Semi-active Sliding Mode Control of Vehicle Suspension with Magneto-rheological Damper

The vehicle semi-active suspension with magneto-theological damper（MRD） has been a hot topic since this decade, in which the robust control synthesis considering load variation is a challenging task. In this paper, a new semi-active controller based upon the inverse model and sliding mode control （SMC） strategies is proposed for the quarter-vehicle suspension with the magneto-rheological （MR） damper, wherein an ideal skyhook suspension is employed as the control reference model and the vehicle sprung mass is considered as an uncertain parameter. According to the asymptotical stability of SMC, the dynamic errors between the plant and reference systems are used to derive the control damping force acquired by the MR quarter-vehicle suspension system. The proposed modified Bouc-wen hysteretic force-velocity （F-v） model and its inverse model of MR damper, as well as the proposed continuous modulation （CM） filtering algorithm without phase shift are employed to convert the control damping force into the direct drive current of the MR damper. Moreover, the proposed semi-active sliding mode controller （SSMC）-based MR quarter-vehicle suspension is systematically evaluated through comparing the time and frequency domain responses of the sprung and unsprung mass displacement accelerations, suspension travel and the tire dynamic force with those of the passive quarter-vehicle suspension, under three kinds of varied amplitude harmonic, rounded pulse and real-road measured random excitations. The evaluation results illustrate that the proposed SSMC can greatly suppress the vehicle suspension vibration due to uncertainty of the load, and thus improve the ride comfort and handling safety. The study establishes a solid theoretical foundation as the universal control scheme for the adaptive semi-active control of the MR full-vehicle suspension decoupled into four MR quarter-vehicle sub-suspension systems.

Skyhook-based Semi-active Control of Full-vehicle Suspension with Magneto-rheological Dampers

The control study of vehicle semi-active suspension with magneto-rheological (MR) dampers has been attracted much attention internationally. However, a simple, real time and easy implementing semi-active controller has not been proposed for the MR full-vehicle suspension system, and a systematic analysis method has not been established for evaluating the multi-objective suspension performances of MR full-vehicle vertical, pitch and roll motions. For this purpose, according to the 7-degree of freedom (DOF) fullvehicle dynamic system, a generalized 7-DOF MR and passive full-vehicle dynamic model is set up by employing the modified Boucwen hysteretic force-velocity (F-v) model of the MR damper. A semi-active controller is synthesized to realize independent control of the four MR quarter-vehicle sub-suspension systems in the full-vehicle, which is on the basis of the proposed modified skyhook damping scheme of MR quarter-vehicle sub-suspension system. The proposed controller can greatly simplify the controller design complexity of MR full-vehicle suspension and has merits of easy implementation in real application, wherein only absolute velocities of sprung and unsprung masses with reference to the road surface are required to measure in real time when the vehicle is moving. Furthermore, a systematic analysis method is established for evaluating the vertical, pitch and roll motion properties of both MR and passive full-vehicle suspensions in a more realistic road excitation manner, in which the harmonic, rounded pulse and real road measured random signals with delay time are employed as different road excitations inserted on the front and rear two wheels, by considering the distance between front and rear wheels in full-vehicle. The above excitations with different amplitudes are further employed as the road excitations inserted on left and right two wheels for evaluating the roll motion property. The multi-objective suspension performances of ride comfort and handling safety of the proposed MR full-vehicle suspension are thus thoroughly evaluated by comparing with those of the passive full-vehicle suspension. The results show that the proposed controller can ideally improve multiobjective suspension performances of the ride comfort and handling safety. The proposed harmonic, rounded pulse and real road measured random signals with delay time and asymmetric amplitudes are suitable for accurately analyzing the vertical, pitch and roll motion properties of MR full-vehicle suspension system in a more realistic road excitation manner. This research has important theoretical significance for improving application study on the intelligent MR semi-active suspension.

