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.

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.

A Review of Electromagnetic Energy Regenerative Suspension System&Key Technologies

The active suspension has undoubtedly improved the performance of the vehicle,however,the trend of“lowcarbonization,intelligence,and informationization”in the automotive industry has put forward higher and more urgent requirements for the suspension system.The automotive industry and researchers favor active energy regeneration suspension technology with safety,comfort,and high energy regenerative efficiency.In this paper,we review the research progress of the structure form,optimization method,and control strategy of electromagnetic energy regenerative suspension.Specifically,comparing the pros and cons of the existing technology in solving the contradiction between dynamic performance and energy regeneration.In addition,the development trend of electromagnetic energy regenerative suspension in the field of structure form,optimization method,and control technology prospects.

Vehicle Ride Comfort Based on Matching Suspension System

The existing investigations of vehicle ride comfort mainly include motion characteristics analysis based on creating a multi-body dynamic simulation model,and the parameters analysis to improve the suspension control for the target.In the study of creating multi-body dynamics simulation models,there is usually without considering calibration and test verification,which make it difficult to ensure the production of engineering.In the study of improving the suspension control parameters for the target,there is a lack of systematic match about comfortable and human characteristics,so it is difficult to implement in the field of driving and leading the vehicle design.In this paper,based on the different characteristic of suspension system that effects on the vehicle ride comfort, according to the suspension system dynamic mechanism,the research methods of vehicle road test,bench test and CAE simulation is used,at the same time,several sensitivity analysis of vehicle ride comfort related to suspension stiffness and damping and speed is made. As a result,the key suspension systematic parameters are given that have important impact on vehicle ride comfort.Through matching parameters,a calibration analysis of suspension system based on human comfort is obtained.The analysis results show that the analysis methods for the design target of making the vehicle with best comfort are effective.On the basis of the theory study,five suspension parameter matching principles are explored to promise the vehicle with perfect ride comfort,which also provide theoretical basis and design methods for the passenger car best match of suspension system stiffness and damping.The research results have the promotional value of practicability and a wide range of engineering application.

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.

Life Prediction Based on Transient Dynamics Analysis of Van Semi-trailer with Air Suspension System

The early fatigue damage in the van-body of the semi-trailer is often caused by the unique mechanical characteristics and the dynamic impact of the loads.The traditional finite element method with static strength analysis cannot support the fatigue design of van-body;thus,the dynamics analysis should be adopted for the endurance performance.The accurate dynamics model to describe the transient impacts of all kinds of uneven road and the proper system transfer functions to calculate the load transfer effects from tire to van-body are two critical factors for transient dynamics analysis.In order to evaluate the dynamic performance,the dynamics model of the trailer with the air suspension is brought forward.Then the analysis method of the power spectral density （PSD） is set up to study the transient responses of the road dynamic impacts.The transient responses transferred from axles to van-body are calculated,such as dynamic stress,dynamic RMS acceleration,and dynamic load factors.Based on the above dynamic responses,the fatigue life of van-body is predicted with the finite element analysis （FEA） method.Applying the test parameters of the trailer with air suspension,the simulation system with Matlab/Simulink is constructed to describe the dynamic responses of the impacts of the tested PSD of the vehicle axles,and then the fatigue life is predicted with FEA method.The simulated results show that the vibration level of the van-body with air suspension is reduced and the fatigue life is improved.The real vehicle tests on different roads are carried out,and the test results validate the accuracy of the simulation system.The proposed fatigue life prediction method is effective for the virtual design of auto-body.

Finite Frequency Fuzzy H∞Control for Uncertain Active Suspension Systems With Sensor Failure

This paper investigates the problem of finite frequency fuzzy H_∞ control for uncertain active vehicle suspension systems, in which sensor failure is taken into account. TakagiSugeno(T-S) fuzzy model is established for considered suspension systems. In order to describe the sensor fault effectively, a corresponding model is introduced. A vital performance index,H_∞ performance, is utilized to measure the drive comfort. In the framework of Kalman-Yakubovich-Popov theory, the H_∞ norm from external perturbation to controlled output is optimized effectively in the frequency domain of 4 Hz-8 Hz to enhance ride comfort level. Meanwhile, three suspension constrained requirements, i.e., ride comfort level, manipulation stability,suspension deflection are also guaranteed. Furthermore, sufficient conditions are developed to design a fuzzy controller to guarantee the desired performance of active suspension systems. Finally, the proposed control scheme is applied to a quarter-vehicle active suspension, and simulation results are given to illustrate the effectiveness of the proposed approach.

