Stochastic minimax semi-active control for MDOF nonlinear uncertain systems under combined harmonic and wide-band noise excitations using MR dampers

A stochastic minimax semi-active control strategy for multi-degrees-of-freedom (MDOF) strongly nonlinear systems under combined harmonic and wide-band noise excitations is proposed. First, a stochastic averaging procedure is introduced for controlled uncertain strongly nonlinear systems using generalized harmonic functions and the control forces produced by Magneto-rheological (MR) dampers are split into the passive part and the active part. Then, a worst-case optimal control strategy is derived by solving a stochastic differential game problem. The worst-case disturbances and the optimal semi-active controls are obtained by solving the Hamilton–Jacobi–Isaacs (HJI) equations with the constraints of disturbance bounds and MR damper dynamics. Finally, the responses of optimally controlled MDOF nonlinear systems are predicted by solving the Fokker–Planck–Kolmogorov (FPK) equation associated with the fully averaged Itô equations. Two examples are worked out in detail to illustrate the proposed control strategy. The effectiveness of the proposed control strategy is verified by using the results from Monte Carlo simulation.     

Time delay in a semi-active damper: modelling the bypass valve

Ride comfort and handling of off-road vehicles can be significantly improved by replacing the normal passive dampers in the vehicle suspension system with controllable, two-state, semi-active dampers. The hydraulic valve, which enables the semi-active damper characteristics to be controlled, is a critical component of a semi-active damper and has a marked influence on suspension performance. Models of the dynamics of a hydraulic bypass valve used on semi-active suspension systems for heavy vehicles were investigated. It is envisaged that similar models will eventually be incorporated into a full vehicle, three-dimensional simulation study. Valve response time (or time delay) is used as a measure of model accuracy because it is an important parameter in the performance of a semi-active damper. Models were created with AMESim, a commercial fluid power simulation environment, and MATLAB. AMESim was found to be capable of dealing with detailed and complex fluid power models. Attempts to solve models of similar complexity in the MATLAB environment were unsuccessful due to numerical stiffness. Experimental work was conducted to obtain dynamic performance data with which to validate model integrity. Several external factors influenced the valve behaviour during experiments. Test bench dynamics significantly influences results and obscures the absolute accuracy of the models and the experimental data. The investigation demonstrated an approach to creating fluid power models for this application that can be used in simulation, but also indicated that substantial effort is required in the process. The accuracy of the current model is not sufficient for design purposes.     

An optimization method designed to improve 3-D vehicle comfort and road holding capability through the use of active and semi-active suspensions

The primary purpose of this paper is to analyze the effects of vibrations on the comfort and road holding capability of road vehicles as observed in the variation of different parameters such as suspension coefficients, road disturbances, and the seat position. This study required the development of a mathematical model to simulate the dynamic behavior of a 3-D vehicle. With this model, various types of non-linear suspensions such as active and semi-active suspensions may be investigated. The results obtained from the simulation of the 3-D vehicle demonstrate that the use of active and semi-active suspension models on road vehicles prove to be beneficial for comfort without unduly compromising road holding capability.     

基于分数阶磁流变液阻尼器模型的车辆悬架组合控制

磁流变液阻尼器的分数阶Bingham模型结构形式简单, 而且可以更好地描述系统的滞回特性. 建立了含有分数阶Bingham模型的单自由度1/4车辆悬架系统模型, 利用磁流变液阻尼器对在路面简谐激励下的非线性车辆悬架系统进行振动控制. 研究了含有分数阶Bingham模型的悬架系统在天棚阻尼半主动控制下的主共振响应, 利用平均法得到了系统的近似解析解. 求解了系统定常解的幅频响应方程, 并根据李雅普诺夫稳定性理论得到了悬架系统的稳定性条件. 通过绘制数值解和解析解的幅频响应曲线对比图, 验证了近似解析解的正确性. 利用簧载质量垂直方向的加速度均方根值分析了半主动控制对车辆乘坐舒适性的影响, 发现天棚阻尼半主动控制策略在低频激励区域反而会降低车辆的乘坐舒适性. 因此提出了一种被动控制与半主动控制相结合的组合控制策略, 并分析了半主动控制参数对振动控制效果的影响. 分析结果表明, 该组合控制策略不但能够提高车辆的乘坐舒适性, 而且能有效抑制悬架系统的主共振振动幅值.      

Semi-active hydropneumatic spring and damper system

This paper is concerned with the development of a semi-active hydropneumatic spring and damper system, comprising of a two state hydropneumatic spring and a two state hydraulic damper. The system was specifically developed to improve the ride comfort and handling of large off-road vehicles. The suspension requirements for good ride comfort and handling for heavy off-road vehicles are discussed with special reference to the advantages of semi-active hydropneumatic springs and semi-active dampers. The layout and functioning of an experimental spring and damper unit used for laboratory tests are discussed. Spring and damper characteristics, as well as valve response times for both the semi-active spring and semi-active damper were determined. A single degree of freedom test rig with a sprung mass of 3 tons was used to perform first order ride comfort tests. Tests include step response and random input response. The test rig was also used to evaluate semi-active control strategies for both spring and damper as well as a control strategy for implementing ride height adjustment without using an external hydraulic pump.     

