Advances in Active Suspension Systems for Road Vehicles

Active suspension systems(ASSs)have been proposed and developed for a few decades,and have now once again become a thriving topic in both academia and industry,due to the high demand for driving comfort and safety and the compatibility of ASSs with vehicle electrification and autonomy.Existing review papers on ASSs mainly cover dynamics modeling and robust control;however,the gap between academic research outcomes and industrial application requirements has not yet been bridged,hindering most ASS research knowledge from being transferred to vehicle companies.This paper comprehensively reviews advances in ASSs for road vehicles,with a focus on hardware structures and control strategies.In particular,state-of-the-art ASSs that have been recently adopted in production cars are discussed in detail,including the representative solutions of Mercedes active body control(ABC)and Audi predictive active suspension;novel concepts that could become alternative candidates are also introduced,including series active variable geometry suspension,and the active wheel-alignment system.ASSs with compact structure,small mass increment,low power consumption,high-frequency response,acceptable economic costs,and high reliability are more likely to be adopted by car manufacturers.In terms of control strategies,the development of future ASSs aims not only to stabilize the chassis attitude and attenuate the chassis vibration,but also to enable ASSs to cooperate with other modules(e.g.,steering and braking)and sensors(e.g.,cameras)within a car,and even with high-level decision-making(e.g.,reference driving speed)in the overall transportation system-strategies that will be compatible with the rapidly developing electric and autonomous vehicles.

Integrated Active Suspension and Anti-Lock Braking Control for Four-Wheel-Independent-Drive Electric Vehicles

This paper presents an integrated control scheme for enhancing the ride comfort and handling performance of a four-wheel-independent-drive electric vehicle through the coordination of active suspension system(ASS)and anti-lock braking system(ABS).First,a longitudinal-vertical coupled vehicle dynamics model is established by integrating a road input model.Then the coupling mechanisms between longitudinal and vertical vehicle dynamics are analyzed.An ASS-ABS integrated control system is proposed,utilizing an H∞controller for ASS to optimize load transfer effect and a neural network sliding mode control for ABS implementation.Finally,the effectiveness of the proposed control scheme is evaluated through comprehensive tests conducted on a hardware-in-loop(HIL)test platform.The HIL test results demonstrate that the proposed control scheme can significantly improve the braking performance and ride comfort compared to conventional ABS control methods.

Stochastic sampled-data multi-objective control of active suspension systems for in-wheel motor driven electric vehicles

This paper addresses the sampled-data multi-objective active suspension control problem for an in-wheel motor driven electric vehicle subject to stochastic sampling periods and asynchronous premise variables.The focus is placed on the scenario that the dynamical state of the half-vehicle active suspension system is transmitted over an in-vehicle controller area network that only permits the transmission of sampled data packets.For this purpose,a stochastic sampling mechanism is developed such that the sampling periods can randomly switch among different values with certain mathematical probabilities.Then,an asynchronous fuzzy sampled-data controller,featuring distinct premise variables from the active suspension system,is constructed to eliminate the stringent requirement that the sampled-data controller has to share the same grades of membership.Furthermore,novel criteria for both stability analysis and controller design are derived in order to guarantee that the resultant closed-loop active suspension system is stochastically stable with simultaneous𝐻2 and𝐻∞performance requirements.Finally,the effectiveness of the proposed stochastic sampled-data multi-objective control method is verified via several numerical cases studies in both time domain and frequency domain under various road disturbance profiles.

Output feedback control and parameters influence analysis of active suspension electro-hydraulic servo actuator

The hydraulic servo actuator of heavy vehicle active suspension is investigated to clarify the correlation between system parameters and the control characteristics of active suspension hydraulic servo system.Accordingly, a nonlinear physical model of electro-hydraulic servo active suspension system is built.Compared with the conventional nonlinear modeling, the model in this study considers the asymmetry of working areas caused by single rod hydraulic cylinder in the suspension system.In accordance with the model, a nonlinear output feedback controller based on backstepping is designed, and the effectiveness of the controller is proved based on the experimental platform.The dynamic response curve of the electro-hydraulic servo control system under the change of parameters is generated based on the simulation model.The sensitivity of electro-hydraulic servo control performance to the change of system physical parameters is investigated, and two evaluation indexes are proposed to quantify and compare the effect of all physical parameter changes on position control system.As revealed by the results, the position control characteristics of suspension actuator are more sensitive to the changes of flow gain of the servo valve, system supply oil pressure and effective working areas of cylinder, and the two evaluation indexes are over 10 times higher than other physical parameters.

