Stochastic sampled-data multi-objective control of active suspension systems for in-wheel motor driven electric vehicles

This paper addresses the sampled-data multi-objective active suspension control problem for an in-wheel motor driven electric vehicle subject to stochastic sampling periods and asynchronous premise variables.The focus is placed on the scenario that the dynamical state of the half-vehicle active suspension system is transmitted over an in-vehicle controller area network that only permits the transmission of sampled data packets.For this purpose,a stochastic sampling mechanism is developed such that the sampling periods can randomly switch among different values with certain mathematical probabilities.Then,an asynchronous fuzzy sampled-data controller,featuring distinct premise variables from the active suspension system,is constructed to eliminate the stringent requirement that the sampled-data controller has to share the same grades of membership.Furthermore,novel criteria for both stability analysis and controller design are derived in order to guarantee that the resultant closed-loop active suspension system is stochastically stable with simultaneous𝐻2 and𝐻∞performance requirements.Finally,the effectiveness of the proposed stochastic sampled-data multi-objective control method is verified via several numerical cases studies in both time domain and frequency domain under various road disturbance profiles.

Semi-active control for vibration attenuation of vehicle suspension with symmetric MR damper

A semi-active force tracking PI controller is formulated and analyzed for a magnetorheological (MR) fluid-based damper in conjunction with a quarter-vehicle model. Two different models of the MR-damper are integrated into the closed-loop system model, which includes: a model based upon the mean force-velocity (f-v) behaviour; and a model synthesis comprising inherent nonsmooth hysteretic force and the force limiting properties of the MR damper. The vehicle models are analyzed to study the vibration attenuation performance of the MR-damper using the semi-active force tracking PI control algorithm. The simulation results are also presented to demonstrate the influence of the damper nonlinearity, specifically the hysteresis, on the suspension performance. The results show that the proposed control strategy can yield superior vibration attenuation performance of the vehicle suspension actuated by the controllable MR-damper not only in the sprung mass resonance and the ride zones, but also in the vicinity of the wheel-hop. The results further show that the presence of damper hystersis deteriorates the suspension performance.

Semi-active Sliding Mode Control of Vehicle Suspension with Magneto-rheological Damper

The vehicle semi-active suspension with magneto-theological damper（MRD） has been a hot topic since this decade, in which the robust control synthesis considering load variation is a challenging task. In this paper, a new semi-active controller based upon the inverse model and sliding mode control （SMC） strategies is proposed for the quarter-vehicle suspension with the magneto-rheological （MR） damper, wherein an ideal skyhook suspension is employed as the control reference model and the vehicle sprung mass is considered as an uncertain parameter. According to the asymptotical stability of SMC, the dynamic errors between the plant and reference systems are used to derive the control damping force acquired by the MR quarter-vehicle suspension system. The proposed modified Bouc-wen hysteretic force-velocity （F-v） model and its inverse model of MR damper, as well as the proposed continuous modulation （CM） filtering algorithm without phase shift are employed to convert the control damping force into the direct drive current of the MR damper. Moreover, the proposed semi-active sliding mode controller （SSMC）-based MR quarter-vehicle suspension is systematically evaluated through comparing the time and frequency domain responses of the sprung and unsprung mass displacement accelerations, suspension travel and the tire dynamic force with those of the passive quarter-vehicle suspension, under three kinds of varied amplitude harmonic, rounded pulse and real-road measured random excitations. The evaluation results illustrate that the proposed SSMC can greatly suppress the vehicle suspension vibration due to uncertainty of the load, and thus improve the ride comfort and handling safety. The study establishes a solid theoretical foundation as the universal control scheme for the adaptive semi-active control of the MR full-vehicle suspension decoupled into four MR quarter-vehicle sub-suspension systems.

Skyhook-based Semi-active Control of Full-vehicle Suspension with Magneto-rheological Dampers