SEMI-ACTIVE CONTROL OF VEHICLE SUSPENSION WITH MAGNETO-RHEOLOGICAL DAMPERS PARTⅡ——EVALUATION OF SUSPENSION PERFORMANCE

The design and analysis of an intelligent vehicle suspension with MR dampers should address hybrid semi-active control goals, such as rejection of current-switching discontinuity and MR-damper hysteresis, asymmetric damping from the symmetric MR-damper design, robustness on the vehicle operation parameter uncertainties and consideration of essential multiple suspension goals. Following the proposed skyhook-based asymmetric semi-active controller （Part I ） for achieving the above goals, herein, a set of suspension performance measures and three kinds of varying amplitude harmonic, rounded pulse and really measured random excitations are systematically defined, and the sensitivity of quarter-vehicle MR-suspension performance to variations in operating conditions is thoroughly analyzed. The results illustrate that the proposed skyhook-based semi-active MR-suspension in the asymmetric mode yields relatively superior dynamic responses to meet the multiple suspension performances of ride, rattle space, road-holding and dynamic tire force transmitted to the pavement, and has desirable robustness on variations in operating conditions of vehicle load and speed and the road roughness.

The Knee Joint Design and Control of Above-knee Intelligent Bionic Leg Based on Magneto-rheological Damper

The above-knee intelligent bionic leg is very helpful to amputees in the area of rehabilitation medicine. This paper first introduces the functional demand of the above-knee prosthesis design. Then, the advantages of the four-bar link mechanism and the magneto-rheological （MR） damper are analyzed in detail. The fixed position of the MR damper is optimized and a virtual prototype of knee joint is given. In the end, the system model of kinematics, dynamics, and controller are given and a control experiment is performed. The control experiment indicates that the intelligent bionic leg with multi-axis knee is able to realize gait tracking of the amputee＇s healthy leg based on semi-active control of the MR damper.

SEMI-ACTIVE CONTROL OF VEHICLE SUSPENSION WITH MAGNETO-RHEOLOGICAL DAMPERS:PART Ⅰ——CONTROLLER SYNTHESIS AND EVALUATION

A modified skyhook-based semi-active controller is proposed for implementing an asymmetric control suspension design with symmetric magneto-rheological （MR） dampers. The controller is formulated in current form, which is modulated by integrating a continuous modulation and an asymmetric damping force generation algorithms, so as to effectively minimize switching and hysteretic effects from the MR-damper. The proposed controller is implemented with a quarter-vehicle MR-suspension model, and its relative response characteristics are thus evaluated in terms of defined performance measures under varying amplitude harmonic, rounded pulse and random excitations. The sensitivity of the semi-active suspension performance to variations in controller parameters is thoroughly evaluated. The results illustrate that the proposed skyhook-based asymmetric semi-active MR-suspension controller has superior robustness on the system parameter variations, and can achieve desirable multi-objective suspension performance.

SEMI-ACTIVE CONTROL OF VEHICLE SUSPENSION WITH MAGNETO-RHEOLOGICAL DAMPERS:PART III—EXPERIMENTAL VALIDATION

A hardware-in-the-loop （HIL） test and simulation platform is developed in the laboratory, so as to validate the performance characteristics of the proposed skyhook-based asymmetric semi-active controller in Part I, and examine the validity of the proposed MR-damper model in a system surrounding. A real-time monitor is designed to assess and monitor the responses of the quarter-vehicle model in the HIL platform, and to select the excitation, controller synthesis, and the output displays. A drive current circuit hardware employing PID feedback technique is developed to compensate for the time delays from the servo-controller and drive current circuit, in which a small resistance is integrated in the current amplifier circuit to provide the feedback signal. The experiments were performed to measure the responses of the quarter-vehicle MR-suspension models with fixed current and the proposed semi-active MR-damping variations, under harmonic, rounded pulse and random road excitations. The measured data were compared with the corresponding model results to examine the model and controller validity, and revealed generally good agreements in the model and tested results and very little sensitivity of the tested responses to variations in the sprung mass. The HIL test results validate the effectiveness of the proposed skyhook-based semi-active asymmetric controller and its high robustness against the vehicle load variations in view of the intelligent vehicle suspension design.

Modeling of Magneto-Rheological Damper with Neural Network

With the revival of magnetorheological technology research in the 1980’s, its application in vehicles is in- creasingly focused on vibration suppression. Based on the importance of magnetorheological damper modeling, non- parametric modeling with neural network, which is a promising development in semi-active online control of vehicles with MR suspension, has been carried out in this study. A two layer neural network with 7 neurons in a hidden layer and 3 inputs and 1 output was established to simulate the behavior of MR damper at different excitation currents. In the neural network modeling, the damping force is a function of displacement, velocity and the applied current. A MR damper for vehicles is fabricated and tested by MTS; the data acquired are utilized for neural network training and vali- dation. The application and validation show that the predicted forces of the neural network match well with the forces tested with a small variance, which demonstrates the effectiveness and precision of neural network modeling.