An alternative control strategy for semi-active dampers on off road vehicles

A control strategy is developed that takes into account the pitch and roll degrees of freedom on an off road wheeled vehicle in order to control discrete adjustable semi-active dampers more effectively. From the literature it was concluded that some existing semi-active control strategies were derived by employing models with either one or two degrees of freedom. If these strategies are applied to control semi-active dampers on a vehicle, each wheel station is controlled separately. The other degrees of freedom of the sprung mass, such as roll and pitch, are therefore not explicitly taken into account. The alternative control strategy determines that combination of damper states that will provide the highest acceleration opposing the movement of the sprung mass (deceleration), or the lowest acceleration in the direction of movement of the sprung mass. Simulation and experimental results indicated that the strategy that minimises the highest absolute value of the roll or the pitch acceleration performed significantly better than an existing semi-active control strategy (based on the absolute and relative damper velocities), especially when ride comfort under off-road conditions was taken into account. Four conventional dampers were modified, adding a by-pass assembly and controllable valve. The effect of using semi-active dampers on an off-road vehicle was evaluated during an extensive experimental programme, using ride comfort as basis. Results showed that the control strategy, as developed in this study, provided better responses in comparison to the passive configuration and an existing control strategy.     

Stochastic optimal active control of a half-car nonlinear suspension under random road excitation

The random response analysis and the stochastic optimal active control of a half-car model with nonlinear suspension stiffness and damping traversing a rough road are studied in this paper. The road roughness height is modeled as the output of a first-order linear filter to Gaussian white noise. Considering the hysteretic nonlinear stiffness and the square damping of the vehicle model, the response statistics of the nonlinear suspension with active control are obtained by using the equivalent linearization method. The performance indexes of the active suspension are evaluated and compared with those of the corresponding passive suspension. It is found that the nonlinear active suspension gives a better vehicle performances like ride comfort, suspension stroke and overall performance. Finally, the theoretical results are verified through Monte Carlo simulation.     

Semi-active hydro-gas suspension system for a tracked vehicle

A semi-active hydro-gas suspension is proposed for a tracked vehicle to improve ride comfort performance, without compromising the road holding and load carrying capabilities of the passive suspension. This is achieved through an active damper used in parallel with a gas spring. The suspension damper parameters are varied by a control mechanism based on sky-hook damping theory, which alters the flow characteristics. A damper prototype has been developed, tested for its flow characteristics, after which it has been integrated into an existing hydro-gas suspension system. An analytical model has been proposed from first principles rather than developing a phenomenological model based on experimental characteristics. This model is validated with experiments carried out on a suspension test rig. In order to compare the performance with the original passive system, an in-plane vehicle model is developed and the simulations clearly show that the semi-active system performance is superior to the passive system.     

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在仿真研究1/4车体二自由度液压半主动悬架的基础上,设计了一种 用于1/2车体的液压半主动悬架的参数自整定模糊PID控制器,并利用模糊控制规则对 PID参数进行在线修改. 以正弦信号路面、脉冲信号路面和C级路面3种典型路面作为输入 信号,应用MATLAB/Simulink控制系统仿真软件对该半主动悬架模型进行的计算机仿真表明, 具有模糊PID控制器的半主动悬架在提高车辆乘坐的舒适性方面要明显优于一般的模糊控制 悬架,具有更好的自适应能力.     

粘滞阻尼器减震结构非线性随机振动的时域显式降维迭代随机模拟法

粘滞阻尼器在大型复杂结构减震设计中应用广泛。由于粘滞阻尼器的非线性阻尼力特性,粘滞阻尼器减震结构非平稳随机地震反应分析是一个典型的局部非线性随机振动问题。利用减震结构动力响应时域显式表达式的降维列式优势,仅针对与粘滞阻尼器相关的局部自由度进行非线性迭代计算,提出了局部非线性随机振动问题的时域显式降维迭代随机模拟法,为设置粘滞阻尼器的大型复杂减震结构非线性地震反应分析提供一种高效的随机振动方法。以安装了四个纵桥向粘滞阻尼器的某主跨1200m悬索桥为工程实例,开展E2水准地震激励下的非线性随机振动分析。计算结果显示,设置阻尼器后,主梁的纵桥向位移得到明显控制,降幅达到80%,大桥的关键截面内力也有5%左右的降幅。     

Development and experimental evaluation of translational semi-active dampers on a high mobility off-road vehicle

This paper describes the further development and experimental evaluation of two-state semi-active translational dampers on a 6×6 high mobility off-road vehicle. As only ride comfort was enhanced during previous work, the low-speed damping characteristics on the semi-active damper was increased in order to improve vehicle handling. The existing passive dampers, as normally fitted to the test vehicle, were modified to the semi-active configuration by adding a bypass assembly and a controllable valve. Experimental work included driving over various repeatable surfaces at different speeds and executing severe lane change manoeuvres. Results indicated that both handling and ride comfort were improved when selecting the semi-active configuration.     

