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.     

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.     

液压互联悬架抗侧倾控制研究（双语出版）

针对车辆减少能量消耗与提高抗侧倾能力需求,提出了一种主/被动可切换的液压互联悬架抗侧倾控制方法。基于9自由度车辆动力学模型,考虑蓄能器、液压缸、液压泵三者之间耦合的体积-流量-压力特性,建立液压互联悬架主动控制时域模型;结合"车身侧倾角-车身侧倾角速度"相平面法及车辆侧向加速度,得到车辆侧倾稳定域,并提出液压互联悬架系统侧倾稳定性控制介入与退出判据;在此基础上,采用Backstepping非线性控制算法设计主动液压互联抗侧倾控制器。最后,分析并改进侧倾稳定性评价指标,通过在MATLAB/Simulink环境下进行高速双移线、鱼钩试验等极端工况数值仿真,验证所提出的液压互联悬架主/被动切换控制系统能在减少能量消耗的情况下能否提高车辆抗侧翻的能力。研究结果表明：所提出的控制系统能有效提高车辆抗侧翻能力;当车辆侧倾状态超出设定的侧倾稳定区域介入线时,液压互联悬架系统由被动模式切换为主动抗侧倾模式,控制车辆侧倾状态回到稳定区域,以提高车辆侧倾稳定性;当判定车辆侧倾状态满足主动控制退出条件时,液压互联悬架系统回到被动模式,以减小能量消耗。     

Nonlinear H∞ control for semi-active suspension

This paper describes the development of a damping control system for semi-active suspension which is based on nonlinear H_∞ control theory instead of conventional linear control theory. A two degrees of freedom system is used as the structure for the vehicle suspension model. Since the structure is bilinear, it's not easy to design the controller. We designed the controller based on the Hamilton-Jacobi inequality by solving a linear Riccati equation. We were able to verify by simulation that nonlinear H_∞ control theory made it possible to control vehicle vibration optimally and smoothly.     

四级阻尼可调式液压互联悬架系统性能研究

提出了一种新型四级阻尼可调式液压互联悬架 （FDAHIS） 系统。FDAHIS系统在被动液压互联悬架系统的阻尼阀上并联了两个常通孔面积不同的电磁开关阀,通过反馈控制策略控制电磁阀开闭状态,调节系统液压流量,从而实现阻尼四级可调。为了研究该系统性能,建立FDAHIS系统模型和七自由度整车模型。通过系统单元台架试验对该模型进行了验证。整车仿真结果表明,与被动的液压互联悬架 （HIS） 系统相比,FDAHIS系统在车辆行驶平顺性和抗俯仰性能方面表现更佳。     

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.     

油气主动悬架非线性模型的建立、仿真与试验验证

本文通过分析油气悬架中存在的气体弹簧刚度非线性特性和摩擦力，建立了主动悬架的非线性模型。分析了悬架的非线性特性对悬架运动的影响。仿真和试验结果表明，非线性模型比线性模型更接近油气悬架的实际情况，根据非线性模型设计的车身高度控制策略比根据线性模型设计的控制策略具有更好的控制效果。     

联合线性和模糊逻辑控制的4自由度主动悬架

文中提出了联合线性和模糊逻辑控制的4自由度汽车主动悬架。该主动悬架以线性控制为主，模糊逻辑控制为辅，前者以车身加速度作为控制量，后者以车身的垂直速度与俯仰速度的线性组合和车身位移作为模糊控制规则的输入变量。最后用Simulink进行仿真，并把所得结果与被动的结果进行比较，说明该系统对提高汽车的平顺性是非常有效的。     

汽车非线性半主动悬架的模糊神经网络控制

考虑磁流变减振器阻尼力和悬架弹性元件非线性特性，建立车辆6自由度的半主动悬架非线性动力学模型。提出了一种基于模糊神经网络系统结构的模型参考自适应控制方法来研究汽车半主动悬架的非线性控制问题，并考虑半车模型前后悬架的输入时滞，对其进行了仿真研究。研究结果表明：运用模糊神经网络非线性控制方法能够使人体和车身垂直加速度、俯仰角加速度都得到很大的衰减，证实这种模糊神经网络控制方法可大大减少路面对车身的振动冲击，提高汽车行驶平顺性。     

Non-fragile multi-objective static output feedback control of vehicle active suspension with time-delay

This paper presents an approach to design a delay-dependent non-fragile H_∞/L₂–L_∞ static output feedback (SOF) controller for active suspension with input time-delay. The control problem of quarter-car active suspension with actuator time-delay is formulated to a H_∞/L₂–L_∞ control problem. By employing a delay-dependent Lyapunov function, new existence conditions of delay-dependent non-fragile SOF H_∞ controller and L₂–L_∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities (BMIs). Then, a procedure based on linear matrix inequality optimisation and a hybrid algorithm of the particle swarm optimisation and differential evolution is used to solve an optimisation problem with BMI constraints. Design and simulation results of non-fragile H_∞/L₂–L_∞ controller for active suspension show that the designed controller not only can achieve the optimal performance and stability of the closed-loop system in spite of the existence of the actuator time-delay, but also has significantly improved the non-fragility characteristics over controller perturbations.     

