Vehicle Body Acceleration Research Articles

An adaptive backstepping sliding mode control strategy for the magnetorheological semi-active suspension

This paper proposes an adaptive backstepping sliding mode control strategy for addressing nonlinear issues in the semi-active suspension systems, such as uncertainties and external disturbances. Firstly, a hyperbolic tangent model is chosen for parameters identification of the magnetorheological (MR) damper, and a model for the semi-active suspension system is established. Secondly, a control strategy is designed by combining the backstepping and sliding mode control strategies, and adaptive methods are employed to mitigate external disturbances, enhance the robustness of the controller, and estimate system uncertainties. Finally, the stability and controllability of the closed-loop system are verified using Lyapunov theory. Under the road excitations of A-Class, B-Class, and speed bump, the dynamic characteristics of the passive control, backstepping sliding mode control, and adaptive backstepping sliding mode control strategies applied to the MR semi-active suspension are analyzed. The vertical acceleration of vehicle body, suspension dynamic deflection, and tire dynamic load are selected as evaluation indexes, the results indicate that this control strategy significantly improved the ride comfort and handling stability of the vehicle.

Design a new algorithm (iL-GA) to optimize controller parameters for an automotive suspension system

Purpose This paper aims to design a PD controller for an active suspension system to improve the car’s moving smoothness. Design/methodology/approach The controller parameters are optimized by an in-loop genetic algorithm (iL-GA). Unlike previous studies that only used conventional GAs to tune coefficients for the controller, the iL-GA designed in this paper provides outstanding efficiency when determining the optimal value range for the system. The optimal value range of parameters is determined by the in-loop algorithm based on criteria related to systematic errors. The optimal values are then calculated by the GA based on this range instead of an uncertain one. Findings Simulation results show that vehicle body acceleration and displacement values are significantly reduced when using the active suspension system compared to the conventional passive suspension system. The phase difference phenomenon does not occur in the iL-GA situation. In addition, the frequency domain investigation also shows the system’s stability when using iL-GA instead of conventional GA. Originality/value To the best of the authors’ knowledge, this is a new application that provides positive effects to the suspension controller. This algorithm can be applied to tune coefficients for direct controllers in the future.

The self-tuning fuzzy sliding mode control method for the suspension system with the LSTM network road identification

As an important component of semi-active suspension (SAS) systems, the built-in solenoid valve adjustable damper (BSVAD) is now widely used in the field because of its advantages of fast response, continuously adjustable damping, and lightweight design. However, only a few studies have discussed the BSVAD-modeling method. Hence, this study proposes a method for constructing an agent model using a feedforward neural network (FNN) for an equivalent BSVAD regulation mechanism. Meanwhile, a new control strategy, i.e., a fuzzy sliding mode control method based on road conditions (RC-FSMC), is proposed for calculating the required damping force. The proposed method identifies and analyzes unsprung mass acceleration characteristics using a long short-term memory network to obtain the road condition of the moving vehicle and inputs the output results into the designed fuzzy rules to adjust the sliding mode switching gain and finally realize road condition-based adaptive control. Finally, through simulation test analysis, the results show that the designed RC-FSMC strategy can effectively reduce vehicle body acceleration and vehicle dynamic load under different road conditions to improve the adaptability of the vehicle to different roads.

Performance enhancements of semi-active vehicle air ISD suspension

To explore an innovative approach for enhancing the vibration isolation performance of vehicle air suspension systems, this study introduces the inerter element into the vehicle air suspension and investigates the dynamic behavior of the semi-active vehicle air ISD (inerter-spring-damper) suspension. Initially, a dynamic model of the quarter semi-active vehicle air ISD suspension is established, followed by conducting multi-objective optimization of the core parameters using the genetic algorithm. Subsequently, the dynamic performance of the semi-active vehicle air ISD suspension is thoroughly examined through simulations and analyses in both the time and frequency domains. The results demonstrate notable improvements in various aspects: the root-mean-square (RMS) value of the vehicle body acceleration in the semi-active vehicle air ISD suspension is reduced by 12.8%, the RMS value of the suspension working space is decreased by 37.3%, and the RMS value of the dynamic tire load experiences an 8.9% reduction. The findings of this paper indicate that the proposed semi-active vehicle air ISD suspension outperforms both the passive vehicle air suspension and the semi-active vehicle air suspension without an inerter, significantly enhancing the vehicle’s ride comfort, handling stability, and driving safety.

