A Modular Computer Model for the Design of Vehicle Dynamics Control Systems1

SUMMARY

This paper describes a multiport approach to computer-aided modeling of vehicle dynamics. The modeling approach produces models that are suitable for the interactive design and evaluation of complex control strategies. The vehicle model which can be used for ride and handling analysis, is built from modular components. The components are programmed using the syntax of the computer aided control system design (CACSD) program EASYS. Seven modeling components are used to create a three-dimensional vehicle dvnamics model. The model is flexible enoug-h to simulate any suspension design with revolute joints.

Each component of the model consists of a FORTRAN subroutine and a main calling module called a macro. To simplify the process of model building, the modeling components in the car model are designed to represent physical elements, such as the spring, damper, link or tire. To create a model, the components, which are represented by blocks, are interconnected through points, located on the blocks, called pons. These ports have been designed to simulate the location of the connection points between the physical elements, as observed in real systems. The construction of multibody models within a CACSD program offers the flexibility of simultaneous interactive simulation of the three-dimensional dvnamics and evaluation of the desien of the controls.

Although modeling of multibody systems using FORTRAN components has been pioneered by Chace, Haug and Orlandea; and bond graph modeling of multibody systems has been investigated by Bos, this approach is novel because:-

The model is included in the control system design program (EASYS). This arrangement allows the designer to exploit the advanced control design tools available in the program. Furthermore, this approach significantly reduces the computation time required for running the model after parameters modification.

The model is built from components that are interconnected by ports which represent the actual physical location of the connection points between the elements. The multiport approach simplifies the model building process for multibody systems. This simplification is achieved by reducing the model of a multibody system to a block diagram form.     

Optimization for Vehicle Suspension II: Frequency Domain

The objective of this study is optimizing the components design of a vehicle suspension system under excitation due to road roughness. The vehicle is modelled as a dynamic system made of masses interconnected by, linear, springs and dampers. The optimizing code provides values corresponding to the caracteristics of masses, dampers and springs which, within a range, minimize the objective function for a defined excitation. This objective function auantifies the vehicle comfort level.

The optimization method used is the sequential linear programming by iteratively applying the Simplex algorithm. The model response is obtained in frequency domain and the vehicle excitation can be either random or deterministic.

The exact nature of the optimization problem, objective function and restrictions, depend on the type of excitation considered.

In succeeding paragraphs, the problem formulation together with a comparison with other authors is presented.     

Simulation of Multibody Vehicles Moving over Elastic Guideways1

This paper describes the present state of a general purpose computer program for calculating the dynamic response of vehicles travelling over guideways which may be elastic.

The linearized state-equations of motion for general multibody vehicles are constructed automatically by the program, these equations are supplemented by the equations for the active subsystems. Finally, the vehicle system equations are combined with the modal equations for elastic guideways and the complete set of coupled equations is solved simultaneously by numerical integration.     

Messungen von Fahrbahn-Unebenheiten paralleler Fahrspuren und Anwendung der Ergebnisse

Measurement of two track road inputs and theoretical application of the results

The calculation of vehicle response to road-surface irregularity inputs requires the spectral densities of the left and right longitudinal track and their statistical dependence

This paper presents some resluts of parallel profile measurements, three typical german roads have been chosen

Random vibration of two vehicle types are digital-simulated. The dynamic tire load shows that independent suspension systems are more advantageous than beam axles, because by wheel tramp this type increases the dynamic tire load.     

Longitudinal Oscillations of Vehicle/Trailer Combinations Induced by Overrun Braking

A mathematical model for the representation of longitudinal oscillations which can occur in car/trailer systems in braking, when the trailer brakes are applied through compression of the towing hitch, is described. The model is used to show how the trailer braking system parameters affect the steady deceleration performance of the vehicle combination, and the stability, in the linear system sense, of the steady motions. The sensitivity of the stability to other system design parameters is also examined.

