Performance analysis of air suspension system of heavy truck with semi-active fuzzy control

In order to analyze and evaluate the performance of the air suspension system of heavy trucks with semi-active fuzzy control, a three-dimensional nonlinear dynamical model of a typical heavy truck with 16-DOF（degree of freedom） is established based on Matlab/Simulink software. The weighted root-mean-square（RMS） acceleration responses of the vertical driver ＇s seat, the pitch and roll angle of the cab, and the dynamic load coefficient（DLC） are chosen as objective functions, and the air suspension system is optimized and analyzed by the semi-active fuzzy control algorithm when vehicles operate under different operation conditions. The results show that the influence of the roll angle of the cab on the heavy truck ride comfort is clear when vehicles move on the road surface conditions of the ISO level D and ISO level E at a velocity over 27.5 m/s. The weighted RMS acceleration responses of vertical driver＇ s seat, the pitch and roll angle of the cab are decreased by 24%, 30% and 25%, respectively,when vehicles move on the road surface condition of the ISO level B at a velocity of 20 m/s. The value of the DLC also significantly decreases when vehicles operate under different operation conditions. Particularly, the DLC value of the tractor driver axle is greatly reduced by 27.4% when the vehicle operates under a vehicle fully-loaded condition on the road surface condition of ISO level B at a velocity of 27.5 m/s.

Hierarchical Control of Ride Height System for Electronically Controlled Air Suspension Based on Variable Structure and Fuzzy Control Theory

The current research of air suspension mainly focuses on the characteristics and design of the air spring. In fact, electronically controlled air suspension （ECAS） has excellent performance in flexible height adjustment during different driving conditions. However, the nonlinearity of the ride height adjusting system and the uneven distribution of payload affect the control accuracy of ride height and the body attitude. Firstly, the three-point measurement system of three height sensors is used to establish the mathematical model of the ride height adjusting system. The decentralized control of ride height and the centralized control of body attitude are presented to design the ride height control system for ECAS. The exact feedback linearization method is adopted for the nonlinear mathematical model of the ride height system. Secondly, according to the hierarchical control theory, the variable structure control （VSC） technique is used to design a controller that is able to adjust the ride height for the quarter-vehicle anywhere, and each quarter-vehicle height control system is independent. Meanwhile, the three-point height signals obtained by three height sensors are tracked to calculate the body pitch and roll attitude over time, and then by calculating the deviation of pitch and roll and its rates, the height control correction is reassigned based on the fuzzy algorithm. Finally, to verify the effectiveness and performance of the proposed combined control strategy, a validating test of ride height control system with and without road disturbance is carried out. Testing results show that the height adjusting time of both lifting and lowering is over 5 s, and the pitch angle and the roll angle of body attitude are less than 0.15°. This research proposes a hierarchical control method that can guarantee the attitude stability, as well as satisfy the ride height tracking system.

Fuzzy Sliding Mode Control for the Vehicle Height and Leveling Adjustment System of an Electronic Air Suspension

The accurate control for the vehicle height and leveling adjustment system of an electronic air suspension(EAS) still is a challenging problem that has not been effectively solved in prior researches. This paper proposes a new adaptive controller to control the vehicle height and to adjust the roll and pitch angles of the vehicle body(leveling control) during the vehicle height adjustment procedures by an EAS system. A nonlinear mechanism model of the full?car vehicle height adjustment system is established to reflect the system dynamic behaviors and to derive the system optimal control law. To deal with the nonlinear characters in the vehicle height and leveling adjustment processes, the nonlinear system model is globally linearized through the state feedback method. On this basis, a fuzzy sliding mode controller(FSMC) is designed to improve the control accuracy of the vehicle height adjustment and to reduce the peak values of the roll and pitch angles of the vehicle body. To verify the effectiveness of the proposed control method more accurately, the full?car EAS system model programmed using AMESim is also given. Then, the co?simulation study of the FSMC performance can be conducted. Finally, actual vehicle tests are performed with a city bus, and the test results illustrate that the vehicle height adjustment performance is effectively guaranteed by the FSMC, and the peak values of the roll and pitch angles of the vehicle body during the vehicle height adjustment procedures are also reduced significantly. This research proposes an effective control methodology for the vehicle height and leveling adjustment system of an EAS, which provides a favorable control performance for the system.