Dynamic Performance Optimization of Monorail Rapid Transit Formation Vehicles Based on Improved Artificial Potential Field Algorithm

This paper presents a new type of monorail rapid transit vehicle, which can operate in formation. In order to optimize the dynamic performance of the formation vehic-les when passing through the small radius curve, this paper first analyzes the structure of the new monorail rapid transit vehicle, and establishes the vehicle dynamic model and multi-body dynamics simulation model. Then the improved artificial potential field algorithm is used to build the formation vehicle operation controller. Finally, the dynamic performance evaluation index of the new mono-rail rapid transit formation vehicle is formulated, and the formation vehicle passing through the small radius curve scene is simulated. The simulation results show that the controller of the formation vehicle with dynamic optimi-zation control can effectively optimize the load transfer coefficient of running wheels, unbalanced centrifugal acce-leration and roll angle of vehicle body when passing thro-ugh the curve. Through this control method, the dynamic performance of formation vehicles passing through small radius curve lines can be optimized.

LQR-Based Suspension for Heavy Vehicles Considering the Time-Varying Characteristics of Vehicle–Road Interaction

The rapidly increasing demand for heavy vehicles in the transportation sector has led to more severe road damage and significantly higher road maintenance costs. Investigation of active suspension system incorporating vehicle–road interaction (VRI) can provide effective means to reduce the road damage and improve the ride comfort of vehicles. In this paper, an active vehicle suspension controller based on the strongly stable and robust linear–quadratic regulator (LQR) principle is developed for the time-varying VRI system. The coupled system is modeled by a quarter-car traveling on the road modeled by an Euler–Bernoulli beam resting on a viscoelastic foundation. Two types of road irregularities, deterministic sine wave and random, are considered in the numerical studies. A time-frozen technique, by which the linear time-varying system is converted to a time sequence of time-invariant systems, is applied to solve for the coupled responses. Three variables, the dynamic tire load, vehicle body acceleration, and suspension relative displacement, are used to assess the effectiveness of the LQR-based controller in comparison to the passive suspension system. The performance of the active control is investigated for different vehicle speeds, vehicle loads, and road profiles. Numerical studies show that the controller can effectively reduce the road damage and improve the ride comfort, with a slight increase in the suspension relative displacement. This work lays a useful foundation in the problem formulation and system parameter influences for future vehicle suspension design and road damage mitigation including VRI.

Design and Characterization of a Non-Linear Variable Inerter in Vehicle Suspension System

Inerter is a two-terminal component in suspension system such that the force at the two terminals is directly proportional to the relative acceleration of these two points. Studies have shown that the inerter can provide satisfactory vibration isolation for a number of suspension applications, including train suspension, building suspension and vehicle suspension. In the context of vehicle suspension, the existing passive inerter has been shown to provide benefits to vehicle dynamics performance measures, such as ride comfort and road holding ability. However, a basic passive inerter has fixed characteristic, and hence its potential is limited. This study overcome this limitation by incorporating variable inertia in inerter flywheel, however its non-linear characteristic needs to be determined. The method of achieving variable inertia in inerter flywheel is through introduction of movable masses or sliders attached with springs into inerter flywheel. The change of moment of inertia is caused by position change of sliders due to centrifugal force when the flywheel is rotating. Results showed that the proposed variable inerter exhibits a non-linear force-acceleration relationship with respect to its operating rotational speed. A vehicle suspension system equipped with a variable inerter is also able to further reduce vertical vehicle body acceleration and vehicle’s dynamic tire load when compared with vehicle suspension system without inerter and equipped with a passive inerter, which indirectly relates to a better vehicle ride and handling performance improvements. Hence, it can be proved that the proposed variable inerter is better than a passive inerter and is able to provide better ride comfort and road holding ability to a vehicle.

Research on Two-Stage Semi-Active ISD Suspension Based on Improved Fuzzy Neural Network PID Control.