The control study of vehicle semi-active suspension with magneto-rheological (MR) dampers has been attracted much attention internationally. However, a simple, real time and easy implementing semi-active controller has not been proposed for the MR full-vehicle suspension system, and a systematic analysis method has not been established for evaluating the multi-objective suspension performances of MR full-vehicle vertical, pitch and roll motions. For this purpose, according to the 7-degree of freedom (DOF) fullvehicle dynamic system, a generalized 7-DOF MR and passive full-vehicle dynamic model is set up by employing the modified Boucwen hysteretic force-velocity (F-v) model of the MR damper. A semi-active controller is synthesized to realize independent control of the four MR quarter-vehicle sub-suspension systems in the full-vehicle, which is on the basis of the proposed modified skyhook damping scheme of MR quarter-vehicle sub-suspension system. The proposed controller can greatly simplify the controller design complexity of MR full-vehicle suspension and has merits of easy implementation in real application, wherein only absolute velocities of sprung and unsprung masses with reference to the road surface are required to measure in real time when the vehicle is moving. Furthermore, a systematic analysis method is established for evaluating the vertical, pitch and roll motion properties of both MR and passive full-vehicle suspensions in a more realistic road excitation manner, in which the harmonic, rounded pulse and real road measured random signals with delay time are employed as different road excitations inserted on the front and rear two wheels, by considering the distance between front and rear wheels in full-vehicle. The above excitations with different amplitudes are further employed as the road excitations inserted on left and right two wheels for evaluating the roll motion property. The multi-objective suspension performances of ride comfort and handling safety of the proposed MR full-vehicle suspension are thus thoroughly evaluated by comparing with those of the passive full-vehicle suspension. The results show that the proposed controller can ideally improve multiobjective suspension performances of the ride comfort and handling safety. The proposed harmonic, rounded pulse and real road measured random signals with delay time and asymmetric amplitudes are suitable for accurately analyzing the vertical, pitch and roll motion properties of MR full-vehicle suspension system in a more realistic road excitation manner. This research has important theoretical significance for improving application study on the intelligent MR semi-active suspension.

SEMI-ACTIVE CONTROL OF VEHICLE SUSPENSION WITH MAGNETO-RHEOLOGICAL DAMPERS:PART Ⅰ——CONTROLLER SYNTHESIS AND EVALUATION

A modified skyhook-based semi-active controller is proposed for implementing an asymmetric control suspension design with symmetric magneto-rheological （MR） dampers. The controller is formulated in current form, which is modulated by integrating a continuous modulation and an asymmetric damping force generation algorithms, so as to effectively minimize switching and hysteretic effects from the MR-damper. The proposed controller is implemented with a quarter-vehicle MR-suspension model, and its relative response characteristics are thus evaluated in terms of defined performance measures under varying amplitude harmonic, rounded pulse and random excitations. The sensitivity of the semi-active suspension performance to variations in controller parameters is thoroughly evaluated. The results illustrate that the proposed skyhook-based asymmetric semi-active MR-suspension controller has superior robustness on the system parameter variations, and can achieve desirable multi-objective suspension performance.

Decentralized Dynamic Event-Triggered Communication and Active Suspension Control of In-Wheel Motor Driven Electric Vehicles with Dynamic Damping

This paper addresses the co-design problem of decentralized dynamic event-triggered communication and active suspension control for an in-wheel motor driven electric vehicle equipped with a dynamic damper. The main objective is to simultaneously improve the desired suspension performance caused by various road disturbances and alleviate the network resource utilization for the concerned in-vehicle networked suspension system. First, a T-S fuzzy active suspension model of an electric vehicle under dynamic damping is established. Second,a novel decentralized dynamic event-triggered communication mechanism is developed to regulate each sensor's data transmissions such that sampled data packets on each sensor are scheduled in an independent manner. In contrast to the traditional static triggering mechanisms, a key feature of the proposed mechanism is that the threshold parameter in the event trigger is adjusted adaptively over time to reduce the network resources occupancy. Third, co-design criteria for the desired event-triggered fuzzy controller and dynamic triggering mechanisms are derived. Finally, comprehensive comparative simulation studies of a 3-degrees-of-freedom quarter suspension model are provided under both bump road disturbance and ISO-2631 classified random road disturbance to validate the effectiveness of the proposed co-design approach. It is shown that ride comfort can be greatly improved in either road disturbance case and the suspension deflection, dynamic tyre load and actuator control input are all kept below the prescribed maximum allowable limits, while simultaneously maintaining desirable communication efficiency.

SEMI-ACTIVE CONTROL OF VEHICLE SUSPENSION WITH MAGNETO-RHEOLOGICAL DAMPERS PARTⅡ——EVALUATION OF SUSPENSION PERFORMANCE

The design and analysis of an intelligent vehicle suspension with MR dampers should address hybrid semi-active control goals, such as rejection of current-switching discontinuity and MR-damper hysteresis, asymmetric damping from the symmetric MR-damper design, robustness on the vehicle operation parameter uncertainties and consideration of essential multiple suspension goals. Following the proposed skyhook-based asymmetric semi-active controller （Part I ） for achieving the above goals, herein, a set of suspension performance measures and three kinds of varying amplitude harmonic, rounded pulse and really measured random excitations are systematically defined, and the sensitivity of quarter-vehicle MR-suspension performance to variations in operating conditions is thoroughly analyzed. The results illustrate that the proposed skyhook-based semi-active MR-suspension in the asymmetric mode yields relatively superior dynamic responses to meet the multiple suspension performances of ride, rattle space, road-holding and dynamic tire force transmitted to the pavement, and has desirable robustness on variations in operating conditions of vehicle load and speed and the road roughness.

