Suspension Travel Research Articles

Enhanced Sliding Mode Control for a Nonlinear Active Suspension Full Car Model

This paper delivers findings on optimal robust control studies of nonlinear full car models. A nonlinear active suspension full car model is used, which considers the dynamic of a hydraulic actuator. The investigation on the benefit of using Sliding Mode Control (SMC) structure for the effective trade-off between road handling. The design of SMC in the chassis/internal subsystem is enhanced by modifying a sliding surface based on Proportional-Integral-Derivatives (PID) with the utilization of particle swarm optimization (PSO) algorithm in obtaining the best optimum value of control parameters. The switching control is designed through the Lyapunov function, which includes the boundedness of uncertainties in sprung masses that can guarantee the stability of the control design. The responses of the proposed controller have improved the disturbance rejection up to 60% as compared to the conventional SMC controller design and shown the high robustness to resist the effect of varying the parameter with minimal output deviations. The study proved that the proposed SMC scheme offers an overall effective performance in full car active suspension control to perform a better ride comfort as well as the road handling ability while maintaining a restriction of suspension travel. An intensive computer simulation (MATLAB Simulink) has been carried out to evaluate the effectiveness of the proposed control algorithm under various road surface conditions.

Multi-objective optimization of vehicle seat suspension with friction under random excitation

A seat suspension contributes greatly to vehicle ride comfort as a result of direct contact with the human body. Friction in a seat suspension produces strong non-smooth nonlinearity in seat dynamics, which makes the simulation-based optimization on the seat suspension’s performance time-consuming. This study tries to address parameter optimization on a vehicle seat suspension with the friction force in an analytical approach. A two degrees of freedom model is firstly established for the human body-seat system with friction and subjected to bandlimited random excitation. The nonlinear model is converted into an equivalent linear model by using Gaussian linearization. The dynamic responses of the linear model have then derived analytically and validated by Monte Carlo simulations. Based on the analytical solution, a multi-objective optimization strategy is proposed for the seat suspension. The acceleration of the human body and the suspension travel are chosen as the objective indexes to evaluate seat performance. Simulation results show that the proposed optimization strategy is efficient, where a global optimum is guaranteed owing to the analytical expression of the objective function. The optimization approach taking advantage of model linearization can be applied to similar mechanical systems with friction.

Road classification using built-in self-scaling method of Bayesian regression

This paper proposes the use of the built-in self-scaling (BS) method for ISO classification of road roughness. The technique employs the transfer function between the vehicle body acceleration as input and the suspension travel as output. This transfer function has a nonzero dc gain, which is important for application of the BS method. Frequency response magnitude patterns corresponding to this transfer function are estimated via Bayesian regression, capitalizing on the inherent properties of the BS method where the prior dc gain is incorporated into the formulation. This strategy leads to high classification accuracy. The proposed approach requires only low-cost sensors. It possesses a short detection time of 0.5s and a short training time of 5s for each road class. The method is model-free and does not require recalibration when the load carried by the vehicle changes. Additionally, it is capable of handling varying vehicle velocity and is effective for both passive and active suspensions. A laboratory-scale experiment shows that the proposed technique increases the percentage of correct classification by an average of 34% in the case of constant road profiles, compared with a state-of-the-art method using augmented Kalman filtering. A corresponding value of 24% is achieved for a varying road profile. The significant improvement in the accuracy of road classification is impactful as it will enable controller design for suspension systems to be enhanced resulting in more comfortable ride and higher vehicle stability.

Comparing the physical principles of action of suspension damping devices based on their influence on the mobility of wheeled vehicles

This paper reports the comparison of two physical principles of action of suspension damping devices based on their influence on the mobility indicators for an 8×8 wheeled machine. A radical difference between these principles of action is the dependence of resistance forces on the speed of the relative movement of working bodies (internal friction: hydraulic shock absorbers) or on the relative movement of working bodies (external friction: friction shock absorbers). Widespread hydraulic shock absorbers have certain disadvantages that do not make it possible to further increase the mobility of wheeled or tracked vehicles without the use of control and recuperation systems. In turn, in friction shock absorbers, the use of new materials has eliminated many of their shortcomings and thus can provide significant advantages. It was established that the application of friction shock absorbers for a given wheeled vehicle did not significantly affect the speed compared to hydraulic ones. The main factor that prevented the implementation of the advantages of friction shock absorbers was the insufficient suspension travel. However, friction shock absorbers absorbed 1.76...2.3 times less power, which reduced the load on nodes and increased efficiency (autonomy). In addition, a more uniform load on suspensions was ensured, which improved their resource, and, due to the prevailing vertical oscillations of the suspended body over the longitudinal-angular ones, the geometric passability improved as well. The comparison of two physical principles of action of damper suspension devices in a wheeled vehicle has shown that the use of friction shock absorbers could provide significant advantages in resolving the task relates to improving the mobility and would fundamentally affect the choice of the suspension energy recuperation system if it is applied.

