Sprung Mass Acceleration Research Articles

State Dependent Riccati Equation Control of an Active Hydro-Pneumatic Suspension System

In this study, a nonlinear active Hydro-Pneumatic (HP) suspension system is modelled. The HP suspension system model is then incorporated into the quarter car model and a nonlinear controller for the vehicle system is developed. A linear structured model with state dependent matrices of the nonlinear quarter car model is derived for use in controller design. A nonlinear control method, State Dependent Riccati Equation control (SDRE) is used to attenuate sprung mass acceleration, suspension deflection, and tire deflection. The performance of the controller is examined in both frequency and time domains. Active HP suspension system is simulated with sinusoidal inputs at discrete amplitudes and frequencies, and the approximate frequency response functions are obtained. The active HP suspension system is simulated with random road inputs and the root mean square values of the responses are used to evaluate the performance of the controller. The results show that the active suspension successfully and simultaneously decreases the sprung mass acceleration, suspension deflection, and tire deflection around body bounce frequency and thus improved ride comfort and road holding are obtained.

Ride Evaluation of Vehicle Suspension Employing Non-Linear Inerter

Inerter is a recent element in suspension systems with the property that the generated force is proportional to the relative acceleration between its two terminals, which is similar to the way a spring reacts to relative displacement and a damper to relative velocity. This paper presents the analysis of a non-linear inerter working in parallel to passive spring and damper of a vehicle suspension to evaluate its effect on vehicles ride. The non-linear inerter was theoretically capable of switching between on and off states depending on whether or not the suspension deflection was beyond a specified free play. In the study, this behavior was represented mathematically as control law which depended on the relative displacement between the sprung and unsprung masses. A mathematical quarter vehicle model incorporating the non-linear inerter was simulated in MATLAB/Simulink to determine the vehicle responses due to road input in the form of step profile for different combinations of free play and inerters on-state proportionality constant called the inertance. Results showed improvements in vehicle ride comfort, as demonstrated by the lower root-mean-squared sprung mass accelerations compared to the ordinary passive suspension with only spring and damper. Additionally, implementation of non-linear inerter gave lower percentage overshoot to step input, indicating better transient response than ordinary passive suspension.

Plumpness Analysis of Indicator Diagram for Vehicle Damper

According to the indicator diagram of damper, the indicator diagram plumpness was proposed as a quantitative index, and its mathematical relationships with the sprung mass acceleration, suspension dynamic travel and tire dynamic load were built. Moreover, the influence of the total area on suspension characteristics was analyzed in time domain and frequency domain. The results show that, the increase of the indicator diagram plumpness can effectively restrain the variation of suspension dynamic travel and tire dynamic load, meanwhile, the body acceleration will be enlarged. Excessive indicator diagram plumpness also affects the dynamic tire load distribution in frequency domain, and it will decrease the driving security. Therefore, it should be reasonably selected from the performance indicators, which is based on the requirement of vehicle demand in the design process.

Response of a quarter car model with optimal magnetorheological damper parameters

In this paper, the control of the stationary response of a quarter car model to random road excitation with a Magnetorheological (MR) damper as a semi-active suspension device is considered. The MR damper is a hypothetical analytical damper whose parameters are determined optimally using a multi-objective optimization technique Non-dominated Sorting Genetic Algorithm II (NSGA II). The hysteretic behaviour of the MR damper is characterized using Bingham and modified Bouc-Wen models. The multi-objective optimization problem is solved by minimizing the difference between the root mean square (rms) sprung mass acceleration, suspension stroke and the road holding responses of the quarter car model with the MR damper and those of the active suspension system based on linear quadratic regulator (LQR) control with the constraint that the MR damper control force lies between ±5 percent of the LQR control force. It is observed that the MR damper suspension systems with optimal parameters perform an order of magnitude better than the passive suspension and perform as well as active suspensions with limited state feedback and closer to the performance of fully active suspensions.