Electrorheological Damper and Its Application for Semi-Active Suspension System

A semi-active control of vehicle suspension system with eleetrorheolngieal （ER） damper is presented. ER fluid characteristics are introduced based on the Bingham plasticity model first. Then ER damper working force is given. Finally a quarter car model with ER damper is constructed. The skyhook control strategy is adopted to simulate the amplitude-frequency characteristics and the vibration of suspension system under random road excitation on the basis of ER damper characteristics. The response curves of the vertical acceleration, the suspension dynamic working space and the tyre dynamic loading are obtained. Simulation results show that the acceleration is reduced effectively and then the ride comfort is improved by the skyhook control law.

μ-Syntheses of Suspension Systems for EMS and EDS Maglev Vehicles

Under model uncertainty and complex disturbance, the robust control strategy should be used in suspension control systems for various Maglev vehicles to obtain ride comfort of passengers. In this paper, the robust controllers are synthesized using μ approach for levitation system of electromagnetic Maglev vehicle and active suspension system of super conducting Maglev vehicle. The numerical simulations for different parameter perturbations and different disturbances are accomplished, and a comparison of μ control and H ∞ control is performed. The simulation results show that, both H ∞ control and μ control for two kinds of Maglev vehicles exhibit good stability robustness to plant model uncertainty, but μ control exhibits better performance robustness than H ∞ control, therefore better ride quality could be obtained by μ control.

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.

Deep learning-based fault diagnostic network of high-speed train secondary suspension systems for immunity to track irregularities and wheel wear

Fault detection and isolation of high-speed train suspension systems is of critical importance to guarantee train running safety. Firstly, the existing methods concerning fault detection or isolation of train suspension systems are briefly reviewed and divided into two categories, i.e., model-based and data-driven approaches. The advantages and disadvantages of these two categories of approaches are briefly summarized. Secondly, a 1D convolution network-based fault diagnostic method for highspeed train suspension systems is designed. To improve the robustness of the method, a Gaussian white noise strategy(GWN-strategy) for immunity to track irregularities and an edge sample training strategy(EST-strategy) for immunity to wheel wear are proposed. The whole network is called GWN-EST-1 DCNN method. Thirdly, to show the performance of this method, a multibody dynamics simulation model of a high-speed train is built to generate the lateral acceleration of a bogie frame corresponding to different track irregularities, wheel profiles, and secondary suspension faults. The simulated signals are then inputted into the diagnostic network, and the results show the correctness and superiority of the GWN-EST-1DCNN method. Finally,the 1DCNN method is further validated using tracking data of a CRH3 train running on a high-speed railway line.

Performance of a novel energy-regenerative active suspension system

A novel energy-regenerative active suspension(NEAS) system was designed to solve the problem of low energy recovery efficiency caused by frequent alternation of energy-recovery mode and active-control mode in a traditional energyregenerative active suspension(TEAS) system. The energy recovery and active control could be implemented simultaneously in the NEAS. The transforming processes and the corresponding computational formulas of power conversion in the NEAS were provided. The simulation results show that the performances of energy recovery of the NEAS are improved, and the selfsustaining of power supply for the NEAS can be realized.

Analyses and Simulation of Fuzzy Logic Control for Suspension System of a Track Vehicle

The vibration caused by terrible road excitation affects the ride quality and safety of track vehicles. The vibration control of suspension systems is a very important factor for modern track vehicles. A fuzzy logic control for suspension system of a track vehicle is presented. A mechanical model and a system of difft, rential equations of motion taking account of the mass of loading wheel are established. Then the fuzzy logic control is applied to control the vibration of suspension system of track vehicles for sine signal and random road surfaces. Numerical simulation shows that the maximum acceleration of suspension system can be reduced to 44 % of the original value for sine signal road surface, and the mean square root of acceleration of suspension system can be reduced to 21% for random road surface. Therefore, the proposed fuzzy logic control is an efficient method for the suspension systems of track vehicles.