Digital simulation of the motions occurring in response to a step input of car braking torque is reported, with the results confirming the predictions of the linear stability analysis, and also showing the influence of backlash in the trailer brake actuating mechanism.

The system is shown to be capable of self-excitation in a “shunting” mode, in which the car and trailer motions are in antiphase, with the stability/damping property critically dependent on drawbar damping, and only weakly dependent on other system parameters. The characteristic frequency of the “shunting” mode oscillations is shown to be controllable via the stiffness of the trailer brake linkage, but this frequency is closely related to the steady drawbar deflection which occurs in uniform deceleration.

The model behaviour described provides a basis for the design of relevant systems whose longitudinal dynamic characteristics will be satisfactory.     

The Lateral Dynamics of Motorcycles and Bicycles

The paper is a review of the state of knowledge and understanding of the steering behaviour of single-track vehicles, with the main accent on vehicle design, and vehicle design analysis and behaviour prediction.

The body of the paper consists of a chronological account of the steps which have been taken in establishing the current position. Scientific study of the motions of two-wheelers has been in progress for more than 100 years, but progress was slow and many conflicting conclusions were drawn until increasing understanding of tyre mechanics, systematic application of the laws of motion for systems of rigid bodies, digital computation and modern numerical methods, and improved mobile measurement, recording, and data processing capabilities allowed the pace to accelerate.

The current position, which is that a good understanding of the relationship between design and performance has been achieved, but that by no means have all the problems of significance been solved, is described at the end of the paper.     

Comparison of All-Wheel Steerings in the System Driver-Vehicle

Different load or tires and a drive on an ice-coated road can overcharge a driver to such an extend, that the result may be an accident. Therefore the aim of development is a self-acting compensation of the vehicle to different vehicle transfer behaviour (invariant vehicle behaviour).

The calculation of so called optimal characteristics shows, that only rear-wheel steering cannot realize this aim of development. Therefore an additional front-wheel angle, which is not influenced by the driver, is necessary. A transfer function can be calculated in order to get controlled steering of the rear wheels without the influence of load.

It is not possible to realize optimal characteristics, because the parameters of the vehicle are difficult to measure. Only an optimal diagnosis and control of driving condition realize a relief for the driver in every driving situation in order to avoid most of the accidents.

The often demanded sideslip angle compensation only worsens driving conditions on ice-coated roads. Therefore systems which identify the driving condition themselves have to be favoured in any case.     

Optimization for Vehicle Suspension I: Time Domain

A numerical procedure for finding the optimum values of a number of parameters describing a model vehicle suspension has been studied. The vehicle has been modelled by dynamic systems of linear springs and dampers, and the goal is to obtain lower acceleration peaks at an elected design point in the vehicle.

The problem is stated as a mathematical programming problem which can be solved by means of the sequential linear programming technique. The procedure has been implemented for a four wheel independent suspension model capable of being subjected to road irregularities and to centrifugal and braking accelerations.     

Dynamic Behaviour of a Mobile Robot Vehicle with a Two Caster and Two Driving Wheel Configuration

The actual trajectory covered by a mobile robot in motion differs from the trajectory planned on the basis of the kinematic characteristics of its directional control system. This difference is essentially related to the behaviour of wheel-road contact, the influence of dynamic loads and the presence of caster wheels.

This paper presents a mathematical model (“ DDPP) which simulates the motion of a generic mobile robot vehicle with a propulsion and directional control system based on two independent driving wheels and two caster wheels.

The differential equations of motion have been obtained by applying modified equations of Lagrange.

The role played by the dynamic loads, the wheel-road contact features and the caster wheels is discussed hereof.     