A Hybrid Approach to Modeling and Control of Vehicle Height for Electronically Controlled Air Suspension

The control problems associated with vehicle height adjustment of electronically controlled air suspension （ECAS） still pose theoretical challenges for researchers, which manifest themselves in the publications on this subject over the last years. This paper deals with modeling and control of a vehicle height adjustment system for ECAS, which is an example of a hybrid dynamical system due to the coexistence and coupling of continuous variables and discrete events. A mixed logical dynamical （MLD） modeling approach is chosen for capturing enough details of the vehicle height adjustment process. The hybrid dynamic model is constructed on the basis of some assumptions and piecewise linear approximation for components nonlinearities. Then, the on-off statuses of solenoid valves and the piecewise approximation process are described by propositional logic, and the hybrid system is transformed into the set of linear mixed-integer equalities and inequalities, denoted as MLD model, automatically by HYSDEL. Using this model, a hybrid model predictive controller （HMPC） is tuned based on online mixed-integer quadratic optimization （MIQP）. Two different scenarios are considered in the simulation, whose results verify the height adjustment effectiveness of the proposed approach. Explicit solutions of the controller are computed to control the vehicle height adjustment system in realtime using an offline multi-parametric programming technology （MPT）, thus convert the controller into an equivalent explicit piecewise affine form. Finally, bench experiments for vehicle height lifting, holding and lowering procedures are conducted, which demonstrate that the HMPC can adjust the vehicle height by controlling the on-off statuses of solenoid valves directly. This research proposes a new modeling and control method for vehicle height adjustment of ECAS, which leads to a closed-loop system with favorable dynamical properties.

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.

Buildup and simulation of a truck model with rear air suspension using leaf spring as guiding rod

A new kind of commercial truck is presented, which has rear air suspension using leaf spring as guiding rod instead of original leaf spring. ADAMS/Car is used as a tool to build the whole truck model. The designed truck＇s constant-radius cornering analysis and its ride performance simulation analysis under B class random road condition are carried out according to national experimental method standards. Compared the simulation results with the field test results indicate that performance index of the designed air suspension truck＇ s constant-radius cornering and its ride performance meets the design requirements and reaches its prospective target. And resuhs from simulation are similar to those from tests in value and trend, which indicates the virtual prototype is correct. The model can be used further to opti,nize suspension parameters and do some design work on the control system of air suspension.

Uncertainty Analysis and Optimization of Quasi-Zero Stifness Air Suspension Based on Polynomial Chaos Method

To improve the vibration isolation performance of suspensions,various new structural forms of suspensions have been proposed.However,there is uncertainty in these new structure suspensions,so the deterministic research cannot refect the performance of the suspension under actual operating conditions.In this paper,a quasi-zero stifness isolator is used in automotive suspensions to form a new suspension−quasi-zero stifness air suspension(QZSAS).Due to the strong nonlinearity and structural complexity of quasi-zero stifness suspensions,changes in structural parameters may cause dramatic changes in suspension performance,so it is of practical importance to study the efect of structural parameter uncertainty on the suspension performance.In order to solve this problem,three suspension structural parameters d_(0),L_(0) and Pc_(0) are selected as random variables,and the polynomial chaos expansion(PCE)theory is used to solve the suspension performance parameters.The sensitivity of the performance parameters to diferent structural parameters was discussed and analyzed in the frequency domain.Furthermore,a multi-objective optimization of the structural parameters d_(0),L_(0) and Pc_(0) of QZSAS was performed with the mean and variance of the root-mean-square(RMS)acceleration values as the optimization objectives.The optimization results show that there is an improvement of about 8%−1_(0)%in the mean value and about 4_(0)%−55%in the standard deviation of acceleration(RMS)values.This paper verifes the feasibility of the PCE method for solving the uncertainty problem of complex nonlinear systems,which provide a reference for the future structural design and optimization of such suspension systems.

