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 loc...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.展开更多
Magnetorheological elastomers(MREs)hold significant promise in various fields such as automotive engineering,and civil engineering,where they serve as intelligent materials.Depending on the application of an external ...Magnetorheological elastomers(MREs)hold significant promise in various fields such as automotive engineering,and civil engineering,where they serve as intelligent materials.Depending on the application of an external magnetic field,these materials exhibit varying magnetorheological and viscoelastic properties,including shear stress,yield stress,dynamic moduli,and damping.In this work,a new type of MRE,termed self-healing MREs(SH-MREs),has been developed by adding a novel self-healing agent into existing MREs.The dynamic modulus and loss factor of SH-MREs with different compositions have been characterized under various conditions of frequency,temperature,and strain.The results show that as the strain value increases,the loss factor also increases.Moreover,the loss factor initially increases and then decreases with increasing magnetic field strength.Although higher concentrations of ferromagnetic particles increase the loss factor,they enhance the operational range due to their better responsiveness to magnetic fields.SH-MREs demonstrate improved damping capabilities,attributed to the formation of coordination bonds between ferromagnetic particles and the self-healing agent.The stable structure increases the viscosity of MREs.The results of the regression model suggest a direct proportionality between sensitivity to the magnetic field and the ferromagnetic particle concentration.展开更多
Low damping characteristics have always been a key sticking points in the development of gas bearings.The application of squeeze film dampers can significantly improve the damping performance of gas lubricated bearing...Low damping characteristics have always been a key sticking points in the development of gas bearings.The application of squeeze film dampers can significantly improve the damping performance of gas lubricated bearings.This paper proposed a novel hermetic diaphragm squeeze film damper(HDSFD)for oil-free turbomachinery supported by gas lubricated bearings.Several types of HDSFDs with symmetrical structure were proposed for good damping performance.By considering the compressibility of the damper fluid,based on hydraulic fluid mechanics theory,a dynamic model of HDSFDs under medium is proposed,which successfully reflects the frequency dependence of force coefficients.Based on the dynamic model,the effects of damper fluid viscosity,bulk modulus of damper fluid,thickness of damper fluid film and plunger thickness on the dynamic stiffness and damping of HDSFDs were analyzed.An experimental test rig was assembled and series of experimental studies on HDSFDs were conducted.The damper fluid transverse flow is added to the existing HDSFD concept,which aims to make the dynamic force coefficients independent of frequency.Although the force coefficient is still frequency dependent,the damping coefficient at high frequency excitation with damper fluid supply twice as that without damper fluid supply.The results serve as a benchmark for the calibration of analytical tools under development.展开更多
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 cau...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.展开更多
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 tot...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.展开更多
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 ...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.展开更多
Sandwich structures are widespread in engineering applications because of their advantageous mechanical properties.Recently,their acoustic performance has also been improved to enable attenuation of low-frequency vibr...Sandwich structures are widespread in engineering applications because of their advantageous mechanical properties.Recently,their acoustic performance has also been improved to enable attenuation of low-frequency vibrations induced by noisy environments.Here,we propose a new design of sandwich plates(SPs)featuring a metamaterial core with an actively tunable low-frequency bandgap.The core contains magnetorheological elastomer(MRE)resonators which are arranged periodically and enable controlling wave attenuation by an external magnetic field.We analytically estimate the sound transmission loss(STL)of the plate using the space harmonic expansion method.The low frequency sound insulation performance is also analyzed by the equivalent dynamic density method,and the accuracy of the obtained results is verified by finite-element simulations.Our results demonstrate that the STL of the proposed plate is enhanced compared with a typical SP analog,and the induced bandgap can be effectively tuned to desired frequencies.This study further advances the field of actively controlled acoustic metamaterials,and paves the way to their practical applications.展开更多
