Robust active suspension design subject to vehicle inertial parameter variations

This paper presents an approach in designing a robust controller for vehicle suspensions considering changes in vehicle inertial properties. A four-degree-of-freedom half-car model with active suspension is studied in this paper, and three main performance requirements are considered. 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 (GH2) 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 GH2 norm as well. By solving the finite number of linear matrix inequalities (LMIs) with the minimization optimization procedure, the controller gains, which are dependent on the time-varying inertial parameters, can be obtained. Numerical simulations on both frequency and bump responses show that the designed parameter-dependent controller can achieve better active suspension performance compared with the passive suspension in spite of the variations of inertial parameters.     

Design of a two‐level controller for an active suspension system

The paper focuses on a control design for a vehicle suspension system in which a balance between different performance demands is achieved. The starting point of the control design is a full–car model which contains nonlinear components, i.e. the dynamics of the dampers and springs and nonlinear actuator dynamics. In order to handle the high complexity of the problem this paper proposes the design of a two‐level controller of an active suspension system. The required control force is computed by applying a high‐level controller, which is designed using a linear parameter varying (LPV) method. For the control design the model is augmented with weighting functions specified by the performance demands and the uncertainty assumptions. The actuator generating the necessary control force is modelled as a nonlinear system for which a low‐level force‐tracking controller is designed. To obtain the low‐level controller a backstepping method is proposed. As an alternative solution a feedback linearization method is also presented. The operation of the controller is illustrated through simulation examples. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Design of a grey-prediction self-organizing fuzzy controller for active suspension systems

Self-organizing fuzzy controllers (SOFCs) have excellent learning capabilities. They have been proposed for the manipulation of active suspension systems. However, it is difficult to select the parameters of an SOFC appropriately, and an SOFC may extensively modify its fuzzy rules during the control process when the parameters selected for it are inappropriate. To eliminate this problem, this study developed a grey-prediction self-organizing fuzzy controller (GPSOFC) for active suspension systems. The GPSOFC introduces a grey-prediction algorithm into an SOFC, in order to pre-correct its fuzzy rules for the control of active suspension systems. This design solves the problem of SOFCs with inappropriately chosen parameters. To evaluate the feasibility of the proposed method, this study applied the GPSOFC to the manipulation of an active hydraulic-servo suspension system, in order to determine its control performance. Experimental results demonstrated that the GPSOFC achieved better control performance than either the SOFC or the passive method of active suspension control.     

Robust passivity-based control design for active nonlinear suspension system

In this article, we propose a novel interconnection and damping assignment passivity-based control (IDA-PBC) design for a quarter car nonlinear active suspension system. As an energy shaping method, IDA-PBC is suitable for applying the main concept of skyhook (SH) control. In addition to the damping term, we utilize the characteristics of the energy shaping method to change the sprung and unsprung masses, thereby strengthening the vibration suppression effect. An IDA-PBC-based controller design for an active suspension system, which includes a nonlinear spring, a nonlinear damper, and mass uncertainty, is proposed. Different from most IDA-PBC applications, which tend to control the position or the velocity, our methods focus on transforming a nonlinear suspension system into a desired linear system with ideal aseismatic properties. Unlike a conventional controller using the SH control strategy, we design a virtual vehicle body and an unsprung mass in addition to the damper coefficients. By deriving the port-Hamiltonian form of the suspension system from its dynamics and rewriting it based on the relative coordinates, we obtain a feedback law that only uses the relative displacement and velocity of the suspension system. We derive the conditions for ensuring the global asymptotical stability of the suspension system and propose the guidelines for parameter selection that can guarantee robust stability against parameter uncertainties.     