Neuro-adaptive optimized control for full active suspension systems with full state constraints

In this paper, an adaptive neural network (NN) optimized control strategy is presented to improve the inherent tradeoff between ride comfort of passengers and the suspension travel for full vehicle active suspension system with state constraints. To the best of our knowledge, the automotive suspension system control using hydraulic actuators is a highly complex nonlinear control task, involving external disturbances and uncertainties. To address it, this paper develops the virtual and actual optimal controllers based on backstepping technique and the identifier-actor-critic structure. Meanwhile, the Barrier Lyapunov functions are developed to prevent the systems from the state constraints and the systems states are limited in the preselected compact sets. It is particularly worth mentioning that the proposed optimal control strategy ensures that all the closed-loop signals remain bounded, while the power of the control input as well as the amplitude of the vertical displacement has been minimized. The simulation results show how the full-car system can be controlled optimally and satisfactorily, and confirm the superiority of proposed method.

Artificial Neural Network Prediction of the Optimal Setup Parameters of a Seven Degrees of Freedom Mathematical Model of a Race Car: IndyCar Case Study

The aim of this paper is the development of a 7-DOF (Degrees Of Freedom) mathematical model of an IndyCar and the implementation of an Artificial Neural Network in order to predict the optimal setup parameters of the car, reducing time and costs for race teams. The mathematical model is created by using MATLABTM and Simulink software starting from a telemetry acquisition at the Houston circuit and is based on Vertical Vehicle Dynamic equations. The optimal setup parameters have been predicted through an Artificial Neural Network (ANN) by using the NFTOOL Toolbox of MATLABTM software. ANN is implemented in a Quarter Car model, firstly, in order to train the network and predict the parameters able to reduce tire deflection and suspension travel in the time domain and the resonance peaks amplitude in the frequency domain. Then, it is implemented in the 7-DOF model in order to predict the best setup parameters able to reduce body movements and the weight transfers of the car.

Optimization of Nonlinear Passive Suspension System to Minimize Road Damage for Heavy Goods Vehicle

Major contributors to the road damage are Heavy Goods Vehicles (HGV), resulting in high maintenance costs of roads. This high cost makes it necessary to look into the issue seriously for minimizing the road damage. An Automobile Engineer can reduce road damage through the efficient design of a suspension system. The design involves satisfying the two conflicting criteria of riding comfort and vehicle handling with the restriction on the suspension travel. This paper involves designing an automobile suspension system, to improve the performance of the vehicle without a significant change in the cost of the suspension system and minimize road damage. To achieve the aforesaid objective, the use of a nonlinear passive suspension is suitable as compared to a linear passive suspension system. For the analysis, a HGV model of vehicle suspension has been considered. The suspension system considered for investigation comprises of a cubical nonlinear spring and a linear damper. Road damage has been represented by the fourth power of the tire dynamic load. A genetic algorithm has been used to optimize the half truck model to minimize road damage. The solution has been obtained using MATLAB and SIMULINK.

Modelling and simulation of active and passive seat suspensions for vibration attenuation of vehicle occupants

Literature on biodynamic modelling of the occupant in a vehicle associates riders’ comfort with human-seat interaction forces and vibration attenuation capabilities of the suspension system. Though the superiority of active suspension systems over passive ones is well established in literature, quantification of this superiority by using the best possible passive suspension system has not been reported. This work attempts to do this. It integrates a nonlinear cushion seat contact force model and a 12 degrees of freedom two-dimensional seated human body model supported by an inclined backrest with a full vehicle model through the seat suspension system. The passive and active proportional integral derivative suspension system parameters are obtained by simultaneously minimizing the seat effective amplitude transmissibility, cushion contact force and head motion using a multi-objective genetic algorithm in MATLAB-SIMULINK co-simulation. The time responses of cushion contact force, head vertical and fore-aft motion are studied for two road profiles—random and bump. Comparative analyses were also done with regard to internal forces, absorbed power and the effect on vehicle chassis. Human body response to different grades of road roughness and vehicle speeds were investigated. The results establish the clear superiority of the active system in all aspects with rise in suspension travel and acceleration of vehicle chassis in the vertical direction for a random road profile. A parameter sensitivity analysis allowed us to identify spring stiffness as the component which needs greatest care during fabrication.

