Optimal preview game theory approach to vehicle stability controller design

Dynamic game theory brings together different features that are keys to many situations in control design: optimisation behaviour, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In the presented methodology, vehicle stability is represented by a cooperative dynamic/difference game such that its two agents (players), namely the driver and the direct yaw controller (DYC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the DYC control algorithm is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degrees-of-freedom vehicle-handling performance model is put into discrete form to develop the game equations of motion. To evaluate the developed control algorithm, CarSim with its built-in nonlinear vehicle model along with the Pacejka tire model is used. The control algorithm is evaluated for a lane change manoeuvre, and the optimal set of steering angle and corrective yaw moment is calculated and fed to the test vehicle. Simulation results show that the optimal preview control algorithm can significantly reduce lateral velocity, yaw rate, and roll angle, which all contribute to enhancing vehicle stability.     

Generalised multi-axle vehicle handling

The familiar two-axle bicycle model and associated basic concepts of vehicle handling are reviewed and used to introduce minor changes in convention from the literature. The two-axle model is extended to a three-axle vehicle to illustrate the effectiveness of the notation combined with a simplifying mathematical identity found in the two-axle vehicle literature. A generalised model is then developed that produces dynamic equations of motion by inspection for a vehicle with an arbitrary number of steerable and non-steerable axles. Furthermore, the vehicle dynamic concepts of understeer and wheelbase are generalised and can be directly computed for various arbitrary vehicle configurations.     

Influence of some vehicle and track parameters on the environmental vibrations induced by railway traffic

A study is performed on the influence of some typical railway vehicle and track parameters on the level of ground vibrations induced in the neighbourhood. The results are obtained from a previously validated simulation framework considering in a first step the vehicle/track subsystem and, in a second step, the response of the soil to the forces resulting from the first analysis. The vehicle is reduced to a simple vertical 3-dof model, corresponding to the superposition of the wheelset, the bogie and the car body. The rail is modelled as a succession of beam elements elastically supported by the sleepers, lying themselves on a flexible foundation representing the ballast and the subgrade. The connection between the wheels and the rails is realised through a non-linear Hertzian contact. The soil motion is obtained from a finite/infinite element model. The investigated vehicle parameters are its type (urban, high speed, freight, etc.) and its speed. For the track, the rail flexural stiffness, the railpad stiffness, the spacing between sleepers and the rail and sleeper masses are considered. In all cases, the parameter value range is defined from a bibliographic browsing. At the end, the paper proposes a table summarising the influence of each studied parameter on three indicators: the vehicle acceleration, the rail velocity and the soil velocity. It namely turns out that the vehicle has a serious influence on the vibration level and should be considered in prediction models.     

Virtual test rig to improve the design and optimisation process of the vehicle steering and suspension systems

A virtual test rig is presented using a three-dimensional model of the elasto-kinematic behaviour of a vehicle. A general approach is put forward to determine the three-dimensional position of the body and the main parameters which influence the handling of the vehicle. For the design process, the variable input data are the longitudinal and lateral acceleration and the curve radius, which are defined by the user as a design goal. For the optimisation process, once the vehicle has been built, the variable input data are the travel of the four struts and the steering wheel angle, which is obtained through monitoring the vehicle. The virtual test rig has been applied to a standard vehicle and the validity of the results has been proven.     

Total dynamic response of a PSS vehicle negotiating asymmetric road excitations

A planar suspension system (PSS) is a novel automobile suspension system in which an individual spring–damper strut is implemented in both the vertical and longitudinal directions, respectively. The wheels in a vehicle with such a suspension system can move back and forth relative to the chassis. When a PSS vehicle experiences asymmetric road excitations, the relative longitudinal motion of wheels with respect to the chassis in two sides of the same axle are not identical, and thus the two wheels at one axle will not be aligned in the same axis. The total dynamic responses, including those of the bounce, pitch and the roll of the PSS vehicle, to the asymmetric road excitation may exhibit different characteristics from those of a conventional vehicle. This paper presents an investigation into the comprehensive dynamic behaviour of a vehicle with the PSS, in such a road condition, on both the straight and curved roads. The study was carried out using an 18 DOF full-car model incorporating a radial-spring tyre–ground contact model and a 2D tyre–ground dynamic friction model. Results demonstrate that the total dynamic behaviour of a PSS vehicle is generally comparable with that of the conventional vehicle, while PSS exhibits significant improvement in absorbing the impact forces along the longitudinal direction when compared to the conventional suspension system. The PSS vehicle is found to be more stable than the conventional vehicle in terms of the directional performance against the disturbance of the road potholes on a straight line manoeuvre, while exhibiting a very similar handling performance on a curved line.     