Kinematics of a smart variable caster mechanism for a vehicle steerable wheel

The lateral force of a tyre is a function of the sideslip and camber angles. The camber angle can provide a significant effect on the stability of a vehicle by increasing or adjusting the required lateral force to keep the vehicle on the road. To control the camber angle and hence, the lateral force of each tyre, we can use the caster angle of the wheel. We introduce a possible variable and controllable caster angle ? in order to adjust the camber angle when the sideslip angle cannot be changed. As long as the left and right wheels are steering together according to a kinematic condition, such as Ackerman, the sideslip angle of the inner wheel cannot be increased independently to alter the reduced lateral force because of weight transfer and reduction of the normal load F _z . A variable caster mechanism can adjust the caster angle of the wheels to achieve their top capacity and maximise the lateral force, when needed. Such a system would potentially increase the safety, stability, and maneuverability of the vehicles. Using the screw theory, this paper will examine the kinematics of a variable caster and present the required mathematical equation to calculate the camber angle as a function of suspension mechanism parameters and other relevant variables. Having a steered wheel about a tilted steering axis will change the position and orientation of the wheel with respect to the body of the car. This paper provides the required kinematics of such a suspension and extracts the equations in special practical situations. The analysis is for an ideal situation in which we substitute the tyre with its equivalent disc at the tyre plane.     

Semi-active control of tracked vehicle suspension incorporating magnetorheological dampers

In past years, the application of magnetorheological (MR) and electrorheological dampers in vehicle suspension has been widely studied, mainly for the purpose of vibration control. This paper presents theoretical study to identify an appropriate semi-active control method for MR-tracked vehicle suspension. Three representative control algorithms are simulated including the skyhook, hybrid and fuzzy-hybrid controllers. A seven degrees-of-freedom tracked vehicle suspension model incorporating MR dampers has been adopted for comparison between the performance of the three controllers. The model differential equations are derived based on Newton's second law of motion and the proposed control methods are developed. The performance of each control method under bump and sinusoidal road profiles for different vehicle speeds is simulated and compared with the performance of the conventional suspension system in time and frequency domains. The results show that the performance of tracked vehicle suspension with MR dampers is substantially improved. Moreover, the fuzzy-hybrid controller offers an excellent integrated performance in reducing the body accelerations as well as wheel bounce responses compared with the classical skyhook and hybrid controllers.     

Nonlinear robust control of integrated vehicle dynamics

A new methodology to design the vehicle GCC (global chassis control) nonlinear controller is developed in this paper. Firstly, to handle the nonlinear coupling between sprung and unsprung masses, the vehicle is treated as a mechanical system of two-rigid-bodies which has 6 DOF (degree of freedom), including longitudinal, lateral, yaw, vertical, roll and pitch dynamics. The system equation is built in the yaw frame based on Lagrange's method, and it has been proved that the derived system remains the important physical properties of the general mechanical system. Then the GCC design problem is formulated as the trajectory tracking problem for a cascade system, with a Lagrange's system interconnecting with a linear system. The nonlinear robust control design problem of this cascade interconnected system is divided into two H _∞ control problems with respect to the two sub-systems. The parameter uncertainties in the system are tackled by adaptive theory, while the external uncertainties and disturbances are dealt with the H _∞ control theory. And the passivity of the mechanical system is applied to construct the solution of nonlinear H _∞ control problem. Finally, the effectiveness of the proposed controller is validated by simulation results even during the emergency manoeuvre.     

基于参考模型的半主动悬架滑模控制

在分析电流变阻尼器工作原理与结构的基础上,基于参考模型设计了1/4车辆悬架系统的滑模控制器.研究了系统在随机路面激励条件下车身加速度、悬架动行程和轮胎动位移等性能指标的控制效果.运用Simu-link在不同的车速和车身质量的情况下进行了仿真分析,结果表明:控制后悬架各性能指标均得到明显改善,滑模控制器性能稳定,对系统参数的改变具有很好的鲁棒性.     