Improving rail vehicle dynamic performance with active suspension

Today,it is difficult to further improve the dynamic performance of rail vehicles with conventional passive suspension.Also,simplified vehicle respectively running gear layouts that significantly could reduce vehicle weights are difficult to realize with modern requirements on passenger vibration comfort and wheel and rail wear.Active suspension is a powerful technology that can improve the vehicle dynamic performance and make simplified vehicle concepts possible.The KTH Railway group has,together with external partners,investigated active suspensions both numerically and experimentally for 15 years.The paper provides a summary of the activities and the most important findings.One major project carried out in close collaboration with the vehicle manufacturer Bombardier and the Swedish Transport Administration was the Green Train project,where a 2-car EMU test bench was used to demonstrate different active technologies.In ongoing projects,a concept of single axle-single suspension running gear is developed with active suspension both for comfort improvement and reduced wheel wear in curves.The results from on-track tests in the Green Train project were so good that the technology is now implemented in commercial trains and the simulation results for the single-axle running gear are very promising.

Decentralized Dynamic Event-Triggered Communication and Active Suspension Control of In-Wheel Motor Driven Electric Vehicles with Dynamic Damping

This paper addresses the co-design problem of decentralized dynamic event-triggered communication and active suspension control for an in-wheel motor driven electric vehicle equipped with a dynamic damper. The main objective is to simultaneously improve the desired suspension performance caused by various road disturbances and alleviate the network resource utilization for the concerned in-vehicle networked suspension system. First, a T-S fuzzy active suspension model of an electric vehicle under dynamic damping is established. Second,a novel decentralized dynamic event-triggered communication mechanism is developed to regulate each sensor's data transmissions such that sampled data packets on each sensor are scheduled in an independent manner. In contrast to the traditional static triggering mechanisms, a key feature of the proposed mechanism is that the threshold parameter in the event trigger is adjusted adaptively over time to reduce the network resources occupancy. Third, co-design criteria for the desired event-triggered fuzzy controller and dynamic triggering mechanisms are derived. Finally, comprehensive comparative simulation studies of a 3-degrees-of-freedom quarter suspension model are provided under both bump road disturbance and ISO-2631 classified random road disturbance to validate the effectiveness of the proposed co-design approach. It is shown that ride comfort can be greatly improved in either road disturbance case and the suspension deflection, dynamic tyre load and actuator control input are all kept below the prescribed maximum allowable limits, while simultaneously maintaining desirable communication efficiency.

Active suspension control of a one-wheel car model using single input rule modules fuzzy reasoning and a disturbance observer

This paper presents the construction of an active suspension control of a one-wheel car model using fuzzy reasoning and a disturbance observer. The one-wheel car model to be treated here can be approximately described as a nonlinear two degrees of freedom system subject to excitation from a road profile. The active control is designed as the fuzzy control inferred by using single input rule modules fuzzy reasoning, and the active control force is released by actuating a pneumatic actuator. The excitation from the road profile is estimated by using a disturbance observer, and the estimate is denoted as one of the variables in the precondition part of the fuzzy control rules. A compensator is inserted to counter the performance degradation due to the delay of the pneumatic actuator. The experimental result indicates that the proposed active suspension system improves much the vibration suppression of the car model. Key words One-wheel car model - Active suspension system - Single input rule modules fuzzy reasoning - Pneumatic actuator - Disturbance observer Document code A CLC number TH16

Fuzzy Chaos Control for Vehicle Lateral Dynamics Based on Active Suspension System

The existing research of the active suspension system（ASS） mainly focuses on the different evaluation indexes and control strategies. Among the different components, the nonlinear characteristics of practical systems and control are usually not considered for vehicle lateral dynamics. But the vehicle model has some shortages on tyre model with side-slip angle, road adhesion coefficient, vertical load and velocity. In this paper, the nonlinear dynamic model of lateral system is considered and also the adaptive neural network of tire is introduced. By nonlinear analysis methods, such as the bifurcation diagram and Lyapunov exponent, it has shown that the lateral dynamics exhibits complicated motions with the forward speed. Then, a fuzzy control method is applied to the lateral system aiming to convert chaos into periodic motion using the linear-state feedback of an available lateral force with changing tire load. Finally, the rapid control prototyping is built to conduct the real vehicle test. By comparison of time response diagram, phase portraits and Lyapunov exponents at different work conditions, the results on step input and S-shaped road indicate that the slip angle and yaw velocity of lateral dynamics enter into stable domain and the results of test are consistent to the simulation and verified the correctness of simulation. And the Lyapunov exponents of the closed-loop system are becoming from positive to negative. This research proposes a fuzzy control method which has sufficient suppress chaotic motions as an effective active suspension system.