Using the lead vehicle as preview sensor in convoy vehicle active suspension control

Both ride quality and roadholding of actively suspended vehicles can be improved by sensing the road ahead of the vehicle and using this information in a preview controller. Previous applications have used look-ahead sensors mounted on the front bumper to measure terrain beneath. Such sensors are vulnerable, potentially confused by water, snow, or other soft obstacles and offer a fixed preview time. For convoy vehicle applications, this paper proposes using the overall response of the preceding vehicle(s) to generate preview controller information for follower vehicles. A robust observer is used to estimate the states of a quarter-car vehicle model, from which road profile is estimated and passed on to the follower vehicle(s) to generate a preview function. The preview-active suspension, implemented in discrete time using a shift register approach to improve simulation time, reduces sprung mass acceleration and dynamic tyre deflection peaks by more than 50% and 40%, respectively. Terrain can change from one vehicle to the next if a loose obstacle is dislodged, or if the vehicle paths are sufficiently different so that one vehicle misses a discrete road event. The resulting spurious preview information can give suspension performance worse than that of a passive or conventional active system. In this paper, each vehicle can effectively estimate the road profile based on its own state trajectory. By comparing its own road estimate with the preview information, preview errors can be detected and suspension control quickly switched from preview to conventional active control to preserve performance improvements compared to passive suspensions.

A new optimization algorithm based on a combination of particle swarm optimization, convergence and divergence operators for single-objective and multi-objective problems

Particle swarm optimization (PSO) is a randomized and population-based optimization method that was inspired by the flocking behaviour of birds and human social interactions. In this work, multi-objective PSO is modified in two stages. In the first stage, PSO is combined with convergence and divergence operators. Here, this method is named CDPSO. In the second stage, to produce a set of Pareto optimal solutions which has good convergence, diversity and distribution, two mechanisms are used. In the first mechanism, a new leader selection method is defined, which uses the periodic iteration and the concept of the particle's neighbour number. This method is named periodic multi-objective algorithm. In the second mechanism, an adaptive elimination method is employed to limit the number of non-dominated solutions in the archive, which has influences on computational time, convergence and diversity of solution. Single-objective results show that CDPSO performs very well on the complex test functions in terms of solution accuracy and convergence speed. Furthermore, some benchmark functions are used to evaluate the performance of periodic multi-objective CDPSO. This analysis demonstrates that the proposed algorithm operates better in three metrics through comparison with three well-known elitist multi-objective evolutionary algorithms. Finally, the algorithm is used for Pareto optimal design of a two-degree of freedom vehicle vibration model. The conflicting objective functions are sprung mass acceleration and relative displacement between sprung mass and tyre. The feasibility and efficiency of periodic multi-objective CDPSO are assessed in comparison with multi-objective modified NSGAII.

Suspension Optimization Based on Ride Comfort and Road-Friendly

In order to analyze suspension’ impact on vehicle ride comfort and road-friendly and the way to chose reasonable suspension parameters，a two DOF suspension model was established. Taking RMS of sprung mass acceleration and dynamic load of unsprung mass, a multi-objective suspension parameters optimization model was carried out by optimal points method. After the optimization，the RMS of body decreases by 36.24%,and the RMS of dynamic load decreases by 17.71%.As is stated above, optimal suspension parameters can improve the ride comfort as well as road-friendly.

Performance of Electromagnetic based Suspension System for Automobiles

This paper is concerned with studying the response of a hybrid magnetic vehicle suspension system. The objective of this work is to produce vehicle body isolation by reducing the sprung mass acceleration and minimize the suspension travel, to produce good road holding ability. Two degrees of freedom quarter car model of a passive suspension system with a cylindrical type hybrid magnet is considered for the analysis. Analytical modelling, simulations and laboratory scale experiments are conducted. The performance of active suspension systems from simulations using MATLAB and experiments are compared with the passive suspension system. The amplitude of vibration of the sprung mass using active suspension is considerably reduced from that of passive system.

The Study on Vehicle EHA Active Suspension with Time-Delay Control

A new vehicle active suspension with Electro-Hydrostatic Actuator (EHA) is suggested. The system consists of two parts: spring and actuator with variable control force. The actuator includes hydraulic cylinder, hydraulic pump, controller, etc. According to bond graph principle, bond graph model of EHA active suspension are built. For vehicle active suspension system, unavoidable time delay may appear in the controllable course. Time-delay influence on the dynamic performance of vehicle active suspension is analyzed. Physical prototype and experimental rig for EHA active suspension is built. Then the tests of suspension prototype with time-delay control are carried out on the developed test rig. The results show that the sprung mass acceleration of the active suspension with time-delay compensation significantly declines by 11.56% under the road input of 1.1Hz and by 12.8% under the road input of 1.5Hz

A Research of Vibration Signal Processing of Air Suspension System

Wavelet transform was utilized in vibrant signal processing of air suspension system. A dynamic model of 1/4 engineering vehicle with air suspension system was established. Road surface signal of B grade was input to the dynamic model. Vibrant acceleration curve of under spring mass and dynamic load curve of air suspension was gained. Noise signal of under spring mass acceleration and dynamic load of air suspension system were filtrated by wavelet decomposition. Vibrant acceleration signal of under spring mass and dynamic load signal of air suspension were extracted by wavelet reconstruction. It can provide a theoretical foundation for identifying dynamic load of air suspension system.