To better improve the ride comfort and handling stability of vehicles, a new two-stage ISD semi-active suspension structure is designed, which consists of the three elements, including an adjustable damper, spring, and inerter. Meanwhile, a new semi-active ISD suspension control strategy is proposed based on this structure. Firstly, the fuzzy neural network's initial parameters are optimized using the grey wolf optimization algorithm. Then, the fuzzy neural network with the optimal parameters is adjusted to the PID parameters. Finally, a 1/4 2-degree-of-freedom ISD semi-active suspension model is constructed in Matlab/Simulink, and the dynamics simulation is carried out for the three schemes using PID control, fuzzy neural network PID control, and improved fuzzy neural network PID control, respectively. The results show that compared with adopting PID control and fuzzy neural network PID control strategy, the vehicle body acceleration and tire dynamic loads are significantly reduced after using the grey wolf optimized fuzzy neural network PID control strategy, which shows that the control strategy proposed in this paper can significantly improve the vehicle smoothness and the stability of the handling.

Estimation of turnout irregularities using vehicle responses with improved BiLSTM and Gaussian process regression

Railway turnout irregularities pose a safety risk, but existing detection methods using expensive trains with inertial navigation systems and laser measurement devices are cost-prohibitive and time-consuming for high-speed railways. This paper proposes a low-cost and real-time solution for estimating railway turnout irregularities using vehicle body acceleration, allowing for continuous monitoring of dynamic changes. A Bayesian-optimized improved bidirectional long short-term memory neural network model (BO-BiLSTM) was proposed in this paper, utilizing the vehicle's vertical and lateral acceleration as input to achieve point estimation of irregularities, with an estimation error approximately 50% lower than that of traditional recurrent neural networks. In addition, an interval estimation model combining BO-BiLSTM and Gaussian process regression (BO-BiLSTM-GPR) was proposed. Compared to the traditional interval estimation method Bootstrap, under the condition of narrow interval width, GPR ensures that over 90% of the measured values fall within the estimated interval and provides a better solution to the trade-off between interval estimation reliability and uncertainty.

Semi-active Suspension Control with PSO Tuned LQR Controller Based on MR Damper

As the Linear Quadratic Regulator (LQR) approach is applied extensively in the system control of automobile suspension, the accuracy improvement of the weighting Q and R matrices is getting concern. The Particle Swarm Optimization (PSO) algorithm is being introduced to identify parameters and optimize matrix Q and R in order to fix the insufficiency of these experienced values because of the fast convergence and a more accurate solution. In this article, a quarter car model and a Bouc-Wen-based magnetorheological (MR) damper model are developed to combine the control of PSO identification and PSO-LQR controller in the semi-active suspension system. The MR damper was performed with an experimental test for running identification using experimental data as input into the Bouc-Wen model to obtain six unknown parameters, where the parameters were estimated with the PSO algorithm. Since the numerical model has been done with all parameters clear, the need for damping force from suspension is obtained by means of running the model using an input current. In the employment of PSO for damper model and vehicle control, the dual applications succeeded in verifying the feasibility of parameter identification in the MR damper and successfully tuned the LQR controller in the semi-active suspension, which decreases the vehicle body acceleration and displacement so that the improvement of ride comfort and drive stability achieved.

Identification of Control-Related Signal Path for Semi-Active Vehicle Suspension with Magnetorheological Dampers