Decoupled 3D moment control using in-wheel motors

Vehicles equipped with in-wheel motors are being studied and developed as a type of electric vehicle. Since these motors are attached to the suspension, a large vertical suspension reaction force is generated during driving. Based on this mechanism, this paper describes the development of a method for independently controlling roll and pitch as well as yaw using driving force distribution control at each wheel. It also details the theoretical calculation of a method for decoupling the dynamic motions. Finally, it describes the application of these 3D dynamic motion control methods to a test vehicle and the confirmation of the performance improvement.     

Simultaneous observation of the wheels’ torques and the vehicle dynamic state

The goal of the present study is to show how it is possible to estimate online the individual torques applied at each wheel of an automotive vehicle by using an unknown input observer together with a simple nonlinear state-space model. The necessary measurements are the steering angle, the usual rotation speed of each wheel plus the vertical load at the centre of each wheel. By doing this, this study anticipates the affordability of a new generation of wheel bearing with embedded measurements of transmitted forces. Successful simulated experimentations using a realistic simulator are shown. Validations are done using classical case studies of longitudinal, lateral and coupled dynamics. The present limits and some possible improvements of the proposed method are also discussed.     

A combined use of phase plane and handling diagram method to study the influence of tyre and vehicle characteristics on stability

This paper deals with in-curve vehicle lateral behaviour and is aimed to find out which vehicle physical characteristics affect significantly its stability. Two different analytical methods, one numerical (phase plane) and the other graphical (handling diagram) are discussed. The numerical model refers to the complete quadricycle, while the graphical one refers to a bicycle model. Both models take into account lateral load transfers and nonlinear Pacejka tyre–road interactions. The influence of centre of mass longitudinal position, tyre cornering stiffness and front/rear roll stiffness ratio on vehicle stability are analysed. The presented results are in good agreement with theoretical expectations about the above parameters influence, and show how some physical characteristics behave as saddle-node bifurcation parameters.     

Simulation study on the operating characteristics of a hybrid hydraulic passenger car with a power split transmission

In this paper, a hybrid hydraulic passenger car (HHPC) coupled with a power split continuously variable transmission (P-CVT) is proposed. This P-CVT is capable of splitting the power from the internal combustion engine into mechanical and hydraulic power flows. By adjusting the ratio of the mechanical power to hydraulic power, the P-CVT enables the transmission ratio to be changed continuously. Meanwhile, the P-CVT system can capture the braking energy and store it in the hydraulic accumulator for the next assistant driving. In order to quantitatively investigate the effect of applying P-CVT on improving the fuel economy and operating performance for the HHPC, a numerical simulation is conducted under typical city driving conditions. The simulation results demonstrate that, the P-CVT permits the engine to be run under a more efficient operating range. The total fuel consumption of the HHPC is reduced by 16.4% under the test conditions, compared with that of the original car.     

Optimisation of lateral car dynamics taking into account parameter uncertainties

Simulation studies on an active all-wheel-steering car show that disturbance of vehicle parameters have high influence on lateral car dynamics. This motivates the need of robust design against such parameter uncertainties. A specific parametrisation is established combining deterministic, velocity-dependent steering control parameters with partly uncertain, velocity-independent vehicle parameters for simultaneous use in a numerical optimisation process. Model-based objectives are formulated and summarised in a multi-objective optimisation problem where especially the lateral steady-state behaviour is improved by an adaption strategy based on measurable uncertainties. The normally distributed uncertainties are generated by optimal Latin hypercube sampling and a response surface based strategy helps to cut down time consuming model evaluations which offers the possibility to use a genetic optimisation algorithm. Optimisation results are discussed in different criterion spaces and the achieved improvements confirm the validity of the proposed procedure.