Research on the Adaptive Fuzzy Control Based on Variable Universe of with Magneto-Rheological Suspension

The magnetic circuit of MR damper was given,Finite Element Analysis and the structure optimization of MR damper were reserched.The theory of a variable domain by adopting an adaptive algorithm based on fuzzy-control was applied in semi-active suspension control with MR damper.The adaptive law for membership functiongs was designed for input and output.Based on 2DOF 1/4 car model with the simulationed for road protile as random input,the control simulation of MR semi-actibe suspension was carried out,results show that spring mass acceleration reduced while an adaptive algorithim with a variable domain fuzzy control was used to compare with ordinary strategy,the riding comfort got improved.

Experimental Research on the Effect of Sinusoidal Excitation on Dynamic Wheel Load of Hydro-Pneumatic Suspension Vehicle

Based on the mathematical model of quarter car body model being put forward, the indoor platform experiment of quarter car body with hydro-pneumatic suspension system was done. During test, the parameters of dynamic wheel load along with the change of vibration amplitude and frequency were investigated. The results show that: the cycle of acceleration of sprung mass has half cycle lag than unsprung mass, and the main parameters of dynamic wheel load has increased significantly along with the increase of vibration amplitude and frequency. At the same time, through analysis the acceleration time responses of sprung and unsprung mass, it can be shown that hydro-pneumatic suspension has good anti-vibration performance.

The Time-Delay Study on Vehicle Active Control Suspension

Actuator is a key factor for vehicle active suspension. A new vehicle active suspension is put forward based on the Electro-Hydrostatic Actuator (EHA).For vehicle active suspension system, unavoidable time delay may appear in the controllable course. The critical time-delay of EHA active suspension is calculated in this paper and time-delay influence on the dynamic performance of vehicle active suspension is analyzed. A time-delay compensation strategy for EHA active suspension is proposed to reduce time delay. A self-adapting fuzzy controller is designed and applied to active suspension system with EHA. Physical prototype and experimental rig for EHA active suspension are built. Then time-delay tests of suspension prototype are carried out on the developed test rig. Test results show that the sprung mass acceleration of the active suspension with time-delay compensation significantly declines by 12.4% under the road input of 1.2Hz and by 13.6% under the road input of 1.6Hz.

Design of a genetic-algorithm-based self-tuning sliding fuzzy controller for an active suspension system

Due to the fixed damping coefficient of the passive suspension system, it is difficult to enhance ride comfort and driving quality. An active suspension system provides extra force through the actuator which allows it to effectively isolate energy from vibrations and improve passenger comfort. This paper investigates ride comfort of a quarter-vehicle active suspension system according to the ISO 2631-1 standard. Using feedback information about the sprung mass acceleration, unsprung mass acceleration, and suspension deflection, an extended Kalman filter is developed to estimate the six unknown state variables: the sprung mass displacement and velocity; unsprung mass displacement and velocity; actuating force; and spool valve displacement. In addition, the road surface irregularities are also estimated. As compared to conventional controllers, the hydraulic actuator has time-varying, uncertain, and highly non-linear characteristics; thus, this paper applies a genetic-algorithm-based self-tuning sliding fuzzy controller and feedback linearization technique to design the actuating force. Simulation results are presented that show that the proposed controller demonstrates significant improvements in the vibration suppression of the vehicle body and ride comfort compared to a linear quadratic Gaussian controller design.

Sliding-mode control for semi-active suspension with actuator dynamics

A sliding-mode controller (SMC) is proposed for semi-active suspensions to achieve ride comfort and handling performance simultaneously. First, a nonlinear quarter-car model of Macpherson strut suspension is established in Matlab/Simulink. Constrained damper force and actuator dynamics are considered for the damper model. System identification is applied to the nonlinear model for obtaining the linear model parameters. Kalman filter is designed based on the linear model and the actuator dynamics to estimate the state responses required for SMC. The sliding surface consists of tyre deflection and sprung mass acceleration. The proposed SMC is evaluated using the nonlinear model for both time and frequency domain responses. Robustness due to the increased sprung mass and deteriorated suspension is also investigated in this paper. Preliminary simulation results show improved ride comfort without sacrificing the road holding performance.

