Decomposition approach to model smart suspension struts

Model and simulation study is the starting point for engineering design and development, especially for developing vehicle control systems. This paper presents a methodology to build models for application of smart struts for vehicle suspension control development. The modeling approach is based on decomposition of the testing data. Per the strut functions, the data is dissected according to both control and physical variables. Then the data sets are characterized to represent different aspects of the strut working behaviors. Next different mathematical equations can be built and optimized to best fit the corresponding data sets, respectively. In this way, the model optimization can be facilitated in comparison to a traditional approach to find out a global optimum set of model parameters for a complicated nonlinear model from a series of testing data. Finally, two struts are introduced as examples for this modeling study: magneto-rheological (MR) dampers and compressible fluid (CF) based struts. The model validation shows that this methodology can truly capture macro-behaviors of these struts.     

Modelling and identifying the parameters of a magneto-rheological damper with a force-lag phenomenon

In this study a model based on the Bouc–Wen–Baber–Noori (BWBN) method was proposed to describe the distorted hysteretic behaviour of a self-constructed magneto-rheological (MR) damper whose mechanical performance was measured with an Instron test machine. The experimental results indicated that the MR damper exhibited a force-lag phenomenon. The parameters of the modified BWBN model were identified with the MATLAB SIMULINK Design and Optimisation toolbox. A comparison between the experimental results and modelling predictions revealed that the proposed model could well present the force-lag phenomenon.     

Experimental analysis of magnetorheological dampers when subjected to impact and shock loading

The vast majority of the investigations for controllable magnetorheological (MR) dampers have focused on their low velocity and low frequency applications. The extensive work in this area has led to a good understanding of MR fluid properties at low velocities and frequencies. Many of the issues pertaining to MR damper behavior in impact and shock applications are relatively unknown. This study provides an experimental analysis of magnetorheological dampers when they are subjected to impact and shock loading. To this end, a drop-tower is developed to apply impulse loads to the dampers. The drop-tower design uses a guided drop-mass, which is released from variable heights to achieve different impact energies. The nominal drop-mass is 55 lb and additional weight may be added to reach a maximum of 500 lb. The nominal drop-mass of 55 lb is used throughout this study. Five drop-heights are investigated: 12, 24, 48, 72 and 96 in., corresponding to impact velocities of 86, 127, 182, 224 and 260 in./s, respectively. Two MR damper configurations are tested, a damper with a single-stage, double-ended piston and a mono-tube damper with a two-stage piston. The results indicate that the two damper configurations exhibit different force–displacement characteristics during impulse loading. For the single-stage, double-ended damper, the peak force occurs close to the beginning of the impact. Conversely, the two-stage, mono-tube damper does not reach the peak force until after the nitrogen accumulator bottoms out. To verify this behavior, a theoretical model of the accumulator is derived and compared to the experimental data. Additionally, the results show that at large impact velocities, the peak force does not depend on the current supplied to the damper, as is commonly the case at low velocities. This phenomenon is hypothesized to be the result of the fluid inertia preventing the fluid from accelerating fast enough to accommodate the rapid piston displacement. Thus, the peak force is primarily attributed to fluid compression, rather than the flow resistance (“valving”) associated with the fluid passing through the MR valve.     

Optimisation of road vehicle passive suspension systems. Part 2. Qualification and case study

As an aid during the concept design phase, the two-dimensional vehicle simulation programme Vehsim2d has been developed (see part 1 of this paper for the vehicle model). The leap-frog optimisation algorithm for constrained problems (LFOPC) has been linked to the multi-body dynamics simulation code (Vehsim2d) to enable the computationally economic optimisation of certain vehicle and suspension design variables. This paper describes the simulation programme, the qualification of the programme, and gives an example of the application of the Vehsim2d/LFOPC system. In particular it is used to optimise the damper characteristics of an existing 22 ton three axle vehicle, over a typical terrain and at a representative speed. By using this system the optimised damper characteristics with respect to ride comfort for the vehicle are computed. The optimum damper characteristics give a 28.5% improvement in the ride comfort of the vehicle over the specified terrain and prescribed speed. Further optimisation runs were performed considering other terrain and different speed values. From these results final damper characteristics for the vehicle are proposed. Using the proposed characteristics, simulations were performed with the more advanced and proven DADS programme. The results show that the damper suggested by the optimisation study is indeed likely to improve the suspension of the vehicle. This study proves that the Vehsim2d/LFOPC vehicle modelling and optimisation system is indeed a valuable tool for a vehicle design team.     

