Quarter Vehicle Model Research Articles

PID Parameters Prediction Using Neural Network for A Linear Quarter Car Suspension Control

Providing control for suspension systems in vehicles is an enhancing factor for comfort and safety. With the improvement of control conditions, it is possible to design a cost-efficient controller which will maintain optimum comfort within harsher environmental conditions. The aim of this study is to design an adaptive PID controller with a predictive neural network model, which will be referred as NPID (NeuralPID), to control a suspension system. For this purpose, a NN (Neural Network) model is designed to produce outputs for PID’s Proportional (P) parameter to provide optimum responses for different road inputs. Also, reliability of the system outputs, which is using adaptive Proportional parameter, is tested. PID parameters for linear quarter vehicle model are decided through Zeigler-Nichols method. An ideal PID model, where Integral (I) and Derivative (D) parameters are bound to Proportional parameter, is used in the system. When the outputs of different controlled and not controlled systems, which are free, PID and NPID, are compared; it has been seen that NPID outputs are more convenient. In addition, it is possible to design controllers, with adaptively adjusting P parameter, which are operating cost-effective.

Constrained model predictive control for time-varying delay systems: Application to an active car suspension

This study investigates the problem of robust model predictive control (RMPC) for active suspension systems with time-varying delays and input constraints. The uncertainty is of convex polytopic type. Based on the Lyapunov-Krasovskii functional method, sufficient stability conditions of the time-varying delays systems are derived by linear matrix inequalities (LMIs) terms. At each time set, a feasible state feedback is obtained by minimizing an upper bound of the ‘worst-case’ quadratic objective function over an infinite horizon subject to constraints on inputs. Finally, a quarter-vehicle model is exploited to demonstrate the effectiveness of the proposed method.

LPV Control of Full-Vehicle Vertical Dynamics using Semi-Active Dampers

Semi-active suspensions enable a mitigation of the design conflict between ride comfort and road-holding by allowing the continuous control of the damper force. During the design of control laws for semi-active dampers, the inherent actuator limits constitute a major performance restriction. Accordingly, these constraints should be explicitly considered during controller design. In this work, the actuator constraints are addressed by LPV control methods which offer a rigorous framework to incorporate them as so-called saturation indicator parameters in the LPV plant. Additionally, saturation indicator dependent weighting filters are employed in a mixed sensitivity scheme in order to honor stability over performance in the event of saturation. Furthermore, the LPV controller is synthesized using a full-vehicle model, which enables the individual tuning of the heave, pitch and roll motion. The full-vehicle model, however, leads to a significant increase in complexity of the controller synthesis problem compared to a quarter-vehicle model. Therefore, a disturbance-feed forward output-feedback controller design is adopted to exploit the separation principle. The performance of the proposed full-vehicle LPV controller is compared to two quarter-vehicle LPV controllers, a Skyhook/Groundhook controller and passive suspension configurations in an extensive simulation investigation. The results illustrate the improved pareto optimum of the LPV full-vehicle controller and the suitability of the proposed design scheme.

Vehicle Active Suspension System performance using Different Control Strategies

The objective of the present work is to investigate the performance of an active suspension system of a typical passenger car through the application of three different control strategies under three different road irregularities. Tested control strategies are PID, LQR and FLC. Road irregularities considered are: a single rectangular pothole, a single cosine bump, and an ISO class-A random road disturbance. A 2-DOF quarter-vehicle model is used to simulate, evaluate and compare performance of these controllers against each other and against the original passive suspension system. Both tire gripping force and actuator force were normalized with respect to vehicle weight to recognize tire separation and enhance readability and interpretation of results. Simulation results showed that, active suspension systems are advantageous compared to passive ones. Active suspension implementing FLC control surpassed both PID and LQR controllers. Improvement of ride comfort was recognized by a reduction of sprung mass displacement and acceleration up to 23.8% and 52% respectively compared to the passive case. Improvement of load capacity is clear with a suspension travel reduction up to 61%. Moreover, vehicle stability was enhanced by increasing the tire separation margin up to 28 % of vehicle weight. An actuator force up to 39.5% of vehicle weight is required. All achieved by active suspension implementing FLC control.