A new model-free adaptive sliding controller for active suspension system

Active suspension systems are designed to provide better ride comfort and handling capability in the automotive industry. Since the active suspension system has nonlinear and time-varying characteristics, it is difficult to establish an accurate dynamic model for designing a model-based controller. Here, a functional approximation (FA) based adaptive sliding controller with fuzzy compensation is proposed for an active suspension system. The FA technique is employed to represent the unknown functions, which releases the model-based requirement of the sliding mode control. In addition, a fuzzy control scheme with online learning ability is employed to compensate for the modeling error of the FA with finite number of terms for reducing the implementation difficulty. To guarantee the control system stability, the update laws of the coefficients in the approximation function and the fuzzy tuning parameters are derived from the Lyapunov theorem. The proposed controller is employed on a quarter-car active suspension system. The simulation results and experimental results show that the proposed controller can suppress the oscillation amplitude of the sprung mass effectively. To evaluate the performance improvement of inducing a fuzzy compensator in this FA adaptive controller, the dynamic responses of the proposed hybrid controller are compared with those of FA-based adaptive sliding controller only.     

非线性主动悬架系统自适应最优控制

针对非线性主动悬架系统多性能指标综合优化问题,提出一类自适应最优控制方法.首先,通过引入一阶低通滤波操作,利用系统输入输出构建结构简单且调节参数少的一类未知非线性动态估计器,在线估计系统未知非线性动态;其次,构建包含乘驾舒适度、悬架行程空间及输入能耗的性能指标函数,采用单层神经网络对最优性能指标函数进行在线逼近,并得到新的哈密尔顿函数;为实现在线求解,构建一类新的基于参数估计误差信息的自适应律,在线更新神经网络权值并计算最优控制律;最后,理论分析闭环系统稳定性和收敛性,并通过专业软件Carsim与Matlab/Simulink搭建的联合仿真平台给出的对比仿真结果,验证所提出方法可有效解决主动悬架系统多目标性能优化控制问题,提升主动悬架系统综合性能.     

汽车主动悬架系统H∞控制器的降阶

基于整车模型设计的主动悬架控制系统,控制器阶数往往较高.在保证主动悬架闭环系统性能的情况下如何尽可能地降低控制器的阶数,是有待解决的问题.本文首先建立汽车7自由度整车悬架模型.针对人体敏感的振动频率范围,设计汽车主动悬架H_∞控制器.在此基础上采用Hankel范数最优降阶法对所设计的高阶控制器进行降阶研究,与模态截取法、均衡截取法进行比较,结果显示Hankel范数最优降阶法能获得更好的降阶效果.对采用降阶和全阶控制器的主动悬架系统进行仿真的结果表明,Hankel范数最优降阶法在较大程度地降低控制器阶数的同时,闭环系统频域和时域特性没有明显降低且汽车乘坐舒适性良好.     

Parameter governors for discrete-time nonlinear systems with pointwise-in-time state and control constraints

Parameter governors are add-on control schemes that adjust parameters (such as gains or offsets) in the nominal control laws to avoid violation of pointwise-in-time state and control constraints and to improve the overall system transient performance via the receding horizon minimization of a cost functional. As compared to more general model predictive controllers, parameter governors tend to be more conservative but the computational effort needed to implement them on-line can be relatively modest because the few parameters to be optimized remain constant over the prediction horizon. In this paper, we discuss the properties of several classes of parameter governors which have a common property in that the governed parameters do not shift the steady-state equilibrium of the states on which the incremental cost function explicitly depends on. This property facilitates the application of meaningful cost functionals. An example, together with simulation results, is reported to provide additional insights into the operation of the proposed parameter governor schemes.     

车辆主动悬架优化设计与仿真分析

基于混合粒子群优化（Hybrid Particle Swarm Optimization,HPSO）算法设计了一种以降低车身加速度（BA）,悬架动行程（SWS）和轮胎动位移（DTD）为目标的车辆主动悬架线性最优控制器。建立了2自由度1/4车辆主动悬架动力学模型,运用混合粒子群优化算法对LQG控制器的权值矩阵进行优化求解,在Matlab/Simulink环境下,对不同工况下的车辆悬架进行了仿真分析。仿真结果表明,经过混合粒子群算法优化后的主动悬架在行驶平顺性和操纵稳定性上有所改善,并且优化后主动悬架性能指标BA,SWS和DTD的均方根值最大分别减少了22.56%,44.27%和19.75%。     

Intelligent feedback linearization control of nonlinear electrohydraulic suspension systems using particle swarm optimization