Adaptive control of discrete-time chaotic systems: a fuzzy control approach

This paper discusses adaptive control of a class of discrete-time chaotic systems from a fuzzy control approach. Using the T–S model of discrete-time chaotic systems, an adaptive control algorithm is developed based on some conventional adaptive control techniques. The resulting adaptively controlled chaotic system is shown to be globally stable, and its robustness is discussed. A simulation example of the chaotic Henon map control is finally presented, to illustrate an application and the performance of the proposed control algorithm.     

设置黏滞阻尼器的纵飘斜拉桥地震响应简化分析方法

针对纵飘体系斜拉桥现有黏滞阻尼器参数设计方法的不足,提出了更为快捷有效的分析方法.首先基于钟摆原理,采用双质点模型简化模拟纵飘斜拉桥的动力响应特征;然后基于能量耗散等效原理,提出了黏滞阻尼器的等效线性模型;最后基于结构动力学原理,建立了设置黏滞阻尼器的纵飘斜拉桥地震响应简化分析方法.在此基础上,针对某主跨392 m的纵飘斜拉桥建立了全桥分析模型,在正弦波作用下,对比分析了全桥模型、双质点简化模型数值解和解析解的计算误差.结果表明:双质点模型数值解计算结果精度较高,可以代替全桥模型的有限元计算结果;解析解与双质点数值解计算结果吻合良好,验证了双质点模型简化分析方法在理论上的可靠性;在不同地震动特性和体系周期下,三者计算误差均满足工程精度要求,表明该简化分析方法具有良好的适用性,可为阻尼器参数优化提供更简便的模型.     

Optimisation of road vehicle passive suspension systems. Part 1. Optimisation algorithm and vehicle model

Numerous problems have in the past been experienced during the development of military vehicle suspension systems. In order to solve some of these problems a two-dimensional multi-body vehicle dynamics simulation model has been developed for computer implementation. This model is linked to a mathematical optimisation algorithm in order to enable the optimisation of vehicle design parameters through the minimisation of a well defined objective function. In part 1 of this paper the concept of multi-disciplinary design optimisation is discussed. This is followed by the presentation of the up to six degrees of freedom vehicle model developed for this study, and a discussion of the specific gradient-based optimisation algorithm selected for the optimisation. In particular the derivation of the set of second-order differential equations, describing the acceleration of the different solid bodies of the vehicle model, is presented. In order to perform the optimisation of the non-linear suspension component characteristics, a six piece-wise continuous and linear approximation is used which is also described in this paper. Part 2 of this study will outline the simulation programme and the qualification of the programme. It will also present a typical case study where the proposed optimisation methodology is applied to improve the damper characteristics of a specific vehicle.     

Gradient-based approximation methods applied to the optimal design of vehicle suspension systems using computational models with severe inherent noise

The principal aim of this paper is to evaluate the feasibility of using gradient-based approximation methods for the optimisation of the spring and damper characteristics of an off-road vehicle, for both ride comfort and handling. The Sequential Quadratic Programming algorithm and the relatively new Dynamic-Q method are the two successive approximation methods used for the optimisation. The determination of the objective function value is performed using computationally expensive numerical simulations that exhibit severe inherent numerical noise. The use of forward finite differences and central finite differences for the determination of the gradients of the objective function within Dynamic-Q is also investigated. This is done in investigating methods for overcoming the difficulties associated with the optimisation of noisy objective functions.A recreational off-road vehicle is modelled in ADAMS, and coupled to MATLAB for the execution of the optimisation process. The full vehicle ADAMS model includes suspension kinematics, a load-dependent tyre model, as well as non-linear springs and dampers. Up to four design variables are considered in modelling the suspension characteristics.It is found that both algorithms perform well in optimising handling. However, difficulties are encountered in obtaining improvements in the design process when ride comfort is considered. Nevertheless, meaningful design configurations are still achievable through the proposed optimisation process, at a relatively low cost in terms of the number of simulations that have to be performed.     

Gradient based iterative parameter identification for Wiener nonlinear systems

This paper focuses on the identification problem of Wiener nonlinear output error systems. The application of the key-term decomposition technique provides a special form of the Wiener model with polynomials, where all the model parameters to be estimated are separated. To solve the identification problem of Wiener nonlinear output error systems with the unmeasurable variables in the information vector, an auxiliary model-based gradient iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates. The performances of the proposed algorithm are analyzed and compared by using numerical examples.     