Non-dimensionalised closed-form parametric analysis of semi-active vehicle suspensions using a quarter-car model

This article provides a non-dimensionalised closed-form analysis of semi-active vehicle suspensions, using a quarter-car model. The derivation of the closed-form solutions for three indices that can be used for ride comfort, vehicle handling, and stability are presented based on non-dimensionalised suspension parameters. The behaviour of semi-active vehicle suspensions is evaluated using skyhook, groundhook, and hybrid control policies, and compared with passive suspensions. The relationship between vibration isolation, suspension deflection, and road holding is studied, using three performance indices based on the mean square of the sprung mass acceleration, rattle space, and tyre deflection, respectively. The results of the study indicate that the hybrid control policy yields significantly better comfort than a passive suspension, without reducing the road-holding quality or increasing the suspension displacement for typical passenger cars. The results also indicate that for typical passenger cars, the hybrid control policy results in a better compromise between comfort, road holding and suspension travel requirements than both the skyhook and groundhook control methods.

Analysis and simulation of semi-active suspension control policies for two-axle off-road vehicle using full model

Ride comfort and vehicle handling of heavy off-road vehicles can be improved with the help of a controlled suspension system. This paper describes the impact of a semi-active and passive system on the driving behaviour of a heavy off-road 4 × 4 wheeled vehicle. The analysis is based on a military vehicle model used for simulating off-road vehicle drives and handling. The analysis covers both transient responses and transmissibility response in frequency domain. To start with, the fundamental skyhook, groundhook and hybrid principles are used for controlling. Frequency response and sprung mass accelerations, suspension and tyre deflection response in time domain are clearly improved using semi-active control policies compare to passive system.

PARETO OPTIMIZATION OF A TWO-DEGREE OF FREEDOM PASSIVE LINEAR SUSPENSION USING A NEW MULTI-OBJECTIVE GENETIC ALGORITHM

The primary function of a suspension system of a vehicle is to isolate the road excitations experienced by the tires from being transmitted to the passengers. In this paper, we formulate an optimal vehicle suspension design problem with the quarter-car vehicle dynamic model. A new multi-objective genetic algorithm is used for Pareto optimization of a two-degree of freedom vehicle vibration model considering the two conflicting functions simultaneously. The important conflicting objective functions that have been considered in this work are, namely, sprung mass acceleration and relative displacement between sprung mass and tire. The comparison of the obtained results with those in the literature demonstrates the superiority of the results of this work. It is shown that the results of 2-objective optimization provide more non-dominated choices for designers to select appropriate choices regarding the condition and purpose of using a vehicle in order to optimal design of a product.

Robust active suspension design subject to vehicle inertial parameter variations

This paper presents an approach in designing a robust controller for vehicle suspensions considering changes in vehicle inertial properties. A four-degree-of-freedom half-car model with active suspension is studied in this paper, and three main performance requirements are considered. Among these requirements, the ride comfort performance is optimized by minimizing the H ? norm of the transfer function from the road disturbance to the sprung mass acceleration, while the road holding performance and the suspension deflection limitation are guaranteed by constraining the generalized H 2 (GH 2) norms of the transfer functions from the road disturbance to the dynamic tyre load and the suspension deflection to be less than their hard limits, respectively. At the same time, the controller saturation problem is considered by constraining its peak response output to be less than a given limit using the GH 2 norm as well. By solving the finite number of linear matrix inequalities (LMIs) with the minimization optimization procedure, the controller gains, which are dependent on the time-varying inertial parameters, can be obtained. Numerical simulations on both frequency and bump responses show that the designed parameter-dependent controller can achieve better active suspension performance compared with the passive suspension in spite of the variations of inertial parameters.

Heavy vehicle dynamics with balanced suspension based on enveloping tire model

The tire-road contact mechanics is the key problem in vehicle ride comfort and road-friendliness research. A flexible roller contact (FRC) tire model with the enveloping property is introduced to reflect the contact history between the tire and the road. Based on D’Alembert principle, an integral balanced suspension (IBS) model is established, considering mass and moment of inertia of the stabilizer rod. The sprung mass acceleration and tire dynamic force for balanced suspension and the traditional quarter-vehicle model are compared respectively for frequency and time domain responses. It is concluded that the quarter-vehicle model can be used to evaluate the ride comfort of vehicles; however, it has some limitations in evaluating the vehicle road-friendliness. Then, the dynamics performances for IBS model are analyzed with the single point contact (SPC) model and FRC model, respectively. These works are expected to propose a new idea for the vehicle-road interaction research.