The core factors governing the performance of active vehicle suspension systems (AVSS) are the inherent trade-offs involving suspension travel, ride comfort, road holding and power consumption. In addition to this, robustness to parameter variations is an essential issue that affects the effectiveness of highly nonlinear electrohydraulic AVSS. Therefore, this paper proposes a nonlinear control approach using dynamic neural network (DNN)-based input–output feedback linearization (FBL) for a quarter-car AVSS. The gains of the proposed controllers and the weights of the DNNs are selected using particle swarm optimization (PSO) algorithm while addressing simultaneously the AVSS trade-offs. Robustness and effectiveness of the proposed controller were demonstrated through simulations.     

基于模糊控制策略的车辆主动悬架研究

建立了车辆整车7自由度模型的主动悬架控制的系统状态方程模型,设计了两种模糊控制策略,方法一针对整车模型,采用一种控制方法,方法二针对整车模型的运动方式,设计不同的模糊控制器,垂直振动模糊控制器,俯仰振动模糊控制器,侧倾振动模糊控制器和逻辑控制器,仿真结果表明,所设计的模糊控制器对提高车辆的舒适性与操纵稳定性有较好的效果.     

非线性车辆悬架系统的滞后分岔及多稳态控制

考虑一类单自由度1/4非线性车辆悬架系统,根据Floquet理论得到周期运动的Floquet乘子用于判定其稳定性;并得到Lyapunov指数用于刻画混沌运动的性质.揭示了系统中一种新的滞后分岔：滞后环由一条稳定的周期轨道、一条不稳定周期轨道和一条周期轨道的倍化序列构成.其中周期轨道的倍化序列在滞后环的边界已经形成混沌轨道;因此随参数改变在该滞后环边界将产生一条稳定周期轨道与一条混沌轨道之间的跳跃现象.并且,若周期倍化序列形成的混沌轨道在滞后环边界处与不稳定周期轨道接触,混沌轨道将产生边界激变而突然消失,并跳跃至另一条稳定的周期轨道.根据线性增益控制法,实现了滞后环内部的多稳态控制,包括从大振幅周期3轨道控制到小振幅周期1轨道,以及周期1轨道控制到混沌轨道.本文研究结果可为车辆悬架的动力学设计提供理论参考.     

地铁车辆车顶吊挂元件动态试验工装设计

为研究地铁车顶吊挂元件所用连接件的连接参数和疲劳特性,设计一套地铁车辆车顶吊挂元件动态试验工装。工装固定在振动试验台上,模拟地铁车辆车顶局部吊挂梁的安装结构,测试车顶吊挂梁连接件在模拟振动环境下的连接参数,为地铁车辆常用紧固件连接参数的选定提供依据。为验证工装的力学特性是否满足试验要求,利用有限元软件校核工装强度,并在其频域内进行随机振动疲劳分析,计算结果表明工装的静强度和疲劳寿命均满足试验要求。     

兼顾平顺性与车高调节的重型车空气悬架控制

空气悬架由于质量轻、刚度以及高度可调等优点在重型车中得到了广泛的应用.空气悬架可以实现重型车的两项重要功能:平顺性保证以及车身高度调节,但是空气悬架的平顺性以及车身高度调节均通过空气弹簧气压腔的气压改变来实现,因此二者是彼此制约和冲突的.然而,目前对空气悬架车高调节的研究追求控制的精确性与稳定性而忽略了平顺性,而对平顺性的研究又几乎不考虑车高变化造成的影响.基于上述动机,本文提出了兼顾平顺性的空气悬架重型车车高调节鲁棒控制方法,实现了平顺性保障下的车高调节曲线精确跟踪控制,提升了重型车空气悬架系统的整体性能.实车参数仿真验证了所提出方法在平顺性与车高调节两项指标中的优越性.     