This paper presents a method for the identification of control-related signal paths dedicated to a semi-active suspension with MR (magnetorheological) dampers, which are installed in place of standard shock absorbers. The main challenge comes from the fact that the semi-active suspension needs to be simultaneously subjected to road-induced excitation and electric currents supplied to the suspension MR dampers, while a response signal needs to be decomposed into road-related and control-related components. During experiments, the front wheels of an all-terrain vehicle were subjected to sinusoidal vibration excitation at a frequency equal to 12 Hz using a dedicated diagnostic station and specialised mechanical exciters. The harmonic type of road-related excitation allowed for its straightforward filtering from identification signals. Additionally, front suspension MR dampers were controlled using a wideband random signal with a 25 Hz bandwidth, different realisations, and several configurations, which differed in the average values and deviations of control currents. The simultaneous control of the right and left suspension MR dampers made it necessary to decompose the vehicle vibration response, i.e., the front vehicle body acceleration signal, into components related to the forces generated by different MR dampers. Measurement signals used for identification were taken from numerous sensors available in the vehicle, e.g., accelerometers, suspension force and deflection sensors, and sensors of electric currents, which control the instantaneous damping parameters of MR dampers. The final identification was carried out for control-related models evaluated in the frequency domain and revealed several resonances of the vehicle response and their dependence on the configurations of control currents. In addition, the parameters of the vehicle model with MR dampers and the diagnostic station were estimated based on the identification results. The analysis of the simulation results of the implemented vehicle model carried out in the frequency domain showed the influence of the vehicle load on the absolute values and phase shifts of control-related signal paths. The potential future application of the identified models lies in the synthesis and implementation of adaptive suspension control algorithms such as FxLMS (filtered-x least mean square). Adaptive vehicle suspensions are especially preferred for their ability to quickly adapt to varying road conditions and vehicle parameters.

A new approach to controlling an active suspension system based on reinforcement learning

Active suspension provides better vehicle control and safety on the road with optimal driving comfort compared to passive suspension. Achieving this requires a good control system that can adapt to any environment. This article uses a deep reinforcement learning method to develop an optimal neural network that meets the comfort requirements according to ISO 2631-5 standards. The algorithm trains the agent without any prior knowledge of the environment. Various simulations were performed, and the results were validated with the literature and the standard until the appropriate reward function was found. Simple and consistent road profiles were used while maintaining constant system parameters during training. The results show that suspension based on deep reinforcement learning reduces vehicle body acceleration and improves ride comfort without sacrificing suspension deflection and dynamic tire loading. The controller expects the RMS value of the acceleration to be 0.228 with a minimum overrun of the suspended mass.

Model reference backstepping control for semi-active air suspension systems with parameter uncertainty

The electronically controlled semi-active air suspension systems have been widely used to improve the vehicle ride comfort and road holding performance by adjusting the damper stiffness. This work focuses on the design of a damping force controller to enhance the ride comfort, road holding and stability under the presence of unknown air spring pressure. Firstly, an improved skyhook suspension reference model is developed to generate the desired dynamic criteria (i.e. vehicle body acceleration, pitch and roll angles). Secondly, by employing the backstepping technique, a novel damping force controller is proposed to approach the desired dynamic criteria. Thirdly, a parameter estimation method is also designed to estimate the air spring pressure to obtain the air spring force. Comparative studies are carried out among passive suspension systems, and the semi-active air suspension systems with the proposed model reference damping force control, traditional backstepping control and existing sliding mode control. Numerical results show that a significant improvement of ride comfort can be observed with the semi-active air suspension system based on the proposed model reference backstepping controller.

Simulation analysis on vertical vehicle dynamics of three in-wheel motor drive configurations

The hub-driven technology provides several remarkable benefits to overcome some of today’s challenges in electrification of the transport sector. Although there are advantages by using in-wheel motors, their application results in increased unsprung masses, which have a negative impact on ride comfort and road holding of the vehicle. A novel but unexplored concept to inhibit the negative effects of the wheel hub motor is the two-stage-suspension structure. To investigate this in-wheel motor design and to compare it with established concepts for reducing the negative effects of the unsprung masses, three full-vehicle models were established. The vehicle models are based on a two-stage-suspension structure, a design where the motor functions as a tuned mass damper and a conventional in-wheel motor design. The suspension parameters of the three in-wheel motor configurations were further optimized using a genetic algorithm with respect to several vertical vehicle performance parameters. Subsequently, the full-vehicle models of the in-wheel motor configurations were compared by simulation in numerous different driving situations regarding their vertical vehicle dynamics. The results demonstrate that the two-stage-suspension causes an increase of the pitching and vertical vehicle body acceleration in several driving conditions, while the acceleration of the motor in general and the roll acceleration of the vehicle body especially during cornering maneuvers can be reduced significantly.