Design of a Road Friendly SAS System for Heavy-Duty Vehicles Based on a Fuzzy-Hybrid-ADD and GH-Control Strategy

Semiactive suspension (SAS) system has been widely used for its outstanding performance in offering competent ride quality, road holding, and handling capacity. However, the road friendliness is also one of the crucial factors that should be attached in the design of the SAS system for heavy-duty vehicles. In this study, a fuzzy controlled hybrid-acceleration driven damper (ADD) and ground hook- (GH-) control strategy is proposed for SAS system of heavy-duty vehicles. Firstly, a quarter-vehicle model with SAS system is constructed. Then, aiming to improve the ride quality and road friendliness, a hybrid-ADD and GH-control strategy is proposed under the coordination of the fuzzy controller. Numerical results show that the ride quality and road friendliness of the SAS system with the proposed control strategy outperform those with traditional hybrid-sky hook and ground hook-control strategy. It is also verified that the proposed strategy is superior to the sole ADD approach and sole ground hook approach in improving the vehicle overall performance.

Tire Force Control Strategy for Semi Active Magnetorheological Damper Suspension System Using Quarter Heavy Vehicle Model

This paper proposed semi active controller scheme for magnetorheological (MR) damper of a heavy vehicle suspension known as Tire Force Control (TFC). A reported algorithm in the literature to reduce tire force is Groundhook (GRD). Thus, the objective of this paper is to investigate the effectiveness of the proposed TFC algorithm compared to GRD. These algorithms are applied to a quarter heavy vehicle models, where the objective of the proposed controller is to reduce unsprung force (tire force). The simulation model was developed and simulated using MATLAB Simulink software. The use of semi active MR damper using TFC is analytically studied. Ride test was conducted at three different speeds and three bump heights, and the simulation results of TFC and GRD are compared and analysed. The results showed that the proposed controller is able to reduced tire force significantly compared to GRD control strategy.

Ground Semi Active Damping Force Estimator (gSADE) for Magnetorheological Damper Suspension System Using Quarter Heavy Vehicle Model

This paper proposed semi active controller scheme for magnetorheological (MR) damper of a heavy vehicle suspension known as Ground Semi Active Damping Force Estimator (gSADE), where it was modified from Semi Active Damping Force Estimator (SADE) algorithm. A reported algorithm known as Groundhook (GRD) was developed where its aim to minimize tire road forces and hence reduce road damage. Thus, the objective of this paper is to investigate the effectiveness of the proposed gSADE algorithm compared to GRD and SADE. These algorithms are applied to a quarter heavy vehicle models and the simulation model was developed and simulated using MATLAB Simulink software. Ride test was conducted at three different speeds and three bump heights, and the simulation results of gSADE, SADE and GRD are compared and analysed. The results showed that the proposed controller is able to reduced tire force significantly compared to GRD control strategy.

Analysis of tire-road contact area in a control oriented test bed for dynamic friction models

The longitudinal and transversal forces distributed over the tire-road contact area are experimentally analyzed to validate the use of the lumped parameters LuGre dynamic friction model for traction-braking control purposes. To perform the analysis, a test bed based on a scaled quarter vehicle model that consists of a roller, a wheel and a servomotor was designed and built. In this device, the roller represents the road and the vehicle mass, and the tire is directly coupled to the shaft of the servomotor. The distribution of forces in the contact tire-road area is measured by means of strain gages. The obtained results show the distribution of normal forces in the tire-road contact area at different vehicle speeds. They confirmed analytic studies previously reported in the literature regarding the trapezoidal shape of the force distribution in the contact area and also allow to conclude that the lumped parameter LuGre dynamic friction models is suitable for representing the friction forces for traction- braking control purposes. All Rights Reserved © 2015 Universidad Nacional Autonoma de Mexico, Centro de Ciencias Aplicadas y Desarrollo Tecnologico. This is an open access item distributed under the Creative Commons CC License BY-NC-ND 4.0.

