensure zero steady-sate offset due to body and maneuvering forces as well as road inputs. The second is a proportional control operating on the vehicle system states for vibration control and performance improvement. The optimal ride performance of the active suspensions based on linear full-state feedback control laws with and without integral control together with the performance of passive suspensions are compared.     

Robustness analysis of bogie suspension components Pareto optimised values

Bogie suspension system of high speed trains can significantly affect vehicle performance. Multiobjective optimisation problems are often formulated and solved to find the Pareto optimised values of the suspension components and improve cost efficiency in railway operations from different perspectives. Uncertainties in the design parameters of suspension system can negatively influence the dynamics behaviour of railway vehicles. In this regard, robustness analysis of a bogie dynamics response with respect to uncertainties in the suspension design parameters is considered. A one-car railway vehicle model with 50 degrees of freedom and wear/comfort Pareto optimised values of bogie suspension components is chosen for the analysis. Longitudinal and lateral primary stiffnesses, longitudinal and vertical secondary stiffnesses, as well as yaw damping are considered as five design parameters. The effects of parameter uncertainties on wear, ride comfort, track shift force, stability, and risk of derailment are studied by varying the design parameters around their respective Pareto optimised values according to a lognormal distribution with different coefficient of variations (COVs). The robustness analysis is carried out based on the maximum entropy concept. The multiplicative dimensional reduction method is utilised to simplify the calculation of fractional moments and improve the computational efficiency. The results showed that the dynamics response of the vehicle with wear/comfort Pareto optimised values of bogie suspension is robust against uncertainties in the design parameters and the probability of failure is small for parameter uncertainties with COV up to 0.1.