Research on control strategy of seven-DOF vehicle active suspension system based on co-simulation

In recent years, since the unique advantages in automotive structures, the vehicle active suspension systems have received widespread attentions. A good active suspension system can reduce the vibration and improve the overall performance of the vehicle. Therefore, the design of the controller for the active suspension system to perform autonomous adjustment plays a vital role in vehicle comfort and safety. For the active suspension of the seven-DOF sport utility vehicle (SUV) model, this paper takes the vehicle body acceleration, tire dynamic load and suspension dynamic travel as the indicators to evaluate the performance, and the proportional-integral-derivative (PID) controller is designed to improve the performance of the vehicle active suspension system. Based on the software of MATLAB/Simulink and Carsim, a closed-loop co-simulation model diagram is established, which includes a PID controller module. Meanwhile, the random road input model and the whole vehicle model are constructed in Carsim. Finally, at the speeds of 70, 90, and 120 km/h, the active suspension system under the designed PID controller is simulated and compared with the passive suspension system. The simulation results show that the active suspension system based on PID controller can effectively improve the overall performance of the vehicle, and then the comfort and safety of the vehicle can be further enhanced.

Adaptive variable domain fuzzy PID control strategy based on road excitation for semi-active suspension using CDC shock absorber

Electronic suspensions can take into account the ride comfort and safety of the vehicle, the continuous damping control (CDC) shock absorber is the core component of the electronic suspension. CDC shock absorber and electronic suspension have a promising future for application in automotive. This paper proposed an adaptive variable domain fuzzy PID control strategy for semi-active suspensive to effectively improve the vibration reduction effect of the automobile suspension system. By analyzing the dynamic performance of the semi-active suspension system coupled with the CDC shock absorber to get the control variables, we deduce the math function of semi-active suspension. In addition, the simulation model of the semi-active suspension based on the bench test of shock absorbers was established. Under the observation of performance indicators, though comparing the new control and other different control strategies, which can prove the effectiveness of the new method. From the simulation results, the shock absorber simulation model is correct and the performance of the proposed control strategies are effective than the traditional PID control and fuzzy control under the random road excitation. In particular, in the 120 km/h case by using VAC, the peak values of the suspension dynamic deflection, vehicle body acceleration, and car body dynamic load are reduced by 49.6%, 50%, and 50%. For a semi-active suspension using the CDC shock absorber, the proposed control method provides better ride comfort to passengers due to lower peak compared with the fuzzy control strategy and the PID control strategy, it can be used as an optimized design method for suspension.

Design a new control algorithm AFSP (Adaptive Fuzzy – Sliding Mode – Proportional – Integral) for automotive suspension system

When a vehicle is driving, the most significant source of oscillations is the irregularities in the surface of the road. An active suspension is utilized to enhance the vehicle’s stability and ride comfort. In this work, the dynamic model with multi variables is considered to simulate vehicle oscillations based on four excitation cases from the road surface. In addition, this research also established the AFSP complex control solution for an active suspension system. This is a completely novel algorithm with many outstanding advantages. The final control signal of the system is synthesized from the signals of the linear controller PI (Proportional – Integral) and the nonlinear controller SMC (Sliding Mode Control). The controller’s parameters will change continuously depending on the established fuzzy rule. According to simulation outcomes, the vehicle body displacement and acceleration dramatically declined when the AFSP algorithm directed an active suspension. The values of acceleration and displacement do not exceed 80% and 20%, compared to the scenario in which the vehicle just utilized the typical passive suspension system. Besides, a phenomenon of “chattering” also does not appear when combining the controllers. Overall, the efficiency of this algorithm is high. This algorithm can be applied to more complex models.

