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.

Advances in Active Suspension Systems for Road Vehicles

Active suspension systems(ASSs)have been proposed and developed for a few decades,and have now once again become a thriving topic in both academia and industry,due to the high demand for driving comfort and safety and the compatibility of ASSs with vehicle electrification and autonomy.Existing review papers on ASSs mainly cover dynamics modeling and robust control;however,the gap between academic research outcomes and industrial application requirements has not yet been bridged,hindering most ASS research knowledge from being transferred to vehicle companies.This paper comprehensively reviews advances in ASSs for road vehicles,with a focus on hardware structures and control strategies.In particular,state-of-the-art ASSs that have been recently adopted in production cars are discussed in detail,including the representative solutions of Mercedes active body control(ABC)and Audi predictive active suspension;novel concepts that could become alternative candidates are also introduced,including series active variable geometry suspension,and the active wheel-alignment system.ASSs with compact structure,small mass increment,low power consumption,high-frequency response,acceptable economic costs,and high reliability are more likely to be adopted by car manufacturers.In terms of control strategies,the development of future ASSs aims not only to stabilize the chassis attitude and attenuate the chassis vibration,but also to enable ASSs to cooperate with other modules(e.g.,steering and braking)and sensors(e.g.,cameras)within a car,and even with high-level decision-making(e.g.,reference driving speed)in the overall transportation system-strategies that will be compatible with the rapidly developing electric and autonomous vehicles.

Adaptive Backstepping Control Design for Semi-Active Suspension of Half-Vehicle With Magnetorheological Damper

This paper investigates the problem of controlling half-vehicle semi-active suspension system involving a magnetorheological(MR)damper.This features a hysteretic behavior that is presently captured through the nonlinear Bouc-Wen model.The control objective is to regulate well the heave and the pitch motions of the chassis despite the road irregularities.The difficulty of the control problem lies in the nonlinearity of the system model,the uncertainty of some of its parameters,and the inaccessibility to measurements of the hysteresis internal state variables.Using Lyapunov control design tools,we design two observers to get online estimates of the hysteresis internal states and a stabilizing adaptive state-feedback regulator.The whole adaptive controller is formally shown to meet the desired control objectives.This theoretical result is confirmed by several simulations demonstrating the supremacy of the latter compared to the skyhook control and passive suspension.

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.

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.

Fuzzy Sliding Mode Control for the Vehicle Height and Leveling Adjustment System of an Electronic Air Suspension

The accurate control for the vehicle height and leveling adjustment system of an electronic air suspension(EAS) still is a challenging problem that has not been effectively solved in prior researches. This paper proposes a new adaptive controller to control the vehicle height and to adjust the roll and pitch angles of the vehicle body(leveling control) during the vehicle height adjustment procedures by an EAS system. A nonlinear mechanism model of the full?car vehicle height adjustment system is established to reflect the system dynamic behaviors and to derive the system optimal control law. To deal with the nonlinear characters in the vehicle height and leveling adjustment processes, the nonlinear system model is globally linearized through the state feedback method. On this basis, a fuzzy sliding mode controller(FSMC) is designed to improve the control accuracy of the vehicle height adjustment and to reduce the peak values of the roll and pitch angles of the vehicle body. To verify the effectiveness of the proposed control method more accurately, the full?car EAS system model programmed using AMESim is also given. Then, the co?simulation study of the FSMC performance can be conducted. Finally, actual vehicle tests are performed with a city bus, and the test results illustrate that the vehicle height adjustment performance is effectively guaranteed by the FSMC, and the peak values of the roll and pitch angles of the vehicle body during the vehicle height adjustment procedures are also reduced significantly. This research proposes an effective control methodology for the vehicle height and leveling adjustment system of an EAS, which provides a favorable control performance for the system.

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.

A Hybrid Approach to Modeling and Control of Vehicle Height for Electronically Controlled Air Suspension