Neuron PI control for semi-active suspension system of tracked vehicle

A neuron proportion integration (PI) control strategy for semi-active suspension system of tracked vehicle was proposed based on its unique structure and the multiple and complex environment of the driving traffic. An adaptive genetic algorithm is used to optimize the parameters of the neuron PI controller. The simulation result of the neuron PI control for semi-active suspension system of tracked vehicle indicates that the vertical amplitude,pitch angle and vertical acceleration of the vehicle are well controlled. The root mean square (RMS) of the vertical amplitude decreases by 37.2%,and 45.2% for the pitch angle,38.6% for the vertical acceleration. The research of neuron PI control experiment for the semi-active suspension system of the tracked vehicle model mining in benthal indicates that the RMS of the weight acceleration vibrating along the vertical direction decreases by 29.5%,the power spectral density resonance peak of the acceleration of the car body decreases by 23.8%.

Observer-based hybrid control algorithm for semi-active suspension systems

In order to improve ride comfort and handling performance of the vehicle, an adaptive hybrid control algorithm is proposed for semi-active suspension systems. The virtues of sky-hook is combined with ground-hook control strategies and a more suitable compromise for the suspension systems is chosen. The hybrid coefficient is tuned according to the longitudinal and lateral acceleration so as to improve the vehicle stability especially in high speed conditions. Damping continuous adjustable absorber is used to continuously control the damping force so as to eliminate the damping force jerk instead of traditional on-off control policy. Based on suspension stroke measured by sensors, unscented Kalman filter is designed to estimate the suspension states in real-time for the realization of hybrid control, which improves the robustness of the control strategy and is adaptive to different types of road profiles. Finally, the proposed control algorithm is validated under the following two typical road profiles: half-sine speed bump road and the random road. The simulation results indicate that the hybrid control algorithm could offer a good coordination between ride comfort and handling of the vehicle.

A new semi-active suspension control strategy through mixed H_2/H_∞ robust technique

A new semi-active suspension control strategy through mixed H2/H∞ robust technique was developed due to its flexibility and robustness to model uncertainties.A full car model with seven degrees of freedom was established to demonstrate the effectiveness of the new control approach.Magneto-rheological(MR) dampers were designed,manufactured and characterized as available semi-active actuators in the developed semi-active suspension system.The four independent mixed H2/H∞ controllers were devised in order to perform a distributed semi-active control system in the vehicle by which the response velocity and reliability can be improved significantly.The performance of the proposed new approach was investigated in time and frequency domains.A good balance between vehicle's comfort and road holding was achieved.An effective and practical control strategy for semi-active suspension system was thus obtained.This new approach exhibits some advantages in implementation,performance flexibility and robustness compared to existing methods.

Electrorheological Damper and Its Application for Semi-Active Suspension System

A semi-active control of vehicle suspension system with eleetrorheolngieal （ER） damper is presented. ER fluid characteristics are introduced based on the Bingham plasticity model first. Then ER damper working force is given. Finally a quarter car model with ER damper is constructed. The skyhook control strategy is adopted to simulate the amplitude-frequency characteristics and the vibration of suspension system under random road excitation on the basis of ER damper characteristics. The response curves of the vertical acceleration, the suspension dynamic working space and the tyre dynamic loading are obtained. Simulation results show that the acceleration is reduced effectively and then the ride comfort is improved by the skyhook control law.

Investigation of Semi-Active Hydro-Pneumatic Suspension for a Heavy Vehicle Based on Electro-Hydraulic Proportional Valve

Hydro-pneumatic suspension is widely used in heavy vehicles due to its nonlinear characteristics of stiffness and damping. However, the conventional passive hydro-pneumatic suspension can’t adjust parameters according to the complicated road environment of heavy vehicles to fulfill the requirements of the vehicle ride comfort. In this paper, a semi-active hydro-pneumatic suspension system based on the electro-hydraulic proportional valve control is proposed, and fuzzy control is used as the control strategy to adjust the?damping force of the semi-active hydro-pneumatic suspension. A 1/4?semi-active hydro-pneumatic suspension model is established, which is co-simulated with AMESim and MATLAB/Simulink. The co-simulation results show that the semi-active hydro-pneumatic suspension system can significantly reduce vibration of the vehicle body, and improve the suspension performance comparing with passive hydro-pneumatic suspension.

Delay-dependent H_(2)/H_(∞) Control for Vehicle Magneto-rheological Semi-active Suspension

The exist researches of the magneto-rheological semi-active suspension(MSAS) control mainly focus on the design of control laws,which aim at obtaining an optimal control strategy to improve the ride comfort and handling stability.In the controller design,the stability of the MSAS system cannot be confirmed owing to the control input time delay considered little.In this paper,a quarter vehicle MSAS model with time-delay is built.Therefore,through formulating the sprung mass acceleration suitably as the optimization object,suspension deflection and tyre dynamic load and coulomb damping force as the constraint objects,with considering the control input time-delay,a delay-dependent state feedback H2/H∞ controller is designed.According to Lyapunov-Krasovskii functional theory,the sufficient conditions for asymptotic stability and the existence of delay-dependent H2/H∞ controller are obtained,and the controller design is transformed into the minimization problem for linear function through linear matrix inequality(LMI).Random road excitation simulations and experiments are carried out.The simulation and experiment results show that the design can preserve the closed-loop stability and achieve the performances for MSAS system in spite of the existence of the control input time-delay.The present study can provide an important basis and method for research on time-delay problem in MSAS and other chassis subsystems.