A comparison of different models of passive seat suspensions

Long duration exposure to vehicle induced vibration causes various ailments to humans. Amongst the various components of the human-vehicle system, the seat suspension plays a major role in determining the level of vibration transferred to humans. However, optimising the suspension for maximising human comfort leads to poor vehicle handling characteristics. Thus, predicting human comfort through various seat suspension models is a widely researched topic. However, the appropriate seat suspension model to be used has not been identified so far. Neither has any prior work reported integrating models of all the components necessary for this analysis, namely human body, cushion, seat suspension and vehicle chassis, each with the appropriate level of complexity. This work uses a two-dimensional 12 DoF seated human body model with inclined backrest support, a nonlinear cushion model, a seat suspension model and a full vehicle model. Two kinds of road profiles – one with random roughness and one with a bump – have been used. It then compares the performance of five different seat suspension models based on a number of human comfort related parameters (seat to head transmissibility, suspension travel, seat acceleration, cushion contact force and head acceleration in both vertical and fore-aft directions) and vehicle handling parameters (vertical, rolling and pitching acceleration of chassis). The results clearly show the superiority of the configuration which involves a spring parallel to an inclined multi-stage damper. A separate analysis was also done to judge whether the integration of the vehicle model (with its associated complication) was necessary for this analysis. A comparison of the human body’s internal forces, moments, acceleration, and absorbed power with and without the vehicle model clearly indicates the need of using the former.

Parametric analysis of vehicle suspension based on air spring and MR damper with semi-active control

Three strategies are used in this paper to investigate suspension systems behaviour. Firstly, the steel coil passive spring (conventional spring) is replaced by air spring, which comprised of an airbag, a connection pipe with a control valve, and a reservoir tank system. The influence of air spring pressure, reservoir volume and connection pipe diameter on suspension system behaviour are investigated. Secondly, a logic control scenario for the oscillation mass of air between spring airbag and the reservoir is applied by using on/off valve controller to study the controlling valve influence on the whole vehicle dynamics responses. Thirdly, the MR damper is used to introduce a variable damping coefficient as a semi-active control (skyhook) strategy of the suspension system. To represent the suspension system with the earlier mentioned strategies, a mathematical model 2-DOF for a quarter car is adopted along with governing equations of the air spring and semi-active skyhook control under the Matlab/Simulink platform. The obtained result, i.e., suspension travel displacement, body acceleration, dynamic tire force, and damper dissipation energy, are calculated in terms of RMS to show up the dynamic behaviour of suspension system considering four configurations in various control styles. The models’ responses were examined versus two road excitations pattern, including harmonic excitation and random road excitation. The results show that using air spring is considerably increased suspension quality, furthered more the suspension system is significantly enhanced when semi-active strategies are applied on air spring and MR damper.

Multiobjective Optimization of an Off-Road Vehicle Suspension Parameter through a Genetic Algorithm Based on the Particle Swarm Optimization

Ride comfort and handling performances are known conflicts for off-road vehicles. Recent publications focus on passenger vehicles on class B and class C roads, while, for off-road vehicles, they should be able to run on rougher roads: class D, class E, or class F roads. In this paper, a quarter vehicle model with nonlinear damping is established to analyze the suspension performance of a medium off-road vehicle on the class F road. The ride comfort, road holding, and handling performance of the vehicle are indicated by the weighted root mean square (RMS) value of the vertical acceleration of the sprung mass, suspension travel, and tire deflection. To optimize these objectives, the genetic algorithm (GA), particle swarm optimization (PSO), and a genetic algorithm based on the particle swarm optimization (GA-PSO) are initiated. The efficiency and accuracy of these algorithms are compared to find the best suspension parameters. The effect of the optimized method is validated by the field test result. The ride comfort, road holding, and handling performance are improved by approximately 20%.