Applying machine learning for cars’semi-active air suspension under soft and rigid roads

To improve the ride quality and enhance the control efficiency of cars’semi-active air suspensions(SASs)under various surfaces of soft and rigid roads,a machine learning(ML)method is proposed based on the optimized rules of the fuzzy control(FC)method and car dynamic model for application in SASs.The root-mean-square(RMS)acceleration of the driver’s seat and car’s pitch angle are chosen as the objective functions.The results indicate that a soft surface obviously influences a car’s ride quality,particularly when it is traveling at a high-velocity range of over 72 km/h.Using the ML method,the car’s ride quality is improved as compared to those of FC and without control under different simulation conditions.In particular,compared with those cars without control,the RMS acceleration of the driver’s seat and car’s pitch angle using the ML method are respectively reduced by 30.20% and 19.95% on the soft road and 34.36% and 21.66% on the rigid road.In addition,to optimize the ML efficiency,its learning data need to be updated under all various operating conditions of cars.

Vehicle height control of electronic air suspension system based on mixed logical dynamical modelling

Due to the coexistence and coupling of continuous variables and discrete events, the vehicle height adjustment process of electronic air suspension system can be regarded as a typical hybrid system. Therefore, the hybrid system theory was applied to design a novel vehicle height control strategy in this paper. A nonlinear mechanism model of the vehicle height adjustment system was established based on vehicle system dynamics and thermodynamic theory for variable-mass gas charge/discharge system. In order to model both the continuous/discrete dynamics of vehicle height adjustment process and the on-off statuses switching of solenoid valves, the framework of mixed logical dynamical(MLD) modelling was used. On the basis of the vehicle height adjustment control strategy, the MLD model of the adjustment process was built by introducing auxiliary logical variables and auxiliary continuous variables. Then, the co-simulation of the nonlinear mechanism model and the MLD model was conducted based on the compiling of HYSDEL. The simulation and experimental results show that the proposed control strategy can not only adjust the vehicle height effectively, but also achieve the on-off statuses direct control of solenoid valves.

Modeling and test on height adjustment system of electrically-controlled air suspension for agricultural vehicles

To reduce the damages of pavement,vehicle components and agricultural product during transportation,an electric control air suspension height adjustment system of agricultural transport vehicle was studied by means of simulation and bench test.For the oscillation phenomenon of vehicle height in driving process,the mathematical model of the vehicle height adjustment system was developed,and the controller of vehicle height based on single neuron adaptive PID control algorithm was designed.The control model was simulated via Matlab/Simulink,and bench test was conducted.Results show that the method is feasible and effective to solve the agricultural vehicle body height unstable phenomenon in the process of switching.Compared with other PID algorithms,the single neuron adaptive PID control in agricultural transport vehicle has shorter response time,faster response speed and more stable switching state.The stability of the designed vehicle height adjustment system and the ride comfort of agricultural transport vehicle were improved.

Height stability control of a large sprayer body based on air suspension using the sliding mode approach

When a high clearance self-propelled sprayer sprays,the sprung mass varies with the amount of liquid in the tank,which causes a change in the height of the sprayer body.This change not only is harmful to the sprayer ride comfort,but also has a greater impact on the sprayer application quality.In this paper,a large-scale high clearance self-propelled sprayer with air suspension was taken as the research object.Based on vehicle dynamics and air thermodynamics theory,a mathematical model of air spring inflation/deflation was established,then a 3 degree of freedom(3-dof)vertical dynamics model of sprayer air suspension was built.On this basis,the height control strategy of the sprayer body was formulated.Due to the nonlinear characteristics of air suspension,two control algorithms,namely sliding mode control and the on-off control,were used to design the suspension height stability controller,respectively.A simulation experiment was carried out by using the sprayer spraying crops as an example.The simulation experiment results showed that sliding mode control and on-off control could track and stabilize the height of the sprayer body when it changed under no excitation and D-grade road random excitation.However,due to strong nonlinearity and hysteresis of the pneumatic system,on-off control precision was poor.With the on-off control method,further reduction of the sprung mass would change the internal parameters of the pneumatic system,cause the air spring over deflation,even worse,the over deflation phenomenon presented a serious trend and cause system instability under random road excitation.Compared with on-off control method,sliding mode control approach had good control ability and precision due to its robustness to change in model parameters.The research will provide a reference for the height stability adjustment of large high clearance self-propelled sprayers during spraying and dosing operations.