Vehicle systems: coupled and interactive dynamics analysis

This article formulates a new direction in vehicle dynamics, described as coupled and interactive vehicle system dynamics. Formalised procedures and analysis of case studies are presented.

An analytical consideration, which explains the physics of coupled system dynamics and its consequences for dynamics of a vehicle, is given for several sets of systems including: (i) driveline and suspension of a 6×6 truck, (ii) a brake mechanism and a limited slip differential of a drive axle and (iii) a 4×4 vehicle steering system and driveline system.

The article introduces a formal procedure to turn coupled system dynamics into interactive dynamics of systems. A new research direction in interactive dynamics of an active steering and a hybrid-electric power transmitting unit is presented and analysed to control power distribution between the drive axles of a 4×4 vehicle. A control strategy integrates energy efficiency and lateral dynamics by decoupling dynamics of the two systems thus forming their interactive dynamics.     

汽车主动悬架自调整模糊控制试验

以汽车操纵稳定性及行驶平顺性为控制目标,提出一种在线可调整的模糊控制算法,其模糊控制规则表可以用解析的方法进行计算。针对简化的汽车模型,为控制悬架系统的振动设计了自调整模糊控制器。与自适应控制主动悬架系统相比较,在两自由度悬架系统试验台架上进行了对比试验研究,结果表明该算法对汽车的振动控制具有明显效果,进一步说明提出的算法对汽车悬架系统的振动控制具有较好的适应性。     

Output feedback H ∞/GH 2 preview control of active vehicle suspensions: a comparison study of LQG preview

This study concerns with multi-objective H _∞/GH ₂ preview control of active vehicle suspensions. This control scheme has two main aspects: first, it allows constrained outputs of the system to vary freely as long as they remain within their given bounds, in order that the best possible performance could be delivered. Secondly, the optimisation as well as constraint fulfilment is done for the worst-case road disturbances to cover all road types. To design a system to perform satisfactorily for a wide range of road irregularities, H _∞-norm is used wherever minimisation is required, and generalised H ₂-norm is used to care for the constraints on suspension working space. Moreover, to ensure desired stability margins for the system, pole location constraints are considered in the design. The proposed approach is evaluated on a quarter-car model and compared with the state-of-the-art preview control algorithm in the literature, namely, Linear quadratic Gaussian preview. Simulation results demonstrate the effectiveness of the proposed approach.     

DSP-based self-organising fuzzy controller for active suspension systems

This study proposed a self-organising fuzzy controller (SOFC) for controlling an active suspension system to evaluate its control performance. During the control process, the SOFC continually updated the learning strategy in the form of fuzzy rules. The fuzzy rule table of this SOFC could be initially set to zero. This not only overcame the difficulty in finding appropriate membership functions and control rules for designing a fuzzy controller, but also solved the database problem where the fuzzy rules of a fuzzy controller, once determined, remained fixed and could not suitably regulate them in real time to optimise the dynamic response of the system required to gain the desired control performance. To demonstrate the applicability of the proposed SOFC for active suspension systems, a quarter-car hydraulic-servo suspension system was designed and constructed to evaluate the feasibility of active suspension control. Additionally, to conform to real-time application requirements in the vehicular industry, the SOFC was implemented with a digital signal processor to control the hydraulic-servo suspension system so that the control performance could be determined. The SOFC has shown a better control performance in suppressing the vibration amplitude of the vehicle body for enhancing the structural safety of the vehicle and increasing the life of the suspension system. It also effectively suppressed the amplitude of the vehicle body acceleration and reduced the tire deflection for improving the ride and the handling quality of a vehicle better than a passive control, as verified in experimental results.     

H 2 optimal control of disturbance-delayed systems with application to vehicle suspensions

Optimal control of systems with time delays among disturbances, such as vehicle suspensions, is a relatively simple but long-standing problem in time-delayed control. We consider the exact H ₂ optimal control of systems with time-delayed disturbances and develop a computationally efficient approach for controller synthesis. We extend the Lyapunov-based H ₂ norm computation to systems with time-delayed disturbances and then derive a concise formula to explicitly evaluate the sensitivity of the system H ₂ norm with respect to controller gains. Thence, a set of necessary conditions for H ₂ optimal control of such systems using static output feedback are obtained in the form of algebraic equations. Gradient-based methods are adapted to optimize the controller gains. The method is also extended to reduced-order and decentralized control. As an application, a passive suspension system for an eight-DOF four-wheel vehicle is designed via structured H ₂ optimization. The results are compared with those of a design based on a Pade expansion for the time delays and a design obtained by neglecting the disturbance delays.     

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。