On the oscillations of a thin-walled structure containing a fluid, in the presence of a hydrodynamic damper : PMM vol. 43, no. 6, 1979, pp. 1095–1101

A model of a hydrodynamic oscillation damper is proposed. The model is used to obtain the equations describing longitudinal oscillations of a structure which includes a shell partially filled with fluid, and contains a hydrodynamic damper. It is shown that the use of the damper leads to considerable increase in the damping of the oscillations of specified frequencies within the structure.

In modern technology one encounters various types of problems connected with restricting the amplitudes of the axisymmetric vibrations of shells and of the longitudinal oscillations of structures consisting of shells partially filled with fluid. Various devices have been proposed [1] for solving these problems. All these devices have a common feature, namely an elastic shell filled with gas and placed in the fluid. The natural frequency of oscillations of such a shell in a fluid can be tuned to required frequency. The effect of such a device is analogous to the effect of a dynamic vibration damper in mechanical systems [2]. A part of the fluid contained in the shell serves as the active mass of the dynamic damper, and for this reason we shall call such devices the hydrodynamic vibration dampers.     

Search algorithm for optimal damping parameters of transfemoral prosthetic limb

In this paper, we developed a mathematical model to find the parameters of prosthetic damper which will provide a similar trajectory for the prosthetic knee joint. Two popular searching methods namely grid searching and optimization are used to determine the damper's parameters. The proposed model is validated with a simulation process using the data of the able-body individuals. We utilized the ground reaction force of sound limb to determine the values of the damper parameters of a prosthetic knee joint for maximum symmetry. Symmetry between knee moments was also improved in the stance period with optimized parameters. Finally, optimization-based searching was observed to be more computationally efficient than the grid-based searching method. The present study will provide a virtual solution to set the prosthetic dampers parameters based on user needs. In the future, the present method can be used for adjusting damping of microprocessor prosthetic knee joint for symmetrical gait pattern.     

Adaptive control and synchronization of a coupled dynamo system with uncertain parameters

This paper treats the adaptive control and synchronization of the coupled dynamo system with unknown parameters. Based on the Lyapunov stability technique, an adaptive control laws are derived such that the coupled dynamo system is asymptotically stable and the two identical dynamo systems are asymptotically synchronized. Also the update rules of the unknown parameters are derived. Finally, numerical simulation of the controlled and synchronized systems are presented.     

Adaptive projective synchronization for a class of switched chaotic systems

This paper addresses the problem of projective synchronization of chaotic systems and switched chaotic systems by adaptive control methods. First, a necessary and sufficient condition is proposed to show how many state variables can realize projective synchronization under a linear feedback controller for the chaotic systems. Then, accordingly, a new algorithm is given to select all state variables that can realize projective synchronization. Furthermore, according to the results of the projective synchronization of chaotic systems, the problem of projective synchronization of the switched chaotic systems comprised by the unified chaotic systems is investigated, and an adaptive global linear feedback controller with only one input channel is designed, which can realize the projective synchronization under the arbitrary switching law. It is worth mentioning that the proposed method can also realize complete synchronization of the switched chaotic systems. Finally, the numerical simulation results verify the correctness and effectiveness of the proposed method.     

A tuning criterion for the inertial tuned damper. Design using phasors in the Argand–Gauss plane

A new approach to the design of a dynamic damper for a monomass oscillator is presented; the design procedure is then applied to control a multimodal oscillator. This new dynamics emerged from an analysis by means of phasors (rotating vectors in the Argand–Gauss plane) which revealed the phase relations between the damper and main oscillator. In particular this work introduces a geometric formalism, based on the use of phasors in the complex plane, for the sizing of inertial dampers applied to multimodal structural oscillators. Their damping effect depends on the fact that the response of the secondary oscillator (the damper) delays the response of the primary mass by 90°, so that the elastic force transmitted by the damper becomes a viscous force on the controlled oscillator. When such condition occurs we say that the damper is “tuned” to the main oscillator; the damping induced by the damper serves to limit the displacement of main oscillator. Our geometrical approach provides a method whose language is close to that of structural mechanics, thus paving the way to the professionals for: (i) sizing the damper parameters and (ii) evaluating the stability to the damped system and its performance limits. The aim of the development is that of exploring the use of dampers to control the response of buildings under horizontal seismic and aerodynamic loads.     