Semi-active control of a vehicle suspension using magneto-rheological damper

A semi-active magneto-rheological (MR) damper was experimentally investigated and compared to an original equipment manufacturer (OEM) damper for a passenger vehicle,by using a quarter car models. A full-scale two-degree-of-freedom quarter car experimental set-up was constructed to study the vehicle suspension. On-off skyhook controller and Fuzzy-Lyapunov skyhook controller (FLSC) were employed to control the input current for MR damper so as to achieve the desired damping force. Tests were done to evaluate the ability of MR damper for controlling vehicle vibration. Test results show that the semi-active MR vehicle suspension vibration control system is feasible. In comparison with OEM damper,on-off and FLSC controlled MR dampers can effectively reduce the acceleration of vehicle sprung mass by about 15% and 24%,respectively.

Experimental Studies on High-Frequency Performance of the Inverse Control Magneto-Rheological Damper

Severe vibration of underground structures may be induced under blast loads. According to the characteristics of the explosion-induced ground shock wave, a new-type damper, inverse control magneto-rheological(MR) damper was designed to control the vibration. The high-frequency performance test of the MR damper was carried out on the small shaking table. It is shown that the performance can be modeled by use of the modified Bouc-Wen model, and the parameters of the model keep stable in the ranqe of 15-50 Hz.

Seismic control of multi-degrees-of-freedom structures by vertical mass isolation method using MR dampers

Vertical mass isolation(VMI)is one of the novel methods for the seismic control of structures.In this method,the entire structure is assumed to consist of two mass and stiffness subsystems,and an isolated layer is located among them.In this study,the magnetorheological damper in three modes:passive-off,passive-on,and semi-active mode with variable voltage between zero and 9 volts was used as an isolated layer between two subsystems.Multi-degrees-of-freedom structures with 5,10,and 15 floors in two dimensions were examined under 11 pairs of near field earthquakes.On each level,the displacement of MR dampers was taken into account.The responses of maximum displacement,maximum inter-story drift,and maximum base shear in controlled and uncontrolled buildings were compared to assess the suggested approach for seismic control of the structures.According to the results,the semi-active control method can reduce the response by more than 12%compared to the uncontrolled mode in terms of maximum displacement of the mass subsystem of the structures.This method can reduce more than 16%and 20%of the responses compared to the uncontrolled mode in terms of maximum inter-story drift and base shear of the structure,respectively.

Development and Application of a Power Law Constitutive Model for Eddy Current Dampers

Eddy current dampers (ECDs) have emerged as highly desirable solutions for vibration control due to theirexceptional damping performance and durability. However, the existing constitutive models present challenges tothe widespread implementation of ECD technology, and there is limited availability of finite element analysis (FEA)software capable of accurately modeling the behavior of ECDs. This study addresses these issues by developing anewconstitutivemodel that is both easily understandable and user-friendly for FEAsoftware. By utilizing numericalresults obtained from electromagnetic FEA, a novel power law constitutive model is proposed to capture thenonlinear behavior of ECDs. The effectiveness of the power law constitutive model is validated throughmechanicalproperty tests and numerical seismic analysis. Furthermore, a detailed description of the application process ofthe power law constitutive model in ANSYS FEA software is provided. To facilitate the preliminary design ofECDs, an analytical derivation of energy dissipation and parameter optimization for ECDs under harmonicmotionis performed. The results demonstrate that the power law constitutive model serves as a viable alternative forconducting dynamic analysis using FEA and optimizing parameters for ECDs.