Dynamic impacts such as wind and earthquakes cause loss of life and economic damage.To ensure safety against these effects,various measures have been taken from past to present and solutions have been developed using ...Dynamic impacts such as wind and earthquakes cause loss of life and economic damage.To ensure safety against these effects,various measures have been taken from past to present and solutions have been developed using different technologies.Tall buildings are more susceptible to vibrations such as wind and earthquakes.Therefore,vibration control has become an important issue in civil engineering.This study optimizes tuned mass damper inerter(TMDI)using far-fault ground motion records.This study derives the optimum parameters of TMDI using the Adaptive Harmony Search algorithm.Structure displacement and total acceleration against earthquake load are analyzed to assess the performance of the TMDI system.The effect of the inerter when connected to different floors is observed,and the results are compared to the conventional tuned mass damper(TMD).It is indicated that the case of connecting the inerter force to the 5th floor gives better results.As a result,TMD and TMDI systems reduce the displacement by 21.87%and 25.45%,respectively,and the total acceleration by 25.45%and 19.59%,respectively.These percentage reductions indicated that the structure resilience against dynamic loads can be increased using control systems.展开更多
To study the seismic resilience of a concrete-framed hospital building with viscous dampers,the elastoplastic time history analysis of a three-story concrete-framed hospital building under moderate and rare earthquake...To study the seismic resilience of a concrete-framed hospital building with viscous dampers,the elastoplastic time history analysis of a three-story concrete-framed hospital building under moderate and rare earthquakes was carried out by finite element analysis software.The structure’s overall response was studied,meanwhile,the seismic resilience of the building was evaluated from three aspects:repair cost,repair time,and casualties.The results show that viscous dampers can effectively reduce the repair cost,repair time,and casualties under earthquakes.Compared with the structure without dampers,the repair cost and repair time of the structure with dampers have been reduced by 67%and 69%respectively under moderate earthquakes,42%and 39%respectively under rare earthquakes,and the seismic resilience grade has been increased from zero to one star.展开更多
Magnetorheological (MR) dampers are one of the most promising new devices for civil infrastructural vibration control applications. However, due to their highly nonlinear dynamic behavior, it is very difficult to obta...Magnetorheological (MR) dampers are one of the most promising new devices for civil infrastructural vibration control applications. However, due to their highly nonlinear dynamic behavior, it is very difficult to obtain of a mathematical model of inverse MR damper that has an explicit relationship between the desired damper force and the command signal (voltage). This force voltage relationship is especially required for the structural vibration control design and simulation using MR dampers. This paper focuses on using a neural network (NN) technique to emulate the inverse MR damper model. The output of the neural network can be used to command the MR damper for generating desired forces. Numerical simulations are also presented to illustrate the effectiveness of this inverse model in semi active vibration control using MR dampers.展开更多
A semi-active force tracking PI controller is formulated and analyzed for a magnetorheological (MR) fluid-based damper in conjunction with a quarter-vehicle model. Two different models of the MR-damper are integrated ...A semi-active force tracking PI controller is formulated and analyzed for a magnetorheological (MR) fluid-based damper in conjunction with a quarter-vehicle model. Two different models of the MR-damper are integrated into the closed-loop system model, which includes: a model based upon the mean force-velocity (f-v) behaviour; and a model synthesis comprising inherent nonsmooth hysteretic force and the force limiting properties of the MR damper. The vehicle models are analyzed to study the vibration attenuation performance of the MR-damper using the semi-active force tracking PI control algorithm. The simulation results are also presented to demonstrate the influence of the damper nonlinearity, specifically the hysteresis, on the suspension performance. The results show that the proposed control strategy can yield superior vibration attenuation performance of the vehicle suspension actuated by the controllable MR-damper not only in the sprung mass resonance and the ride zones, but also in the vicinity of the wheel-hop. The results further show that the presence of damper hystersis deteriorates the suspension performance.展开更多
This paper investigates the problem of controlling half-vehicle semi-active suspension system involving a magnetorheological(MR)damper.This features a hysteretic behavior that is presently captured through the nonline...This paper investigates the problem of controlling half-vehicle semi-active suspension system involving a magnetorheological(MR)damper.This features a hysteretic behavior that is presently captured through the nonlinear Bouc-Wen model.The control objective is to regulate well the heave and the pitch motions of the chassis despite the road irregularities.The difficulty of the control problem lies in the nonlinearity of the system model,the uncertainty of some of its parameters,and the inaccessibility to measurements of the hysteresis internal state variables.Using Lyapunov control design tools,we design two observers to get online estimates of the hysteresis internal states and a stabilizing adaptive state-feedback regulator.The whole adaptive controller is formally shown to meet the desired control objectives.This theoretical result is confirmed by several simulations demonstrating the supremacy of the latter compared to the skyhook control and passive suspension.展开更多
文摘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.