Symmetric and Asymmetric Underplatform Dampers for Turbine Blades

Friction damping devices like underplatform dampers are widely used in turbomachinery applications to reduce vibration amplitudes and to increase lifetime and reliability of the bladed disk. Nowadays, in practical applications, a variety of different underplatform damper geometries is applied. Nevertheless, a detailed study of the in.uence of the geometric and dynamic properties of the damper is still not available. Within this paper the most frequently applied damper types like cylindrical and wedge as well as asymmetrical dampers are investigated and compared to each other with respect to their effectiveness. Especially the in.uence of the damper geometry on the resonance frequency and vibration amplitude is pointed out. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust synchronization of drive–response chaotic systems via adaptive sliding mode control

A robust adaptive sliding control scheme is developed in this study to achieve synchronization for two identical chaotic systems in the presence of uncertain system parameters, external disturbances and nonlinear control inputs. An adaptation algorithm is given based on the Lyapunov stability theory. Using this adaptation technique to estimate the upper-bounds of parameter variation and external disturbance uncertainties, an adaptive sliding mode controller is then constructed without requiring the bounds of parameter and disturbance uncertainties to be known in advance. It is proven that the proposed adaptive sliding mode controller can maintain the existence of sliding mode in finite time in uncertain chaotic systems. Finally, numerical simulations are presented to show the effectiveness of the proposed control scheme.     

基于自适应控制的四元数时滞神经网络的有限时间同步

文章主要研究了自适应控制下四元数时滞神经网络的有限时间完全同步,通过设计一组有效新颖的自适应控制器,使得主从系统实现有限时间同步,并计算出停息时间的理论估计.利用Lyapunov函数方法和不等式技巧,给出了四元数时滞神经网络主从系统有限时间同步的充分条件.最后,通过数值仿真验证了所得理论结果的有效性.     

Hybrid control variates-based simulation method for structural reliability analysis of some problems with low failure probability

The safety analysis of systems with nonlinear performance function and small probability of failure is a challenge in the field of reliability analysis. In this study, an efficient approach is presented for approximating small failure probabilities. To meet this aim, by introducing Probability Density Function (PDF) control variates, the original failure probability integral was reformulated based on the Control Variates Technique (CVT). Accordingly, using the adaptive cooperation of the subset simulation (SubSim) and the CVT, a new formulation was offered for the approximation of small failure probabilities. The proposed formulation involves a probability term (resulting from a fast-moving SubSim) and an adaptive weighting term that refines the obtained probability. Several numerical and engineering problems, involving nonlinear performance functions and system-level reliability problems, are solved by the proposed approach and common reliability methods. Results showed that the proposed simulation approach is not only more efficient, but is also robust than common reliability methods. It also presents a good potential for application in engineering reliability problems.     

Transitions to chaos in squeeze-film dampers

This work reports on a numerical study undertaken to investigate the imbalance response of a rigid rotor supported by squeeze-film dampers. Two types of damper configurations were considered, namely, dampers without centering springs, and eccentrically operated dampers with centering springs. For a rotor fitted with squeeze-film dampers without centering springs, the study revealed the existence of three regimes of chaotic motion. The route to chaos in the first regime was attributed to a sequence of period-doubling bifurcations of the period-1 (synchronous) rotor response. A period-3 (one-third subharmonic) rotor whirl orbit, which was born from a saddle-node bifurcation, was found to co-exist with the chaotic attractor. The period-3 orbit was also observed to undergo a sequence of period-doubling bifurcations resulting in chaotic vibrations of the rotor. The route to chaos in the third regime of chaotic rotor response, which occurred immediately after the disappearance of the period-3 orbit due to a saddle-node bifurcation, was attributed to a possible boundary crisis. The transitions to chaotic vibrations in the rotor supported by eccentric squeeze-film dampers with centering springs were via the period-doubling cascade and type 3 intermittency routes. The type 3 intermittency transition to chaos was due to an inverse period-doubling bifurcation of the period-2 (one-half subharmonic) rotor response. The unbalance response of the squeeze-film-damper supported rotor presented in this work leads to unique non-synchronous and chaotic vibration signatures. The latter provide some useful insights into the design and development of fault diagnostic tools for rotating machinery that operate in highly nonlinear regimes.