A vehicle-bridge interaction vibration model considering bridge deck pavement

The bridge pavement subjected to vehicle loads is the most vulnerable component in the highway bridge and overloaded vehicles can result in serious damage to the bridge pavement more easily. Therefore, it is necessary to consider the pavement in vehicle-bridge interaction (VBI) system. However, the bridge pavement is not considered in the traditional VBI system or the viscoelasticity of bridge pavement is ignored. In this study, a new vehicle-pavement-bridge interaction (VPBI) system is established. The viscoelastic asphalt pavement is simulated with the continuously and uniformly distributed spring-damper. The equivalent stiffness coefficient and equivalent damping coefficient of the pavement are determined through dynamic mechanical analysis (DMA) test and finite element method. The equations of motion for VPBI system can be derived using Lagrange equation and the modal superposition method. Then the crucial parameters such as displacement at mid-span of bridge, acceleration of vehicle body, tire contact force, and pavement deformation are obtained. The effects of vehicle velocity, bridge span, tire contact area, pavement stiffness coefficient, and pavement damping coefficient on VPBI responses are analyzed. The results show that (1) The pavement is compressive during vehicle passing bridge and its dynamic deformation fluctuates around initially static deformation of pavement. (2) Increasing the stiffness of pavement can rapidly reduce the deformation of pavement, while the pavement damping has the opposite effect. (3) The increase of bridge span can conduct exponentially growth of dynamic responses of VPBI system. The pavement deformation will increase by 7.9% if the bridge span is lengthened by 5 m. This study provides a reliability response analysis method for VPBI system.

Optimal Design and Dynamic Performance Analysis of Vehicle Suspension Employing an Eccentric Inerter

This paper concerns the dynamic performance analysis of the vehicle ISD (inerter-spring-damper) suspension employing an eccentric inerter. Firstly, the quarter car model of the two basic vehicle suspension layouts involving an eccentric inerter, namely, the series-connected layout and the parallel-connected layout, is established. Then, by considering the overall performance such as the vehicle body acceleration, the suspension working space, and the dynamic tire load, the key parameters of the two suspensions are optimized by using the genetic algorithm. Simulation analysis results indicate that the series-connected vehicle ISD suspension is superior to the parallel-connected one, and all of the RMS values of the body acceleration, the suspension working space, and the dynamic tire load are decreased significantly by comparing to the conventional suspension, while the improvement of the parallel-connected vehicle ISD suspension is relatively poor. At last, the impact of the flywheel eccentricity and the screw pitch on the dynamic performance indices of the two suspensions is discussed, and the trade-offs among the three performances are analyzed, which will provide a guide method for the suspension design when considering the eccentric factor.

Numerical analysis of train-track-subgrade dynamic performance with crumb rubber in ballast layer

• Coupled DEM-FDM-MBD model to study train-track-subgrade dynamic responses. • Crumb rubber (or tire-derived aggregates) effects on train-track-subgrade dynamic responses. • Crumb rubber size effects on the train-track-subgrade dynamic responses presented by ballast friction energy dissipation. Crumb rubber (CR) has been proposed to apply in the ballast or sub-ballast layer for ballast degradation mitigation and vibration (noise) reduction. The CR can change the ballast layer stiffness, which can affect the train-track-subgrade dynamic performance and cause travel comfort and safety issues. Towards this, this study aims at confirming 1) how much the CR application can affect the dynamic performance of train and ballast layer; 2) to what extent the CR-ballast layer can distribute the train loadings to reduce subgrade surface stress. To achieve this aim, a whole train-track-subgrade system model was built by coupling multibody dynamics (MD), discrete element method (DEM) and finite difference method (FDM). The MD was used to build the train, including one vehicle body, two bogies and four wheelsets. The DEM was used to build the ballasted track, including rail, sleepers and ballast layer. The FDM was used to build the subgrade. Using the coupled model, the dynamic performance of train and track were studied, including the vehicle body acceleration, wheel-rail force, rail dynamical bending moment, sleeper acceleration, sleeper displacement and ballast acceleration. In addition, the energy dissipation of the ballast bed was also presented. For the subgrade, the subgrade surface acceleration and surface stress were measured and analysed. In the model, different CR size and percentage were considered. Results show that using the CR in ballast layer can increase the accelerations of sleeper, rail and train. But it can decrease the ballast degradation, subgrade surface acceleration and subgrade surface stress. CR helps consume train loading energy, reducing the energy that has to be consumed by ballast friction. Small size CR (8–22.4 mm) has greater influence on dynamic performance of the whole train-track-subgrade system than big size CR (9.5–63 mm). In summary, 10% percentage of CR-ballast mixture is recommended, and for CR size it is difficult to give a recommendation. Small size CR increase ballast acceleration more than big size CR, but small size CR are better at improving sleeper displacement, subgrade stress and ballast bed stress.