Investigation of Slow-Active Suspension System’s Non-linearity on The Performance of The Anti-lock Brake System

This paper presents an advanced integrated controller design for military vehicle slow-active suspension system and anti-lock brake system (ABS) considering the effect of the suspension components non-linearity on the braking dynamics. The presented investigation is applied to a quarter vehicle model using the Magic Formula tire model and the actual characteristics for suspension damper (throttle valve) and spring (gas spring). The suspension controller is designed based on LQR using a linearized vehicle model and the ABS controller is designed based on ON/OF control methodology using tire skid ratio of 15% as a reference value. The mathematical derivations as well as the control techniques are numerically implemented in MATLAB environment. Several simulation results are carried out considering typical performance measures such as stopping time, stopping distance and vehicle body vertical acceleration. The results illustrated that, the integrated controller reduces the stopping distance on different road surfaces and therefore improves the braking performance to avoid or reduce the impact of vehicle accident.

A study of an electric parking brake system for emergency braking

In this paper, an emergency braking control with electric parking brake (EPB) actuator is proposed and studied. Emergency braking requires a good slip ratio control algorithm to guarantee the brake stability. It is well known that the X-by-wire technologies have considerable advantages over the traditional hydraulic system, especially, bringing great strengths to complex control systems. As one of the brake-by-wire systems, EPB has been used as an advanced parking system in some luxury cars. However, it still has some untapped potential, e.g., dynamic braking. The paper proposes a sliding mode control (SMC) algorithm to effectively control the dc motor in EPB system to attenuate the torque tracking error. Simulation results from a quarter vehicle model with EPB actuator as a spare dynamic braking system show that the proposed control architecture with three sliding surfaces can effectively improve the emergency braking performance in the typical simulation manoeuvres employed and significantly reduce the tracking errors.

Effect Analysis of Vehicle System Parameters on Dynamic Response of Pavement

In order to study the damage of a semirigid pavement under vehicle loads with varied parameters, the random dynamic loads applied on the pavement by a running vehicle were computed with two degrees of freedom, quarter-vehicle model, and then a three-dimensional finite element analysis model of semirigid asphalt pavement was established. With the peak stress index of each pavement layer, the effect of varied vehicle parameters on pavement response was studied. The results indicated that the stress wave frequency of each pavement layer was similar to that of the dynamic random load, and, with increased pavement depth, the wave effect decreased. The pavement response increased with increased suspension stiffness and tire stiffness and decreased with increased suspension damping and tire damping. Furthermore, compared to the stiffness, the response variation induced by the damping was orders of magnitude lower. Compared with the traditional time response analysis method, the peak response analysis of the pavement structure was more scientific, rational, and intuitive, which could be useful for the study of vehicle-pavement interaction and road damage.

Recent Developments on Time-Delay Neural Networks

Over the past several decades, an amount of attention has been devoted to neural networks, which have wide applications in many areas, such as signal processing, pattern recognition, and combinatorial optimization. On the other hand, time delays occur in electronic implementation of analog neural networks because of the transmission of signal and the finite switching speed of amplifiers and can lead to the instability and poor performance of systems; thus neural networks with time delay have also been studied extensively because numerous interesting results have been obtained over the last decade, including stability analysis, state estimation, and passivity. In this special issue, we have accepted seven papers. The paper titled “New Pinning Synchronization of Complex Networks with Time-Varying Coupling Strength, NonDelayed and Delayed Coupling” by G. Wang et al. studies the pinning synchronization problem for a class of complex networks by a stochastic viewpoint, in which both time-varying coupling strength and nondelayed and delayed coupling are included. The paper titled “A Novel Model of Conforming Delaunay Triangulation for Sensor Network Configuration” by Y. Ma et al. proposes a new method for solvingDelaunayTriangulation problem,which is called endpoint triangle’s circumcircle model (ETCM).The paper titled “Multimodel Modeling and Predictive Control for DirectDrive Wind Turbine with Permanent Magnet Synchronous Generator” by L. Wang et al. establishes a method based on multimodel modeling and predictive control is proposed for the optimal operation of direct-drive wind turbine with permanent magnet synchronous generator. The paper titled “Independent Component Analysis Based on Information Bottleneck” by Q. Ke et al. provides the equivalence of two algorithms of independent component analysis (ICA) based on the information bottleneck (IB). In “Nonlinear Time-Delay Suspension Adaptive Neural Network Active Control” by Y. Zhu and S. Zhu, a quarter-vehicle magnetorheological active suspension nonlinear model with time delay is established, and an adaptive neural network structure for magnetorheological active suspension is presented. The paper titled “An Adaptive Regulator for Space Teleoperation System in Task Space” by C. Ge et al. studies the problem of the gravity information for bilateral teleoperation. The paper titled “Robust Stabilization of Linear Switching Systems with both Input and Communication Delays” by L. Jia and Z. Sheng considers the stabilization control of a class of linear switching systems with time delays in both the input and the communication channels.