车辆悬架用电磁执行器的建模与试验研究

应用电磁感应的基本原理,设计了一种新型的车辆主动悬架用电磁直线执行器,该执行器具有响应快,出力大和动行程大的特点.通过两种不同的建模手段,即有限元建模和集总元件动力学建模的电磁力仿真对比分析,两者基本吻合,表明了执行器模型的准确性.利用所建立的有限元模型,研究了执行器结构参数如气隙厚度和次级铜层厚度对电磁力的影响规律,并选取合理的参数进行执行器的样件试制.通过对加工后的样机模型进行电磁力响应的试验测试,并分别与有限元模型和集总元件动力学数学模型进行相应的比较,试验数据与仿真结果基本一致,进一步验证了模型的准确性.     

Active vibration control for nonlinear vehicle suspension with actuator delay via I/O feedback linearization

The problem of nonlinear vibration control for active vehicle suspension systems with actuator delay is considered. Through feedback linearization, the open-loop nonlinearity is eliminated by the feedback nonlinear term. Based on the finite spectrum assignment, the quarter-car suspension system with actuator delay is converted into an equivalent delay-free one. The nonlinear control includes a linear feedback term, a feedforward compensator, and a control memory term, which can be derived from a Riccati equation and a Sylvester equation, so that the effects produced by the road disturbances and the actuator delay are compensated, respectively. A predictor is designed to implement the predictive state in the designed control. Moreover, a reduced-order observer is constructed to solve its physical unrealisability problem. The stability proofs for the zero dynamics and the closed-loop system are provided. Numerical simulations illustrate the effectiveness and the simplicity of the designed control.     

Robust H-infinity control for constrained uncertain systems and its application to active suspension

This paper presents an LMI based robust H-infinity control scheme for constrained systems with normbounded uncertainties.The uncertainties are incorporated in the evaluation of the H-infinity norm and the time-domain constraints.The robust closed-loop properties inclusive of stability,H-infinity performance and the satisfaction of the timedomain constraints are discussed.Analysis and simulation results for a 2 DOF quarter-car model show possible improvements on ride comfort,while robustly respecting safety related constraints such as good road holding,limited suspension strokes and actuator saturation.     

MotionView及HyperStudy在全地形车前悬架设计中的应用

为解决全地形车大行程前悬架的悬架跳动与前束角变化的协调问题,研究一款全地形车前悬架的运动学模型.在MotionView中建立该全地形车前悬架的运动学模型,借助HyperStudy对悬架跳动与前束角变化关系曲线进行优化,获得与理想曲线较接近的结果.     

Adaptive backstepping‐based control design for uncertain nonlinear active suspension system with input delay

This paper addresses the control problem of adaptive backstepping control for a class of nonlinear active suspension systems considering the model uncertainties and actuator input delays and presents a novel adaptive backstepping‐based controller design method. Based on the established nonlinear active suspension model, a projector operator–based adaptive control law is first developed to estimate the uncertain sprung‐mass online, and then the desirable controller design and stability analysis are conducted by combining backstepping technique and Lyapunov stability theory, which can not only deal with the actuator input delay but also achieve better dynamics performances and safety constraints requirements of the closed‐loop control system. Furthermore, the relationship between the input delay and the state variables of this vehicle suspension system is derived to present a simple and effective method of calculating the critical input delay. Finally, a numerical simulation investigation is provided to illustrate the effectiveness of the proposed controller.     

Truncation nonlinear filters for state estimation with nonlinear inequality constraints

The paper focuses on the state estimation problem of nonlinear non-Gaussian systems with state subject to a nonlinear inequality constraint. Taking into account the available additional information about the state given by the constraint increases the estimate quality compared to classical state estimation methods which cannot utilize the information. Considering the constraint in the form of an inequality involving a nonlinear function of the state makes the state estimation problem difficult and hence treated only marginally. In this paper, a generic local filter for the inequality constrained estimation problem is proposed. It covers the extended Kalman filter, unscented Kalman filter, and divided difference filter as special cases and enforces the constraint by truncating the conditional density of the state. The truncation is computationally cheap, yet it provides high estimate quality of the constrained estimate. The same idea is then utilized in a truncation Gaussian mixture filter which is also proposed in the paper to increase the estimate quality further by providing a global constrained estimate. Superior estimate quality and computational efficiency of the proposed filters are illustrated in two numerical examples.