Analytical calculation method and simulation of deformation and stress of Z-type guide arm for interconnected air suspensions

To design and check the strength of the Z-type guide arm of interconnected air suspensions for semi-trailers rapidly and effectively,this paper proposes the analytical calculation methods of its deformation and stress.First,based on the guide arm structure,it is marked as two parts by its mountpoint on the axle as the boundary.The part containing the eye was marked as Arm-1.The other part was marked as Arm-2.Then the analytical formulas of their stiffness and stress were derived,respectively.With a case study,the deformation and the stress were computed and simulated.The results show that the values computed are close to those simulated.The relative deviations are not more than 5.0%.The results show that the analytical formulas are acceptable.Moreover,it can be seen that for the superimposed Arm-1,when the other structural parameters are fixed,the position of the maximum stress is affected by the thickness ratio of the end thickness to the root thickness for each piece.Finally,a stiffness test was performed on the Z-type guide arm.The results show that the computed stiffness values are closed to those tested and the relative deviations are not more than 3.5%.This further verified the validity of the established model and methods.

Vehicle height and leveling control of electronically controlled air suspension using mixed logical dynamical approach

Vehicle height and leveling control of electronically controlled air suspension(ECAS) still poses theoretical challenges for researchers that have not been adequately addressed in prior research. This paper investigates the design and verification of a new controller to adjust the vehicle height and to regulate the roll and pitch angles of the vehicle body(leveling control) during the height adjustment procedures. A nonlinear mechanism model of the vehicle height adjustment system is formulated to describe the dynamic behaviors of the system. By using mixed logical dynamical(MLD) approach, a novel control strategy is proposed to adjust the vehicle height by controlling the on-off statuses of the solenoid valves directly. On this basis, a correction algorithm is also designed to regulate the durations of the on-off statuses of the solenoid valves based on pulse width modulated(PWM) technology, thus the effective leveling control of the vehicle body can be guaranteed. Finally, simulations and vehicle tests results are presented to demonstrate the effectiveness and applicability of the proposed control methodology.

Stiffness-damping matching method of an ECAS system based on LQG control

A novel method of matching stiffness and continuous variable damping of an ECAS(electronically controlled air suspension) based on LQG(linear quadratic Gaussian) control was proposed to simultaneously improve the road-friendliness and ride comfort of a two-axle school bus.Taking account of the suspension nonlinearities and target-height-dependent variation in suspension characteristics,a stiffness model of the ECAS mounted on the drive axle of the bus was developed based on thermodynamics and the key parameters were obtained through field tests.By determining the proper range of the target height for the ECAS of the fully-loaded bus based on the design requirements of vehicle body bounce frequency,the control algorithm of the target suspension height(i.e.,stiffness) was derived according to driving speed and road roughness.Taking account of the nonlinearities of a continuous variable semi-active damper,the damping force was obtained through the subtraction of the air spring force from the optimum integrated suspension force,which was calculated based on LQG control.Finally,a GA(genetic algorithm)-based matching method between stepped variable damping and stiffness was employed as a benchmark to evaluate the effectiveness of the LQG-based matching method.Simulation results indicate that compared with the GA-based matching method,both dynamic tire force and vehicle body vertical acceleration responses are markedly reduced around the vehicle body bounce frequency employing the LQG-based matching method,with peak values of the dynamic tire force PSD(power spectral density) decreased by 73.6%,60.8% and 71.9% in the three cases,and corresponding reduction are 71.3%,59.4% and 68.2% for the vehicle body vertical acceleration.A strong robustness to variation of driving speed and road roughness is also observed for the LQG-based matching method.

Simulation and analysis of a Truck Model’s ride comfort based on fuzzy adaptive control theory

This paper tried to analyse and verify the fuzzy adaptive control strategy of electronic control air suspension system for heavy truck. Created the seven-freedoms vehicle suspension model, and the road input model; with Matlab/Simulink toolboxes and modules, built dynamical system simulation model for heavy truck with air suspension, fuzzy adaptive control model, height control model for air spring, and intelligent control and analyse on root mean square value of acceleration of gravity center of the vehicle under excitation of road. Results show that the fuzzy control had less help to the body vibration on the better pavement, but had the better benefit on the bad road, and the vehicle’s root mean square value of acceleration of gravity center is less than passive suspension’s obviously.