Skyhook Surface Sliding Mode Control on Semi-Active Vehicle Suspension System for Ride Comfort Enhancement

A skyhook surface sliding mode control method was proposed and applied to the control on the semi-active vehicle suspension system for its ride comfort enhancement. A two degree of freedom dynamic model of a vehicle semi-active suspension system was given, which focused on the passenger’s ride comfort perform-ance. A simulation with the given initial conditions has been devised in MATLAB/SIMULINK. The simula-tion results were showing that there was an enhanced level of ride comfort for the vehicle semi-active sus-pension system with the skyhook surface sliding mode controller.

The Model Reference Adaptive Fuzzy Control for the Vehicle Semi-Active Suspension

The LQG control system is employed as vehicle suspension's optimal target system, which has an adaptive ability to the road conditions and vehicle speed in a limited bandwidth. In order to keep the optimal performances when the suspension parameters change, a model reference adaptive fuzzy control (MRAFC) strategy is presented. The LQG control system serves as the reference model in the MRAFC system. The simulation results indicate that the presented MRAFC system can adapt to the parameters variation of vehicle suspension and track the optimality of the LQG control system, the presented vehicle suspension MRAFC system has the ability to adapt to road conditions and suspension parameters change.

A tunable fuzzy logic controller for the vehicle semi-active suspension system

On the basis of analyzing the system constitution of vehicle semi-active suspension, a 4-DOF (degree of freedom) dynamic model is established. A tunable fuzzy logic controller is designed by using without quantification method and taking into account the uncertainty, nonlinearity and complexity of parameters for a vehicle suspension system. Simulation to test the performance of this controller is performed under random excitations and definite disturbances of a C grade road, and the effects of time delay and changes of system parameters on the vehicle suspension system are researched. The numerical simulation shows that the performance of the designed tunable fuzzy logic controller is effective, stable and reliable.

Fuzzy Logic Control for Semi-Active Suspension System of Tracked Vehicle

The model of half a tracked vehicle semi-active suspension is established. The fuzzy logic controller of the semi-active suspension system is constructed. The acceleration of driver's seat and its time derivative are used as the inputs of the fuzzy logic controller, and the fuzzy logic controller output determines the semi-active suspension controllable damping force. The fuzzy logic controller is to minimize the mean square root of acceleration of the driver's seat. The control forces of controllable dampers behind the first road wheel are obtained by time delay, and the delay times are determined by the vehicle speed and axles distances. The simulation results show that this control method can decrease the acceleration of driver's seat and the suspension travel of the first road wheel, the ride quality is improved obviously.

Semi-active control of a vehicle suspension using magneto-rheological damper

A semi-active magneto-rheological （MR） damper was experimentally investigated and compared to an original equipment manufacturer （OEM） damper for a passenger vehicle, by using a quarter car models. A full-scale two-degree-of-freedom quarter car experimental set-up was constructed to study the vehicle suspension. On-off skyhook controller and Fuzzy-Lyapunov skyhook controller （FLSC） were employed to control the input current for MR damper so as to achieve the desired damping force. Tests were done to evaluate the ability of MR damper for controlling vehicle vibration. Test results show that the semi-active MR vehicle suspension vibration control system is feasible. In comparison with OEM damper, on-off and FLSC controlled MR dampers can effectively reduce the acceleration of vehicle sprtmg mass by about 15% and 24%, respectively.

A new controller for the semi-active suspension system with magnetorheological dampers

A new sliding mode controller for semi-active suspension system with magnetorheological (MR) damper is presented in this paper. In the proposed sliding mode controller, a semi-active suspension based on the skyhook damper system is chosen as the reference model to be followed, and the control law is so determined that the asymptotically stable error dynamics occurs between the controlled state and the reference model state. Numerical simulations are carried out to study the performance of the new sliding mode controller. The results show that the proposed controller yields almost perfect tracking to the reference model and has a high robustness against model parameter uncertainties and disturbances.

Control method for semi-active suspension based on virtual prototype

The simple dynamic model is often adopted to deal with control questions in research on semi-active suspension. The model has more theoretic meanings than authentic ones because of difference between practical and physical models. The virtual prototype has remarkable advantages in its application simulation processes. It is not only faster and more veracious, but also of better visualization of the simulation results.