Comfort improvement in railway vehicles via optimal control of adaptive pneumatic suspensions

ABSTRACT This paper presents an adaptive optimal control strategy focused on improving ride comfort by minimising the root mean square of accelerations measured at seven locations on the carbody floor. It requires preview knowledge of both the train speed and the standard track quality (not the deterministic track disturbances) and differs from other works in considering pointwise constraints (upper and lower secondary suspension travel limits). Adaptive control is achieved by varying the diameter of the restriction orifice which connects the pneumatic spring to the auxiliary air reservoir, which confers different dynamic stiffness and damping to the front and rear secondary suspensions. Decision maps with the front and rear optimal diameters for five track irregularity levels and six different speeds were obtained using a Monte Carlo strategy based on solving the optimal control problem for 240 stochastic realisations of time-varying track irregularities of 300 s. Results show that the adaptive optimal control provides a successful compromise between comfort and safety which overshadows the conventional passive approach: it improves comfort up to 50% with respect to stiff passive configurations and it guarantees constraint fulfilment unlike compliant passive configurations.

Vortex‐Induced Vibration Suppression of Bridges by Inerter‐Based Dynamic Vibration Absorbers

The vortex‐induced vibration may cause fatigue of a bridge structure, affecting the safety of vehicles and the comfort of pedestrians. Inerter is a two‐terminal device, which has been applied in many areas. This paper studies the problem of suppressing the vortex‐induced vibration of a bridge by using an inerter‐based dynamic vibration absorber (IDVA). The performances in terms of the suspension travel and the vertical displacement of the bridge with different IDVAs in suppressing vortex‐induced vibration are compared, and the effect of the installation position of IDVA on the performance of suppressing vortex‐induced vibration is shown. The performance indexes for the vertical displacement of six IDVA arrangements are obtained by using an iterative method, where the performance indexes for the vertical displacement are minimized by using the optimization toolbox in a commercial software. The result shows that the optimal installation positions and the number of suitable installation positions are affected by the resonant mode. Among the six arrangements, one arrangement is identified to have the best performance of suppressing vortex‐induced vibration. All the six arrangements have reduced the suspension travel performance.

A comparative analysis between some dynamic models for the vehicle suspension system

This article deals a comparative analysis between several representative dynamic models for the suspension system of the motor vehicles, namely quarter-vehicle, half-vehicle and full-vehicle models. The dynamic model of the suspension system contains the guiding linkages of the front and rear wheels/axle, by case, along with the elastic and dissipative suspension elements (helical springs, shock absorbers/dampers, buffers limiting the expansion & compression suspension travel, bushings, tires). The dynamic analysis (simulation) of the considered models was carried out with the help of virtual prototyping software solution ADAMS (currently developed by MSC Software Corporation), by considering the dynamic with shock regime, which consists in the sudden release of the car to fall on the ground from a given height. This is one of the standard tests in automotive industry for evaluating the comfort performance of the vehicles.

Strongly perturbed sliding mode adaptive control of vehicle active suspension system considering actuator nonlinearity

Aiming at the problem of improving driving comfort under the condition of ensuring driving safety and limited suspension travel, this paper proposes a sliding mode adaptive controller suitable for strong disturbance action. Considering the nonlinear characteristics of the hydraulic actuator, a one-half vehicle suspension model with uncertain parameters and external disturbances is established. In the sliding mode design part of the controller, the sliding mode equivalent control items of the vertical and pitch subsystems are derived, and the optimised constant velocity approach law is adopted. The sliding mode switching control item is given to ensure that the controller can effectively adjust the vehicle body posture when the system is subjected to strong external disturbance. Finally, by selecting the adaptive law, the controller can adapt to the uncertainty of the vehicle body parameters. The simulation results for the specific example considered in this work show that the control strategy can greatly improve the ride comfort under the premise of ensuring the safety of the vehicle and the stability of the steering. Compared with the backstepping adaptive control, the control strategy of this paper shows superiority when the system is subjected to strong disturbance.

Hardware in the Loop Testing of Adaptive Inertia Weight PSO-Tuned LQR Applied to Vehicle Suspension Control

This paper presents an adaptive inertia weight particle swarm optimization (AIWPSO) employed for solving the multiobjective weight optimization problem of LQR applied for the vehicle active suspension system (ASS). To meet the competing control objectives of ASS including the ride comfort, road handling, and suspension travel, the state feedback controller design for ASS is formulated as an optimization problem and an improved PSO is employed for finding the optimal weights of the linear-quadratic regulator (LQR). Specifically, for solving the premature convergence of the particles and imbalance between exploration and exploitation capabilities of PSO, an adaptive inertia weight that updates the velocity of the particles based on the success rate is used. The efficacy of the AIWPSO-tuned LQR is experimentally tested on a quarter-car ASS plant using the hardware in loop (HIL) testing for an uneven road surface. Experimental results highlight that, compared to conventional PSO-tuned LQR, the proposed scheme can significantly minimize the vehicle body acceleration due to irregular road profile while guaranteeing the minimum tire friction for passenger safety. The ISO 2361-1 standards adopted to evaluate the ride and health criteria substantiate that the proposed scheme reduces the vibration dose value by 25.34% for a bumpy road profile. Moreover, the cumulative power spectral density (CPSD) of vehicle body acceleration assessed in both low- and high-frequency regions manifests the significant improvement in the ride comfort.