Fuzzy Logic Control for Suspension Systems of Tracked Vehicles

A scheme of fuzzy logic control for the suspension system of a tracked vehicle is presented. A mechanical model for the whole body of a tracked vehicle, which is totally a fifteen-degree-of-freedom system, is established. The model includes the vertical motion, the pitch motion as well as the roll motion of the tracked vehicle. In contrast to most previous studies, the coupling effect among the vertical, the pitch and the roll motions of the suspension system of a tracked vehicle is considered simultaneously. The simulation of fuzzy logic control under road surface with random excitation shows that the acceleration, pitch angle and roll angle of suspension system can be efficiently controlled.

Vibration Control of Vehicle Suspension System by Electrorheological Damper

An overview of electrorheological （ER） fluid characteristics is given. Based on the Bingham plasticity model and a simple parallel-plate model, the operation principle of ER damper is presented and a four-DOF dynamic model of a vehicle suspension is constructed. Then a semi-active control of vehicle suspension system by ER damper is obtained. According to the semi-active control theory, the acceleration frequency characteristic is achieved with Matlab toolbox. Simulation results show that the vibration of the suspension system is well controlled.

A Study of IVECO Automobile Suspension System by Simulation

For analyzing the ride comfort performance, a dynamical model of an IVECO vehicle was built in this paper. The simulation study of the IVECO vehicle suspension performance on random uneven road is carried out by means of the dynamical model. The effects of suspension system parameters on the vehicle ride comfort parameter, i. e. , the root mean square （ RMS） of the vibrating acceleration of the vehicle body, are analyzed. The optimal parameters and initial value of the suspension system can be determined by the model and the method of this paper.

OPTIMAL CONTROL OF AN ACTIVE SUSPENSION SYSTEMEMPLOYING HIGH SPEED ON/OFF SOLENOID VALVE

Previous studies have confirmed that an active suspension system with high speed ON/OFF solenoid valves could provide the same vibration isolation efficiency as that of system with pressure proportional valve. In this study, by using Linear-quadratic optimization technique and Kalman filter method, an optimal regulator controller with a state observer was designed for the proposed system. Simulation and experimental research was conducted on a quarter car model. The simulation analysis of the system frequency characteristic suggested that the peak value of magnitude response curve in the case of system with an optimal controller would be lowered significantly, and the experiment results also showed that an improvement in the vibration isolation effect was obtained in using the designed optimal controller over the sky hook damper controller.

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.

Parameter Identification Based on a Modified PSO Applied to Suspension System

This paper presents a novel modified particle swarm optimization algorithm (MPSO) for both offline and online parametric identification of dynamic models. The MPSO is applied for identifying a suspension system introduced by a quarter-car model. A novel mutation mechanism is employed in MPSO to enhance global search ability and increase convergence speed of basic PSO (BPSO) algorithm. MPSO optimization is used to find the optimum values of parameters by minimizing the sum of squares error. The performance of the MPSO is compared with other optimization methods including BPSO and Genetic Algorithm (GA) in offline parameter identification. The simulating results show that this algorithm not only has advantage of convergence property over BPSO and GA, but also can avoid the premature convergence problem effectively. The MPSO algorithm is also improved to detect and determine the variation of parameters. This novel algorithm is successfully applied for online parameter identification of suspension system.

Design, Development and Testing of an Air Damper to Control the Resonant Response of a SDOF Quarter-Car Suspension System

An air damper possesses the advantages that there are no long term changes in the damping properties, there is no dependence on working temperature and additionally, it has less manufacturing and maintenance costs. As such, an air damper has been designed and developed based on the Maxwell type model concept in the approach of Nishihara and Asami [1]. The cylinder-piston and air-tank type damper characteristics such as air damping ratio and air spring rate have been studied by changing the length and diameter of the capillary pipe between the air cylinder and the air tank, operating air pressure and the air tank volume. A SDOF quarter-car vehicle suspension system using the developed air enclosed cylinder-piston and air-tank type damper has been analyzed for its motion transmissibility characteristics. Optimal values of the air damping ratio at various values of air spring rate have been determined for minimum motion transmissibility of the sprung mass. An experimental setup has been developed for SDOF quarter-car suspension system model using the developed air enclosed cylinder-piston and air-tank type damper to determine the motion transmissibility characteristics of the sprung mass. An attendant air pressure control system has been designed to vary air damping in the developed air damper. The results of the theoretical analysis have been compared with the experimental analysis.