Contribution to the modeling of a pneumatic semi-active control of vehicle suspension

This paper contributes to the modeling of a semi-active control of a quarter vehicle model using air springs. A conventional mass-spring-damper model has been used along with an air spring. Based on the theory of thermodynamics, the dynamic equation of the air spring model was established. The simulation model was implemented using MATLAB and the transfer functions with varying parameters were calculated. The simulation results show that air spring pressure, the valve diameter, the dumping coefficient and the mechanical stiffness affect the dynamic response of the system. A semi-active control methodology was then established by controlling the valve diameter using two declinations of an on-off logic switch based on the velocity of the suspended mass and the relative velocity at both ends of the air spring. The obtained results show reduced oscillation amplitudes around the natural frequency of the system.

A Method of Acquiring Dynamic Road Roughness Based on Vehicle-Road Vertical Coupling

A method of acquiring dynamic road roughness was proposed. At first, road elevation data was measured and road surface spectrum was analyzed. Secondly, the simplified interaction dynamic model of quarter vehicle and the Euler- Bernoulli beam road, visco-elastic Kelvin foundation were built to obtain the wheel dynamic load. In its effect, the beam bending vibration differential equations was built, and road surface vertical displacement solution was acquired by inte- gral transform method under the action of vehicle-road vertical coupling. These were the basis of article study and the im- portant issues. Finally, the dynamic road roughness was analyzed by applying stochastic process theory and the linear su- perposition method. The conclusion was that the dynamic road roughness was linear superposition on the initial road roughness and road vertical displacement. What was proposed the concept on dynamic road roughness is an important in- novation in the vehicle-road dynamics field. This method provided a more accurate road excitation in the course of the vehicle-road dynamic simulation analysis.

Evaluation of on–off semi-active vehicle suspension systems by using the hardware-in-the-loop approach and the software-in-the-loop approach

Three controllers, namely the skyhook controller, the mixed-single-sensor controller and the groundhook controller, are compared using two validation approaches, namely the hardware-in-the-loop approach and the software-in-the-loop approach. The software-in-the-loop approach considers the dynamics (e.g. the body heave, the yaw, the roll, the pitch and the force) and the geometric parameters (the motion ratio of the suspension) without the real-time constraints. This allows an easier debugging and design procedure to be carried out for the control systems. The hardware-in-the-loop approach includes a commercial magnetorheological damper for testing the dynamic and transient responses in a control system. It is of interest to compare the conclusions generated under both approaches. The hardware-in-the-loop approach considers an on–off magnetorheological damper, and a quarter-vehicle model in a real-time embedded system. Two types of test were applied: chirp surface road tests and type F surface tests (ISO 8606:1995). For the software-in-the-loop approach the non-linearities and dynamics due to the geometric and physical component characteristics of a vehicle model were simulated by CarSim® software, while the non-linear magnetorheological damper model and the controller were running in MATLAB®/Simulink®. The classical tests for the vehicle, namely the dynamics bounce sine sweep test, the double-lane-change test and the fishhook test, were applied. In the hardware-in-the-loop approach, the best controller was the skyhook controller for comfort and the groundhook controller for road holding. In the software-in-the-loop approach, the mixed-single-sensor controller is the best for comfort, and the groundhook controller can be used in emergency driving conditions since it improves the stability, the road holding and the wheel tramp. The best controller in the hardware-in-the-loop approach and the best controller in the software-in-the-loop approach are not the same since the motion ratio of the automotive suspensions influences the performance of the semiactive control systems; the inclusion of this geometric parameter in further analysis and synthesis of semiactive suspension systems is recommended.