Effectiveness evaluation of hydro-pneumatic and semi-active cab suspension for the improvement of ride comfort of agricultural tractors

Advances have been made to agricultural tractors to improve their ride comfort. However, the ride comfort of tractors is relatively low compared to that of passenger vehicles. Many researchers have developed various types of suspension for tractors. While most studies have focused on the geometry of the suspension, few studies have been carried out on the development of a control algorithm for tractor suspension.In this paper, to improve the ride comfort of an agricultural tractor, a hydro-pneumatic suspension model with a semi-active suspension control is developed with computer simulation, and the effectiveness of the suspension is evaluated before the vehicle is equipped with the suspension and placed into production.An optimal control algorithm for the semi-active suspension of the tractor is developed using a linear quadratic Gaussian. In the simulation, a hydro-pneumatic suspension system model is developed using SimulationX and is applied to a full vehicle model using MATLAB/Simulink. The suspension is assessed by experiments and simulations. The ride comfort using the ride comfort index according to ISO 2631 is evaluated by comparing a vehicle with a passive cab suspension to that with a hydro-pneumatic suspension applied with the semi-active control.     

质量阻尼器的发展

广泛评述了调谐质量阻尼器(TMD)、多重调谐质量阻尼器(MTMD)、主动质量阻尼器(AMD)、半主动 TMD(SATMD)、主动调谐/主被动调谐/混合质量阻尼器(ATMD/APTMD/HMD)的研究现状.TMD, MTMD, AMD, SATMD, ATMD/APTMD/HMD能够有效地减小结构的风振与地震反应.指出强震下结构设置TMD, MTMD, AMD, SATMD, ATMD/APTMD/HMD的主要目的是限制结构屈服的进一步发展.因此,基于非线性结构模型的TMD, MTMD, AMD, SATMD, ATMD/APTMD/HMD研究具有重要意义.指出了TMD, MTMD, AMD, SATMD, ATMD/APTMD/HMD 有待于进一步研究的若干问题.提出了结构主动多重调谐质量阻尼器(AMTMD)和多重主被动调谐质量阻尼器(MAPTMD)的新控制策略.介绍了AMTMD和MAPTMD的研究进展并指出了进一步研究的发展方向.      

分布式驱动电动汽车主动悬架T–S模糊控制研究

分布式驱动电动汽车,由于簧下质量增大,导致车轮振动加剧,进而影响车辆平顺性及行驶安全性。为有效抑制分布式驱动电动汽车垂向振动恶化,设计了一种主动悬架T–S模糊控制器,构建了分布式驱动电动汽车1/4悬架动力学模型,基于Matlab/Simulink在B级随机路面及变路面工况下进行动力学仿真,考虑了控制器在车辆参数不确定时的自适应性,探究了T–S模糊控制器在车辆变参数条件下的控制效果,并与PID控制的主动悬架及传统的被动悬架进行比较,通过硬件在环实验验证了控制效果。结果表明,所提出的分布式驱动电动汽车主动悬架T–S模糊控制策略可有效提升车辆的平顺性指标,相对于PID控制及被动悬架,T–S模糊控制也具有更好的多工况自适应能力。

     

Nonlinear Stiffness of a Magneto-Rheological Damper

The last decade has witnessed an important role of magneto-rheological dampers in the semi-active vibration control on the basis of empirical models. Those models established by fitting experimental data, however, do not offer any explicit expressions for the stiffness and the damping of magneto-rheological dampers. Hence, it is not easy for engineers to get any intuitive information about the effects of stiffness and damping of a magneto-rheological damper on the dynamic performance of a controlled system. To manifest the nonlinear properties of a magneto-rheological damper, this paper presents the hysteretic phenomena and the additional nonlinear stiffness of a typical magneto-rheological damper in terms of equivalent linear stiffness and equivalent linear damping. Then, it gives a brief discussion about the effect of nonlinear stiffness on the vibration control through the numerical simulations and an experiment for the semi-active suspension of a quarter car model with a magneto-rheological damper installed. Both numerical simulations and experimental results show that the additional nonlinear stiffness in the magneto-rheological damper is remarkable, and should be taken into consideration in the design of vibration control.     