Multi-Objective Model Predictive Control for Vehicle Active Suspension System

This paper puts forward a multi-objective model predictive control scheme in order to address the conflicting control objectives of a vehicle active suspension system. The key problem in designing an active suspension controller is that the controller has to realize a feasible control input that can satisfy the competing control requirements such as ride comfort, suspension travel and road handling. Hence, in this work, these constraints are integrated into an optimal control framework and a finite horizon model predictive controller is used to solve the multi-objective cost function. The key advantage of the proposed scheme is that the model predictive control design finds the optimal control input by solving the discrete time algebraic Riccati equation. This guarantees not only a robust closed loop system but also a realizable control effort, without violating the hard constraints of the active suspension system. The proposed model predictive control design is experimentally validated on a laboratory scale quarter car suspension system using hardware-in-loop testing. The performance of the model predictive control scheme is compared with the one of the unconstrained linear quadratic regulator and tested for four realistic road profiles. The experimental results substantiate that the suspension system controlled by the model predictive controller offers better ride comfort and road handling features when compared to the conventional linear quadratic regulator.

Pointwise‐constrained optimal control of a semiactive vehicle suspension

SummaryThis article presents an optimal control strategy (OCS) for semiactive vehicle suspensions with road profile sensors. The suspension is modeled as a quarter‐car model with a magnetorheological (MR) damper. The OCS main objective is to minimize the fourth‐power acceleration of the sprung mass. In addition, three pointwise constraints of the model are taken into account when the optimal control problem is solved: suspension travel limits (upper and lower) and tyre vertical force. In order to deal with a large number of constraints, we implement the gradient optimization method based on the method of moving asymptotes routine, which shows very good performance reaching optimal controls while satisfying the constrains. The solution has been compared with two passive MR damper configurations (low and high damping) as well as Skyhook and Balance control strategies for three different road inputs. Results show that OCS fulfills the constraints and reduces the sprung mass acceleration peak and the root‐mean‐quad acceleration up to 59%, in comparison to passive strategies.

Vibration control of an active horizontal seat suspension with a permanent magnet synchronous motor

This paper describes the control design of an active horizontal seat suspension with an electromagnetic actuator. First, physical and mathematical models of an active vibration reduction system with a seated human body are established. Then, a novel control strategy for the permanent magnet synchronous motor is developed to improve the vibro-isolation properties of the horizontal seat suspension. A multi-criteria optimisation is employed to obtain control system parameters that allow simultaneous minimisation of two conflicting vibro-isolation criteria, i.e. the seat effective amplitude transmissibility (SEAT) factor and the suspension travel. Finally, a laboratory investigation of the effectiveness of the active system is conducted and the dynamic performance of the system is compared with that of a corresponding conventional passive suspension system.

Analysis of the Influence of Suspension Actuator Limitations on Ride Comfort in Passenger Cars Using Model Predictive Control

Active suspension systems help to deliver superior ride comfort and can be used to resolve the objective conflict between ride comfort and road-holding. Currently, there exists no method for analyzing the influence of actuator limitations, such as maximum force and maximum rate of change, on the achievable ride comfort. This research paper presents a method that is capable of doing this. It uses model predictive control to eliminate the influence of feedback controller performance and to integrate both actuator limitations and necessary constraints on dynamic wheel-load variation and suspension travel. Various scenarios are simulated, such as driving over a speed bump and inner city driving, as well as driving on a country road and motorway driving, using a state-of-the-art quarter-car model, parameterized for a luxury class vehicle. It is analyzed how comfort, or in one scenario road-holding, can be improved with consideration for the actuator limitations. The results indicate that actuator rate limitation has a strong influence on vertical vehicle dynamics control system performance, and that relatively small maximum forces of around 1000 to 2000 N are sufficient to successfully reject disturbances from road irregularities, provided the actuator is capable of supplying the forces at a sufficiently high rate of change.