Modeling and Validation of Quarter Vehicle Traction Model

This manuscript provides modeling and validation of a quarter car vehicle model to study the wheel dynamics behavior in longitudinal direction. The model is consists of a longitudinal slip model subsystem, a quarter body dynamic and tire subsystems. The quarter vehicle model was then validated using an instrumented experimental vehicle based on the driver input from brake and throttle pedals. Vehicle transient handling dynamic tests known as sudden braking test was performed for the purpose of validation. Several behaviors of the vehicle dynamics were observed during braking maneuvers such as body longitudinal velocity, wheel linear velocity and tire longitudinal slip at a quarter of the vehicle. Comparisons of the experimental results and model responses with sudden braking imposed motions were made. Consequently, the trends between simulation results and experimental data were found almost similar with an acceptable level of error for the application at hand.

Implementation of LQR Controller on Electromagnetic Suspension System for Passenger’s Car

In the past few decades, researchers have been focusing on improving control strategy for automotive active suspension system. There are few configurations used in active suspension mechanism and one of them is Electromagnetic Suspension (EMS) System. In this study, the implementation of a Linear Quadratic Regulator (LQR) controller in an EMS System for vehicle Active Suspension System (ASS) was investigated. This provides an optimal control solution for the active suspension system. Quarter vehicle model of an electromagnetic suspension was derived and employed to study the implementation of the LQR controller. Detailed parametric analysis for the proposed controller and implementation results will be presented in this paper. This is done by investigating the effect of weighting parameters in the performance index of the optimal control strategy in stabilising the vehicle response. The controller’s performance was compared against a passive suspension system based on a commercial passenger’s car. Parametric analyses revealed the importance of weighting parameters in the optimal control formulation. Finally, it was proven that LQR controller strategy provides a satisfactory improvement for the EMS system compared to passive suspension performance

Output-Feedback-Based $H_{\infty}$ Control for Vehicle Suspension Systems With Control Delay

This paper deals with the problem of output-feedback H∞ control for a class of active quarter-car suspension systems with control delay. The dynamic system of the suspension systems is first formed in terms of the control objectives, i.e., ride comfort, road holding, suspension deflection, and maximum actuator control force. Then, the objective is to the design of the dynamic output-feedback H∞ controller in order to ensure asymptotic stability of the closed-loop system with H∞ disturbance attenuation level and the output constraints. Furthermore, using Lyapunov theory and linear matrix inequality (LMI) approach, the existence of admissible controllers is formulated in terms of LMIs. With these satisfied conditions, a desired dynamic output-feedback controller can be readily constructed. Finally, a quarter-vehicle model is exploited to demonstrate the effectiveness of the proposed method.

Characterisation of magneto-rheological damper and its use in semi-active control of quarter car model

In this paper, analytical characterisation of the magneto-rheological (MR) damper is done using a new modified algebraic model. This model along with the obtained model parameters is used as a semi-active suspension device in a quarter car model and the stationary response of the vehicle traversing on a rough road is obtained. The control part consists of two nested controllers. For the system controller a model reference skyhook sliding mode controller (SMC) is used and for the damper controller a continuous state algorithm is built to determine the input voltage so as to gain the desired damping force. The analytical model is subsequently used in the quarter car vehicle model and the vehicular responses are studied for constant input voltages to the MR dampers. Results show that the semi-active controller can achieve compatible performance as that of active suspension controller except for a little deterioration.

Optimization of Damper Top Mount Characteristics to Improve Vehicle Ride Comfort and Harshness

A novel optimization technique for optimizing the damper top mount characteristics to improve vehicle ride comfort and harshness is developed. The proposed optimization technique employs a new combined objective function based on ride comfort, harshness, and impact harshness evaluation. A detailed and accurate damper top mount mathematical model is implemented inside a validated quarter vehicle model to provide a realistic simulation environment for the optimization study. The ride comfort and harshness of the quarter vehicle are evaluated by analyzing the body acceleration in different frequency ranges. In addition, the top mount deformation is considered as a penalty factor for the system performance. The influence of the ride comfort and harshness weighting parameters of the proposed objective function on the optimal damper top mount characteristics is studied. The dynamic stiffness of the damper top mount is used to describe the optimum damper top mount characteristics for different optimization case studies. The proposed optimization routine is able to find the optimum characteristics of the damper top mount which improve the ride comfort and the harshness performances together.