The control problems associated with vehicle height adjustment of electronically controlled air suspension （ECAS） still pose theoretical challenges for researchers, which manifest themselves in the publications on this subject over the last years. This paper deals with modeling and control of a vehicle height adjustment system for ECAS, which is an example of a hybrid dynamical system due to the coexistence and coupling of continuous variables and discrete events. A mixed logical dynamical （MLD） modeling approach is chosen for capturing enough details of the vehicle height adjustment process. The hybrid dynamic model is constructed on the basis of some assumptions and piecewise linear approximation for components nonlinearities. Then, the on-off statuses of solenoid valves and the piecewise approximation process are described by propositional logic, and the hybrid system is transformed into the set of linear mixed-integer equalities and inequalities, denoted as MLD model, automatically by HYSDEL. Using this model, a hybrid model predictive controller （HMPC） is tuned based on online mixed-integer quadratic optimization （MIQP）. Two different scenarios are considered in the simulation, whose results verify the height adjustment effectiveness of the proposed approach. Explicit solutions of the controller are computed to control the vehicle height adjustment system in realtime using an offline multi-parametric programming technology （MPT）, thus convert the controller into an equivalent explicit piecewise affine form. Finally, bench experiments for vehicle height lifting, holding and lowering procedures are conducted, which demonstrate that the HMPC can adjust the vehicle height by controlling the on-off statuses of solenoid valves directly. This research proposes a new modeling and control method for vehicle height adjustment of ECAS, which leads to a closed-loop system with favorable dynamical properties.

Fuzzy Chaos Control for Vehicle Lateral Dynamics Based on Active Suspension System

The existing research of the active suspension system（ASS） mainly focuses on the different evaluation indexes and control strategies. Among the different components, the nonlinear characteristics of practical systems and control are usually not considered for vehicle lateral dynamics. But the vehicle model has some shortages on tyre model with side-slip angle, road adhesion coefficient, vertical load and velocity. In this paper, the nonlinear dynamic model of lateral system is considered and also the adaptive neural network of tire is introduced. By nonlinear analysis methods, such as the bifurcation diagram and Lyapunov exponent, it has shown that the lateral dynamics exhibits complicated motions with the forward speed. Then, a fuzzy control method is applied to the lateral system aiming to convert chaos into periodic motion using the linear-state feedback of an available lateral force with changing tire load. Finally, the rapid control prototyping is built to conduct the real vehicle test. By comparison of time response diagram, phase portraits and Lyapunov exponents at different work conditions, the results on step input and S-shaped road indicate that the slip angle and yaw velocity of lateral dynamics enter into stable domain and the results of test are consistent to the simulation and verified the correctness of simulation. And the Lyapunov exponents of the closed-loop system are becoming from positive to negative. This research proposes a fuzzy control method which has sufficient suppress chaotic motions as an effective active suspension system.

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.

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.

Robust adaptive control of hypersonic vehicle considering inlet unstart

In this paper,a model reference adaptive control(MRAC)augmentation method of a linear controller is proposed for air-breathing hypersonic vehicle(AHV)during inlet unstart.With the development of hypersonic flight technology,hypersonic vehicles have been gradually moving to the stage of weaponization.During the maneuvers,changes of attitude,Mach number and the back pressure can cause the inlet unstart phenomenon of scramjet.Inlet unstart causes significant changes in the aerodynamics of AHV,which may lead to deterioration of the tracking performance or instability of the control system.Therefore,we firstly establish the model of hypersonic vehicle considering inlet unstart,in which the changes of aerodynamics caused by inlet unstart is described as nonlinear uncertainty.Then,an MRAC augmentation method of a linear controller is proposed and the radial basis function(RBF)neural network is used to schedule the adaptive parameters of MRAC.Furthermore,the Lyapunov function is constructed to prove the stability of the proposed method.Finally,numerical simulations show that compared with the linear control method,the proposed method can stabilize the attitude of the hypersonic vehicle more quickly after the inlet unstart,which provides favorable conditions for inlet restart,thus verifying the effectiveness of the augmentation method proposed in the paper.

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.

A Study of Electric Vehicle Suspension Control System Based on an Improved Half-vehicle Model

An improved half-vehicle model has been proposed for active suspension control systems, in contrast to existing models, it allows to explore the nature of the effect of vehicle speed changes by introducing a state vector of vehicle pitch angle. Three control strategies of linear quadratic control （LQ）, improved LQ （ILQ） and wheelbase preview LQ （WLQ） have been implemented into the proposed model. ILQ has integrated an additional control parameter into LQ by concerning the correlation between acceleration values and their corresponding pitch angles. Simulation results have showed the effectiveness of the proposed model in terms of LQ, ILQ and WLQ control strategies.