A Novel Energy-regenerative Active Suspension for Vehicles

In order to regenerate electric power from the vibration excited by road unevenness,a novel energy- regenerative active suspension for vehicles was proposed with the description of its structure and its working principle with two modes switched in different operating conditions.Then,the novel active system was modeled and simulated to show the performance improvement in ride comfort in its electrical motor mode.Finally,the performance tests of the actuator prototype were carried out,which proves its capability for damping in its regenerative braking mode.The research results can provide useful guidance for the similar electrical active suspension design and development.

Sampled-Data Asynchronous Fuzzy Output Feedback Control for Active Suspension Systems in Restricted Frequency Domain

This paper proposes a novel sampled-data asynchronous fuzzy output feedback control approach for active suspension systems in restricted frequency domain.In order to better investigate uncertain suspension dynamics,the sampleddata Takagi-Sugeno(T-S)fuzzy half-car active suspension(HCAS)system is considered,which is further modelled as a continuous system with an input delay.Firstly,considering that the fuzzy system and the fuzzy controller cannot share the identical premises due to the existence of input delay,a reconstructed method is employed to synchronize the time scales of membership functions between the fuzzy controller and the fuzzy system.Secondly,since external disturbances often belong to a restricted frequency range,a finite frequency control criterion is presented for control synthesis to reduce conservatism.Thirdly,given a full information of state variables is hardly available in practical suspension systems,a two-stage method is proposed to calculate the static output feedback control gains.Moreover,an iterative algorithm is proposed to compute the optimum solution.Finally,numerical simulations verify the effectiveness of the proposed controllers.

Signal frequency based self－tuning fuzzy controller for semi－active suspension system

A new kind of fuzzy control scheme, based on the identification of the signal' s main frequency and the behavior of the ER damper, is proposed to control the semi-active suspension system. This method ad-justs the fuzzy controller to achieve the best isolation effect by analyzing the main frequency' s characters and inspecting the change of system parameters. The input of the fuzzy controller is the main frequency and the op-timal damping ratio is the output. Simulation results indicated that the proposed control method is very effec-tive in isolating the vibration.

Pneumatic active suspension system for a one-wheel car model using fuzzy reasoning and a disturbance observer

This paper presents the construction of a pneumatic active suspension system for a one-wheel car model using fuzzy reasoning and a disturbance observer. The one-wheel car model can be approximately described as a nonlinear two degrees of freedom system subject to excitation from a road profile. The active control is composed of fuzzy and disturbance controls, and the active control force is constructed by actuating a pneumatic actuator. A phase lead-lag compensator is inserted to counter the performance degradation due to the delay of the pneumatic actuator. The experimental result indicates that the proposed active suspension improves much the vibration suppression of the car model.

Automobile active suspension system with fuzzy control

A quarter-automobile active suspension model was proposed. High speed on/off solenoid valves were used as control valves and fuzzy control was chosen as control method . Based on force analyses of system parts, a mathematical model of the active suspension system was established and simplified by linearization method. Simulation study was conducted with Matlab and three scale coefficients of fuzzy controller (ke, kec, ku) were acquired. And an experimental device was designed and produced. The results indicate that the active suspension system can achieve better vibration isolation performance than passive suspension system, the displacement amplitude of automobile body can be reduced to 55%. Fuzzy control is an effective control method for active suspension system.

Static-Output-Feedback Based Robust Fuzzy Wheelbase Preview Control for Uncertain Active Suspensions With Time Delay and Finite Frequency Constraint

This paper proposes a static-output-feedback based robust fuzzy wheelbase preview control algorithm for uncertain active suspensions with time delay and finite frequency constraint.Firstly,a Takagi-Sugeno(T-S)fuzzy augmented model is established to formulate the half-car active suspension system with consideration of time delay,sprung mass variation and wheelbase preview information.Secondly,in view of the resonation between human’s organs and vertical vibrations in the frequency range of 4–8 Hz,a finite frequency control criterion in terms of H∞norm is developed to improve ride comfort.Meanwhile,other mechanical constraints are also considered and satisfied via generalized H2 norm.Thirdly,in order to maintain the feasibility of the controller despite of some state variables are not online-measured,a two stage approach is adopted to derive a static output feedback controller.Finally,numerical simulation results illustrate the excellent performance of the proposed controller.

Computer simulation of active suspension based on the full-vehicle model

Abstract: The current method to solve the problem of active suspension control for a vehicle is often dealt with a quarter-car or half-car model. But it is not enough to use this kind of model for practical applications. In this paper, based on considering the influence of factors such as, seat and passengers, a MDOF(multi-degree-of-freedom) model describing the vehicle motion is set up. The MODF model, which is 8DOF of four independent suspensions and four wheel tracks, is more applicable by comparison of its analysis result with some conventional vehicle models. Therefore, it is more suitable to use the 8DOF full-car model than a conventional 4DOF half-car model in the active control design for car vibration. Based on the derived 8DOF model, a controller is designed by using LQ (linear quadratic ) control theory, and the appropriate control scheme is selected by testing various performance indexes. Computer simulation is carried out for a passenger car running on a road with step disturbance and random road disturbance expressed by Power Spectral Density (PSD). Vibrations corresponding to ride comfort are derived under the foregoing road disturbances. The response results for uncontrolled and controlled system are compared. The response of vehicle vibration is greatly suppressed and quickly damped, which testifies the effect of the active suspension. The results achieved for various controllers are compared to investigate the influence of different control schemes on the control effect.