Optimal control of the dynamic stability for robotic vehicles in rough terrain

In this paper, we mount semi-active suspensions between the wheels and platform of a robotic vehicle to absorb the vibrations caused by movement over rough terrain. The semi-active suspension consists of a spring and a magneto-rheological damper. By combining the dynamic model of the suspended robotic vehicle and the control model of the damper, we propose a new methodology to evaluate the dynamic stability of the vehicle. The model considers the configuration of semi-active suspensions and the road-holding ability of robotic vehicles. Based on the stability criterion, we use the particle swarm optimization method to search the optimum semi-active damping characteristics. The control model of the semi-active damper is checked by sinusoidal response analysis. To verify the dynamic stability criterion and the control method, we evaluate the proposed methodology by simulating a rough pavement condition and comparing the effectiveness of the method to a passive suspension. The results show that the proposed stability criterion is feasible, and the optimal control method yields a substantially improved dynamic stability when the vehicle moves through rough terrain.     

Experimental evaluation of an unsophisticated two state semi-active damper

This paper describes the experimental evaluation of a two-state damper, used as the variable force element in a semi-active suspension. The study was necessary to establish the influence of non-ideal operating conditions when existing control strategies were evaluated in a practical environment. Three existing control strategies, each derived by using a different approach, were chosen for evaluation purposes and to experimentally determine the feasibility of semi-active suspensions. The control valve used to switch between states consisted of a pressure-dependent logic element and a directional spool valve. Characterization of the valve revealed a highly non-linear behaviour when switching between states. Experimental results indicated that two state semi-active dampers, which should offer a substantial cost saving over continuous variable dampers, especially in heavy wheeled vehicle applications, provide significant ride improvement potential. Furthermore, it was established that more complex phenomena existed than those normally taken into account during the usual theoretical evaluation of semi-active dampers.     

Comparative research on semi-active control strategies for magneto-rheological suspension

This paper presents the comparison results of a study to identify an appropriate semi-active control algorithm for a MR suspension system from a variety of semi-active control algorithms for use with MR dampers. Five representative control algorithms are considered including the skyhook controller, the hybrid controller, the LQG controller, the sliding mode controller and the fuzzy logic controller. To compare the control performances of the five control algorithms, a quarter car model with a MR damper is adopted as the baseline model for our analysis. After deriving the governing motion equations of the proposed dynamic model, five controllers are developed. Then each control policy is applied to the baseline model equipped with a MR damper. The performances of each control algorithm under various road conditions are compared along with the equivalent passive model in both time and frequency domains through the numerical simulation. Subsequently, a road test is performed to validate the actual control performance. The results show that the performance of a MR suspension system is highly dependent on the choice of algorithm employed, and the sliding mode control strategy exhibits an excellent integrated performance.     

斜拉索振动的模糊半主动控制研究

考虑拉索垂度及抗弯刚度的影响,得出了索-阻尼器系统振动偏微分方程;用中心差分法将偏微分方程在空间内离散,导出了系统的面内振动常微分方程组;提出了使用MR阻尼器(Magnetorheological Damper)作为控制设备,模糊集为基础的半主动控制算法,并运用提出的算法对索-阻尼器系统进行了振动控制分析。本文方法的优势在于算法自身的鲁棒性、处理非线性问题的能力强和不需要结构的精确数学模型,算法需要的输入变量少,可以解决实际工程中斜拉索的振动响应信息难以测量的困难。模糊算法的输出直接控制MR阻尼器的输入电压。与LQR-Clipped算法不同,MR阻尼器的输入电压可以是零与最大值之间的任意值。本文以实际斜拉桥拉索为例,分析了拉索的振动控制效果,结果表明本文提出的模糊半主动控制算法,使MR阻尼器的功能得到了更好的发挥,比MR被动控制效果好,且可以减小控制力。     

斜拉索振动控制中MR阻尼器选型的研究

以全索全时段振动响应的均方根(RMS)评价MR阻尼器对斜拉索的减振效果。计算结果表明MR阻尼器型号是影响斜拉索减振效果的最主要因素。斜拉索的减振效果在选用合适的MR阻尼器时达到最佳。进而研究了MR阻尼器型号与阻尼器安装位置、施加的电压、斜拉索基频(张力、索长、质量)、激励荷载(类型、频率、幅值)等各种因素的关系,为MR阻尼器合理选型提供了优化设计的方法。型号选用主要是与斜拉索基频和MR阻尼器安装位置有关。在引起索基频变化的因素中,索质量对型号的选取影响最大;而索长对型号影响不大。对于索质量较大、张力较大、MR阻尼器安装位置较低、外界激励较大、频谱特征多变、低频为主时需要较强的MR阻尼器。进一步研究表明,半主动控制与开环控制的最优MR阻尼器型号有较好的一致性,因此半主动控制所选用的MR阻尼器型号可参照被动控制时最优MR阻尼器型号。