Implementation of Fuzzy Logic Control into an Equivalent Minimization Strategy for Adaptive Energy Management of A Parallel Hybrid Electric Vehicle

As government agencies continue to tighten emissions regulations due to the continued increase in greenhouse gas production, automotive industries are seeking to produce increasingly efficient vehicle technology. Hybrid electric vehicles (HEVs) have been introduced to mitigate problems while improving fuel economy. HEVs have led to the demand of creating more advanced controls software to consider multiple components for propulsive power in a vehicle. A large section in the software development process is the implementation of an optimal energy management strategy meant to improve the overall fuel efficiency of the vehicle. Optimal strategies can be implemented when driving conditions are known a prior. The Equivalent Consumption Minimization Strategy (ECMS) is an optimal control strategy that uses an equivalence factor to equate electrical to mechanical power when performing torque split determination between the internal combustion engine and electric motor for propulsive and regenerative torque. This equivalence factor is determined from offline vehicle simulations using a sensitivity analysis to provide optimal fuel economy results while maintaining predetermined high voltage battery state of charge (SOC) constraints. When the control hierarchy is modified or different driving styles are applied, the analysis must be redone to update the equivalence factor. The goal of this work is to implement a fuzzy logic controller that dynamically updates the equivalence factor to improve fuel economy, maintain a strict charge sustaining window of operation for the high voltage battery, and reduce computational time required during algorithm development. The adaptive algorithm is validated against global optimum fuel economy and charge sustaining results from a sensitivity analysis performed for multiple drive cycles. Results show a maximum fuel economy improvement of 9.82% when using a mild driving style and a 95% success rate when maintaining an ending SOC within 5% of the desired SOC regardless of starting SOC.

Vibration Control of Vehicle Suspension System by Electrorheological Damper

An overview of electrorheological （ER） fluid characteristics is given. Based on the Bingham plasticity model and a simple parallel-plate model, the operation principle of ER damper is presented and a four-DOF dynamic model of a vehicle suspension is constructed. Then a semi-active control of vehicle suspension system by ER damper is obtained. According to the semi-active control theory, the acceleration frequency characteristic is achieved with Matlab toolbox. Simulation results show that the vibration of the suspension system is well controlled.

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.

Active suspension with optimal control based on a full vehicle model

The 7-DOF model of a full vehicle with an active suspension is developed in this paper.The model is written into the state equation style.Actuator forces are treated as inputs in the state equations.Based on the basic optimal control theory,the optimal gains for the control system are figured out.So an optimal controller is developed and implemented using Matlab/Simulink,where the Riccati equation with coupling terms is deduced using the Hamilton equation.The all state feedback is chosen for the controller.The gains for all vehicle variables are traded off so that majority of indexes were up to optimal.The active suspension with optimal control is simulated in frequency domain and time domain separately,and compared with a passive suspension.Throughout all the simulation results,the optimal controller developed in this paper works well in the majority of instances.In all,the comfort and ride performance of the vehicle are improved under the active suspension with optimal control.

Model Based Adaptive Control and Disturbance Compensation for Underwater Vehicles

Underwater vehicles are being emphasized as highly integrated and intelligent devices for a significant number of oceanic operations. However, their precise operation is usually hindered by disturbances from a tether or manipulator because their propellers are unable to realize a stable suspension. A dynamic multi-body model-based adaptive controller was designed to allow the controller of the vehicle to observe and compensate for disturbances from a tether or manipulator. Disturbances, including those from a tether or manipulator, are deduced for the observation of the controller. An analysis of a tether disturbance covers the conditions of the surface, the underwater area, and the vehicle end point. Interactions between the vehicle and manipulator are mainly composed of coupling forces and restoring moments.To verify the robustness of the controller, path-following experiments on a streamlined autonomous underwater vehicle experiencing various disturbances were conducted in Song Hua Lake in China. Furthermore,path-following experiments for a tethered open frame remote operated vehicle were verified for accurate cruising with a controller and an observer, and vehicle and manipulator coordinate motion control during the simulation and experiments verified the effectiveness of the controller and observer for underwater operation. This study provides instructions for the control of an underwater vehicle experiencing disturbances from a tether or manipulator.

Linear Quadratic Integral Control for the Active Suspension of Vehicle

The quarter model of an active suspension is established in the form of controllable autoregressive moving average （CARMA） model. An accelerometer can be mounted on the wheel hub for measuring road disturbance; this signal is used to identify the CARMA model parameters by recursive forgetting factors least square method. The linear quadratic integral （LQI） control method for the active suspension is presented. The LQI control algorithm is fit for vehicle suspension control, for the control performance index can comprise multi controlled variables. The simulation results show that the vertical acceleration and suspension travel both are decreased with the LQI control in the low frequency band, and the suspension travel is increased with the LQI control in the middle or high frequency band. The suspension travel is very small in the middle or high frequency band, the suspension bottoming stop will not happen, so the vehicle ride quality can be improved apparently by the LQI control.