基金the National Natural Science Foundation of China(No.52003142).
文摘Magnetorheological elastomers(MREs)hold significant promise in various fields such as automotive engineering,and civil engineering,where they serve as intelligent materials.Depending on the application of an external magnetic field,these materials exhibit varying magnetorheological and viscoelastic properties,including shear stress,yield stress,dynamic moduli,and damping.In this work,a new type of MRE,termed self-healing MREs(SH-MREs),has been developed by adding a novel self-healing agent into existing MREs.The dynamic modulus and loss factor of SH-MREs with different compositions have been characterized under various conditions of frequency,temperature,and strain.The results show that as the strain value increases,the loss factor also increases.Moreover,the loss factor initially increases and then decreases with increasing magnetic field strength.Although higher concentrations of ferromagnetic particles increase the loss factor,they enhance the operational range due to their better responsiveness to magnetic fields.SH-MREs demonstrate improved damping capabilities,attributed to the formation of coordination bonds between ferromagnetic particles and the self-healing agent.The stable structure increases the viscosity of MREs.The results of the regression model suggest a direct proportionality between sensitivity to the magnetic field and the ferromagnetic particle concentration.
基金Supported by National Key Research and Development Program of China (Grant No.2021YFF0600208)National Natural Science Foundation of China (Grant No.52005170)Hunan Provincial Science and Technology Innovation Program of China (Grant No.2020RC4018)。
文摘Low damping characteristics have always been a key sticking points in the development of gas bearings.The application of squeeze film dampers can significantly improve the damping performance of gas lubricated bearings.This paper proposed a novel hermetic diaphragm squeeze film damper(HDSFD)for oil-free turbomachinery supported by gas lubricated bearings.Several types of HDSFDs with symmetrical structure were proposed for good damping performance.By considering the compressibility of the damper fluid,based on hydraulic fluid mechanics theory,a dynamic model of HDSFDs under medium is proposed,which successfully reflects the frequency dependence of force coefficients.Based on the dynamic model,the effects of damper fluid viscosity,bulk modulus of damper fluid,thickness of damper fluid film and plunger thickness on the dynamic stiffness and damping of HDSFDs were analyzed.An experimental test rig was assembled and series of experimental studies on HDSFDs were conducted.The damper fluid transverse flow is added to the existing HDSFD concept,which aims to make the dynamic force coefficients independent of frequency.Although the force coefficient is still frequency dependent,the damping coefficient at high frequency excitation with damper fluid supply twice as that without damper fluid supply.The results serve as a benchmark for the calibration of analytical tools under development.
基金Fundamental Research Funds for the National Natural Science Foundation of China under Grant No.52078084the Natural Science Foundation of Chongqing (cstc2021jcyj-msxmX0623)+2 种基金the 111 project of the Ministry of Educationthe Bureau of Foreign Experts of China under Grant No.B18062China Postdoctoral Science Foundation under Grant No.2021M690838。
文摘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.
文摘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.
基金This research was funded by the Natural Science Research Project of Higher Education Institutions in Anhui Province(Grant No.2022AH040045)the Anhui Provincial Natural Science Foundation(Grant No.2008085QE245)the Project of Science and Technology Plan of Department of Housing and Urban-Rural Development of Anhui Province(Grant No.2021-YF22).
文摘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.
基金Project supported by the National Natural Science Foundation of China(Nos.12472007 and 12072084)the Fundamental Research Funds for the Central Universities of China。
文摘Sandwich structures are widespread in engineering applications because of their advantageous mechanical properties.Recently,their acoustic performance has also been improved to enable attenuation of low-frequency vibrations induced by noisy environments.Here,we propose a new design of sandwich plates(SPs)featuring a metamaterial core with an actively tunable low-frequency bandgap.The core contains magnetorheological elastomer(MRE)resonators which are arranged periodically and enable controlling wave attenuation by an external magnetic field.We analytically estimate the sound transmission loss(STL)of the plate using the space harmonic expansion method.The low frequency sound insulation performance is also analyzed by the equivalent dynamic density method,and the accuracy of the obtained results is verified by finite-element simulations.Our results demonstrate that the STL of the proposed plate is enhanced compared with a typical SP analog,and the induced bandgap can be effectively tuned to desired frequencies.This study further advances the field of actively controlled acoustic metamaterials,and paves the way to their practical applications.