Design and optimization of a semi-active suspension system for railway applications

The present work focused on the application of innovative damping technologies in order to improve railway vehicle performances in terms of dynamic stability and comfort. As a benchmark case-study, the secondary sus- pension stage was selected and different control techniques were investigated, such as skyhook, dynamic compensation, and sliding mode control. The final aim was to investigate which control schemes are suitable for optimal exploitation of the non-linear behavior of the actuators. The performance improvement achieved by adoption of the semi-active dampers on a standard high-speed train was evaluated in terms of passenger comfort. Different control strategies have been investigated by comparing a simple SISO （single input single output） regulator based on the skyhook damper ap- proach with a centralized regulator. The centralized regulator allows for the estimation of a near optimal set of control forces that minimize car-body accelerations with respect to constraints imposed by limited performance of semi-active actuators. Simulation results show that best results is obtained using a mixed approach that considers the simultaneous applications of model based and feedback compensation control terms.

Linear Quadratic Integral Control for the Active Suspension of Vehicle

The quarter model of an active suspension is established in the form of controllable autoregressive moving average （CARMA） model. An accelerometer can be mounted on the wheel hub for measuring road disturbance; this signal is used to identify the CARMA model parameters by recursive forgetting factors least square method. The linear quadratic integral （LQI） control method for the active suspension is presented. The LQI control algorithm is fit for vehicle suspension control, for the control performance index can comprise multi controlled variables. The simulation results show that the vertical acceleration and suspension travel both are decreased with the LQI control in the low frequency band, and the suspension travel is increased with the LQI control in the middle or high frequency band. The suspension travel is very small in the middle or high frequency band, the suspension bottoming stop will not happen, so the vehicle ride quality can be improved apparently by the LQI control.

Robust Active Suspension Design Subject to Vehicle Inertial Parameter Variations

This paper presents an approach in designing a robust controller for vehicle suspensions considering changes in vehicle inertial properties. A four-degree-of-freedom half-car model with active suspension is studied in this paper, and three main performance requirements are considered. Among these requirements, the ride comfort performance is optimized by minimizing the Ho~ norm of the transfer function from the road disturbance to the sprung mass acceleration, while the road holding performance and the suspension deflection limitation are guaranteed by constraining the generalized H2 （GH2） norms of the transfer functions from the road disturbance to the dynamic tyre load and the suspension deflection to be less than their hard limits, respectively. At the same time, the controller saturation problem is considered by constraining its peak response output to be less than a given limit using the GH2 norm as well. By solving the finite number of linear matrix inequalities （LMIs） with the minimization optimization procedure, the controller gains, which are dependent on the time-varying inertial parameters, can be obtained. Numerical simulations on both frequency and bump responses show that the designed parameter-dependent controller can achieve better active suspension performance compared with the passive suspension in spite of the variations of inertial parameters.

A study of active suspension based on full DOF vehicle model

This paper presents a MDOF (multi-degree-of-freedom) model to describe the vehicle motion, considering influences of factors such as, seat and passengers. The model is four-independent-suspension and four-wheel-track with 8DOF, and has proved more appropriate compared with some conventional vehicle models. Based on the derived 8DOF model, a controller for this model is designed by the use of H∞ control theory, Furthermore the appropriate control scheme is selected by testing various performance indexes. The study shows that satisfying results can be obtained by using an appropriate vehicle model, even if a low order controller and a general control strategy are adopted.

Active suspension with optimal control based on a full vehicle model

The 7-DOF model of a full vehicle with an active suspension is developed in this paper.The model is written into the state equation style.Actuator forces are treated as inputs in the state equations.Based on the basic optimal control theory,the optimal gains for the control system are figured out.So an optimal controller is developed and implemented using Matlab/Simulink,where the Riccati equation with coupling terms is deduced using the Hamilton equation.The all state feedback is chosen for the controller.The gains for all vehicle variables are traded off so that majority of indexes were up to optimal.The active suspension with optimal control is simulated in frequency domain and time domain separately,and compared with a passive suspension.Throughout all the simulation results,the optimal controller developed in this paper works well in the majority of instances.In all,the comfort and ride performance of the vehicle are improved under the active suspension with optimal control.