Vibration attenuation performance of wind turbine tower using a prestressed tuned mass damper under seismic excitation

With the rapid development of large megawatt wind turbines,the operation environment of wind turbine towers(WTTs)has become increasingly complex.In particular,seismic excitation can create a resonance response and cause excessive vibration of the WTT.To investigate the vibration attenuation performance of the WTT under seismic excitations,a novel passive vibration control device,called a prestressed tuned mass damper(PS-TMD),is presented in this study.First,a mathematical model is established based on structural dynamics under seismic excitation.Then,the mathematical analytical expression of the dynamic coefficient is deduced,and the parameter design method is obtained by system tuning optimization.Next,based on a theoretical analysis and parameter design,the numerical results showed that the PS-TMD was able to effectively mitigate the resonance under the harmonic basal acceleration.Finally,the time-history analysis method is used to verify the effectiveness of the traditional pendulum tuned mass damper(PTMD)and the novel PS-TMD device,and the results indicate that the vibration attenuation performance of the PS-TMD is better than the PTMD.In addition,the PS-TMD avoids the nonlinear effect due to the large oscillation angle,and has the potential to dissipate hysteretic energy under seismic excitation.

Parameters Optimization and Performance Evaluation of the Tuned Inerter Damper for the Seismic Protection of Adjacent Building Structures

In order to improve the seismic performance of adjacent buildings,two types of tuned inerter damper(TID)damping systems for adjacent buildings are proposed,which are composed of springs,inerter devices and dampers in serial or in parallel.The dynamic equations of TID adjacent building damping systems were derived,and the H2 norm criterion was used to optimize and adjust them,so that the system had the optimum damping performance under white noise random excitation.Taking TID frequency ratio and damping ratio as optimization parameters,the optimum analytical solutions of the displacement frequency response of the undamped structure under white noise excitation were obtained.The results showed that compared with the classic TMD,TID could obtain a better damping effect in the adjacent buildings.Comparing the TIDs composed of serial or parallel,it was found that the parallel TIDs had more significant advantages in controlling the peak displacement frequency response,while the H2 norm of the displacement frequency response of the damping system under the coupling of serial TID was smaller.Taking the adjacent building composed of two ten-story frame structures as an example,the displacement and energy collection time history analysis of the adjacent building coupled with the optimum design parameter TIDs were carried out.It was found that TID had a better damping effect in the full-time range compared with the classic TMD.This paper also studied the potential power of TID in adjacent buildings,which can be converted into available power resources during earthquakes.

Structure Analysis for a New Type of Vane Hydraulic Damper Using Magneto-rheological Fluid

Over recent years the progress in actuator and microelectronics technology has made intelligent suspension systems feasible.Based on conventional vane hydraulic damper,a new vane magneto-rheological fluid(MRF) damper with fail-safe capability is designed.Firstly,the mathematical model of damping moment is deduced based on the parallel-plate model and Bingham model of MR fluids.Secondly,some influence factors of damping adjustable multiple are analyzed to provide some ways for augmenting the damping adjustable multiple under the condition of keeping initial damping moment invariable.Finally,the magnetic circuit is designed,and magnetic field distribution is simulated with the magnetic finite element analysis software-ANSOFT.The theory and simulation results confirm that the damping adjustable range of vane MRF damper can meet the requirement of heavy vehicle semi-active suspension system.

Hysteresis-induced bifurcation and chaos in a magneto-rheological suspension system under external excitation

The magneto-rheological damper （MRD） is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom （2-DOF） MR suspension system was established first, by employing the modified Bouc-Wen force-velocity （F-v） hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface. The largest Lyapunov exponent （LLE） was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density （PSD） diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy （K entropy） were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system.

Fuzzy Hybrid Control of Vibration Attitude of Full Car via Magneto-rheological Suspensions

A magneto-rheological（MR） semi-active suspension system with the controllable damping forces has received more attention in reducing the vibration of a vehicle. However, many control strategies only discussed one or two vibration states of the vehicle based on a quarter-car model or a half vehicle model via MR suspensions. They cannot provide a satisfying whole-vehicle performance on a road test. Hence, a full car vibration model via an MR suspension system is proposed. To reduce the heave, pitch and roll motion of the vehicle body and the vertical vibration of four wheels, a fuzzy hybrid controller for vibration attitude of full car via MR suspensions is proposed. First, a skyhook-fuzzy control scheme is designed to reduce the heave, roll and pitch motion of the vehicle body. Second, a revised ground hook control strategy is adopted to decrease the vertical vibration of the wheels. Finally, a hybrid control scheme based on a fuzzy reasoning method is proposed to tune the hybrid damping parameter, which is suitable for coordination the attitude of the vehicle body and the wheels. A test and control system for the vibration attitude of full car is set up. It is implemented on a car equipped with four MR suspensions. The results on random highway and rough road indicate that the fuzzy hybrid controller can decrease the vibration accelerations of the vehicle body and the wheels to 65%-80% and 80%-90%, respectively. It reduces the automotive vibrations of heave, roll and pitch more effectively than a passive suspension and an MR suspension with a traditional hybrid control scheme so that it achieves better ride comfort and road holding concurrently. This paper proposes a new fuzzy hybrid control（FHC） method for reducing vibration attitude of full car via MR suspensions and develops a road test to evaluate the FHC.