基金supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP)and the Ministry of Trade,Industry&Energy,Republic of Korea (RS-2024-00441420RS-2024-00442817).
文摘Dynamic impacts such as wind and earthquakes cause loss of life and economic damage.To ensure safety against these effects,various measures have been taken from past to present and solutions have been developed using different technologies.Tall buildings are more susceptible to vibrations such as wind and earthquakes.Therefore,vibration control has become an important issue in civil engineering.This study optimizes tuned mass damper inerter(TMDI)using far-fault ground motion records.This study derives the optimum parameters of TMDI using the Adaptive Harmony Search algorithm.Structure displacement and total acceleration against earthquake load are analyzed to assess the performance of the TMDI system.The effect of the inerter when connected to different floors is observed,and the results are compared to the conventional tuned mass damper(TMD).It is indicated that the case of connecting the inerter force to the 5th floor gives better results.As a result,TMD and TMDI systems reduce the displacement by 21.87%and 25.45%,respectively,and the total acceleration by 25.45%and 19.59%,respectively.These percentage reductions indicated that the structure resilience against dynamic loads can be increased using control systems.
基金Financial support for this work was provided by the Science and Technology Commission of Shanghai Municipality(Project No.22YF1409500).
文摘To study the seismic resilience of a concrete-framed hospital building with viscous dampers,the elastoplastic time history analysis of a three-story concrete-framed hospital building under moderate and rare earthquakes was carried out by finite element analysis software.The structure’s overall response was studied,meanwhile,the seismic resilience of the building was evaluated from three aspects:repair cost,repair time,and casualties.The results show that viscous dampers can effectively reduce the repair cost,repair time,and casualties under earthquakes.Compared with the structure without dampers,the repair cost and repair time of the structure with dampers have been reduced by 67%and 69%respectively under moderate earthquakes,42%and 39%respectively under rare earthquakes,and the seismic resilience grade has been increased from zero to one star.
文摘Magnetorheological (MR) dampers are one of the most promising new devices for civil infrastructural vibration control applications. However, due to their highly nonlinear dynamic behavior, it is very difficult to obtain of a mathematical model of inverse MR damper that has an explicit relationship between the desired damper force and the command signal (voltage). This force voltage relationship is especially required for the structural vibration control design and simulation using MR dampers. This paper focuses on using a neural network (NN) technique to emulate the inverse MR damper model. The output of the neural network can be used to command the MR damper for generating desired forces. Numerical simulations are also presented to illustrate the effectiveness of this inverse model in semi active vibration control using MR dampers.
文摘A semi-active force tracking PI controller is formulated and analyzed for a magnetorheological (MR) fluid-based damper in conjunction with a quarter-vehicle model. Two different models of the MR-damper are integrated into the closed-loop system model, which includes: a model based upon the mean force-velocity (f-v) behaviour; and a model synthesis comprising inherent nonsmooth hysteretic force and the force limiting properties of the MR damper. The vehicle models are analyzed to study the vibration attenuation performance of the MR-damper using the semi-active force tracking PI control algorithm. The simulation results are also presented to demonstrate the influence of the damper nonlinearity, specifically the hysteresis, on the suspension performance. The results show that the proposed control strategy can yield superior vibration attenuation performance of the vehicle suspension actuated by the controllable MR-damper not only in the sprung mass resonance and the ride zones, but also in the vicinity of the wheel-hop. The results further show that the presence of damper hystersis deteriorates the suspension performance.
文摘This paper investigates the problem of controlling half-vehicle semi-active suspension system involving a magnetorheological(MR)damper.This features a hysteretic behavior that is presently captured through the nonlinear Bouc-Wen model.The control objective is to regulate well the heave and the pitch motions of the chassis despite the road irregularities.The difficulty of the control problem lies in the nonlinearity of the system model,the uncertainty of some of its parameters,and the inaccessibility to measurements of the hysteresis internal state variables.Using Lyapunov control design tools,we design two observers to get online estimates of the hysteresis internal states and a stabilizing adaptive state-feedback regulator.The whole adaptive controller is formally shown to meet the desired control objectives.This theoretical result is confirmed by several simulations demonstrating the supremacy of the latter compared to the skyhook control and passive suspension.