A new variable stiffness absorber based on magneto-rheological elastomer

A new adaptive variable stiffness absorber was proposed based on a smart material, magnetorheological elastomer (MRE), and its vibration control performance was investigated. Before developing the proposed absorber, the MREs were firstly fabricated by curing a mixture of 704 silicon rubber, carbonyl iron particles and a small amount of silicone oil under an external magnetic field. Then the mechanical properties of the fabricated MREs were measured. On the basis of the measured mechanical characteristics, the MRE absorber was developed and its working characteristics were also tested under various input currents and excited frequencies. Finally, the control responses of a two-degree-of-freedom dynamic system with a MRE absorber were presented under a chirp input and used to evaluate the effectiveness of the MRE absorber.

Magneto-rheological elastomer (MRE) based composite structures for micro-vibration control

Magneto-rheological elastomers （MILEs） are used to construct composite structures for micro-vibration control of equipment under stochastic support-motion excitations. The dynamic behavior of MREs as a smart viscoelastic material is characterized by a complex modulus dependent on vibration frequency and controllable by external magnetic fields. Frequency-domain solution methods for stochastic micro-vibration response analysis of the MRE-based structural systems are developed to derive the system frequency-response function matrices and the expressions of the velocity response spectrum. With these equations, the root-mean-square （RMS） velocity responses in terms of the one-third octave frequency band spectrum can be calculated. Further, the optimization problem of the complex moduli of the MRE cores is defined by minimizing the velocity response spectra and the RMS velocity responses through altering the applied magnetic fields. Simulation results illustrate the influences of MRE parameters on the RMS velocity responses and the high response reduction capacities of the MRE-based structures. In addition, the developed frequency-domain analysis methods are applicable to sandwich beam structures with arbitrary cores characterized by complex shear moduli under stochastic excitations described by power spectral density functions, and are valid for a wide frequency range.

超高层Tuned Mass Damper防震支撑系统技术研究应用

超高层建筑是现代城市建设的重要标志之一,其高度已经超过了传统建筑的极限。然而,随着建筑高度不断增加,地震的破坏力也越来越强,超高层建筑面临着更加严峻的安全挑战。因此,研究超高层建筑防震支撑系统技术非常重要,Tuned Mass Damper(TMD)是一种被广泛研究和应用的超高层建筑防震支撑系统技术,TMD最初是在20世纪60年代提出的,最早应用于桥梁上,后来,TMD被引入到建筑领域,并得到广泛的应用。通过精确调节质量、阻尼和弹性等参数来削弱地震引起的建筑物减震效应,从而减少了建筑物因地震造成的损害和崩塌的风险.

Delay-dependent H_(2)/H_(∞) Control for Vehicle Magneto-rheological Semi-active Suspension

The exist researches of the magneto-rheological semi-active suspension(MSAS) control mainly focus on the design of control laws,which aim at obtaining an optimal control strategy to improve the ride comfort and handling stability.In the controller design,the stability of the MSAS system cannot be confirmed owing to the control input time delay considered little.In this paper,a quarter vehicle MSAS model with time-delay is built.Therefore,through formulating the sprung mass acceleration suitably as the optimization object,suspension deflection and tyre dynamic load and coulomb damping force as the constraint objects,with considering the control input time-delay,a delay-dependent state feedback H2/H∞ controller is designed.According to Lyapunov-Krasovskii functional theory,the sufficient conditions for asymptotic stability and the existence of delay-dependent H2/H∞ controller are obtained,and the controller design is transformed into the minimization problem for linear function through linear matrix inequality(LMI).Random road excitation simulations and experiments are carried out.The simulation and experiment results show that the design can preserve the closed-loop stability and achieve the performances for MSAS system in spite of the existence of the control input time-delay.The present study can provide an important basis and method for research on time-delay problem in MSAS and other chassis subsystems.