Nähere Untersuchungen zur stationären Kurvenfahrt von Einspurfahrzeugen

Detailed Investigations of the Steady State Turning of Single Track Vehicles

In the paper the steady state turning of single track vehicles on a horizontal, even road is investigated, supposing the air to be at rest. The vehicle model used has six degrees of freedom: rolling, yawing, pitching and bouncing of the vehicle, rotation of the front wheel system (steering) relatively to the main frame and distortion of the rear wheel system due to limited stiffness of its linkage, and also takes into account wind drag and gyroscopic effects generated by wheels and other vehicle components. A special importance is given to the geometry of the vehicle

The results show a comparison of two types of motorcycles with different geometries and tires. To characterize the vehicle behaviour the roll, side slip and steering angle as functions of the normal acceleration are used. A more detailed study in respect to the steering torque is added.     

General Purpose Vehicle System Dynamics Software Based on Multibody Formalisms

This paper pursues two objectives: Firstly, to review the state-of-the-art of general purpose vehicle system dynamics software and secondly, to describe two representatives, the program MEDYNA and the program NEWEUL. The general modeling requirements for vehicle dynamics software, the multibody system approach and a comparative discussion of multibody software are given. The two programs NEWEUL and MEDYNA are described with respect to modeling options, computational methods, software engineering as well as their interfaces to other software. The applicability of these programs is demonstrated on two selected examples, one from road vehicle problems and the other from wheel/rail dynamics. It is concluded that general purpose software based on multibody formalisms will play the same role for mechanical systems, especially vehicle systems, as finite element methods play for elastic structures.     

General Purpose Vehicle System Dynamics Software Based on Multibody Formalisms

SUMMARY

This paper pursues two objectives: Firstly, to review the state-of-the-art of general purpose vehicle system dynamics software and secondly, to describe two representatives, the program MEDYNA and the program NEWEUL. The general modeling requirements for vehicle dynamics software, the multibody system approach and a comparative discussion of multibody software are given. The two programs NEWEUL and MEDYNA are described with respect to modeling options, computational methods, software engineering as well as their interfaces to other software. The applicability of these programs is demonstrated on two selected examples, one from road vehicle problems and the other from wheel/rail dynamics. It is concluded that general purpose software based on multibody formalisms will play the same role for mechanical systems, especially vehicle systems, as finite element methods play for elastic structures.     

Critical Speed and Limit Speed in Phenomena of Lateral Instability on Railway Vehicles

A comparison between theoretical calculations on dynamic lateral behaviour of railway vehicles and experimental results shows quite a sizeable difference between the calculated critical speed and the actual speed at which side impact phenomena will repeatedly occur between wheel flange and rail (running speed limit), such impact speed being remarkably lower than calculated.

Another typical experimental aspect is that the running speed limit will considerably vary for the same vehicle depending on the test track conditions. Such difference is usually attributed to alterations of the wheel-rail contact surfaces, only.

This paper will discuss some concurrent causes which may prove far from negligible, such as the effects of track defects, an amplification of the dynamic lateral displacement between wheel and rail on approaching the critical speed, the track mechanical properties, and in particular the track lateral rigidity.

The influence of some geometrical factors typical of the wheel-rail contact, such as side clearance and linearized conicity, will also be discussed. The approach is based on the application of statistical methods to dynamic linear systems.     

Active Suspension Control; Performance Comparisons Using Control Laws Applied to a Full Vehicle Model

Based on a mathematical model of an actively suspended vehicle, the effects of the following issues in deriving the control laws are studied:

(a)representation of the ground surface as integrated or filtered white noise.

(b)cross-correlation between left and right track inputs.

(c)wheelbase time delay between front and rear inputs.

The third of these issues is shown to be by far the most important. Considerable improvements at the rear suspension can be obtained if the control law includes the information that the rear input is simply a delayed version of the front input. Effectively this provides feedforward terms in the control law for the rear actuator. For the full state feedback case, these improvements are indicated by reductions in the rear body acceleration and rear dynamic tyre load of around 20% and 40% respectively with no increase in suspension working space.     

A Driver Model Based on the Cerebellar Model Articulation Controller

A model of driver behavior is described which is based on a current theory of neurophysiological processes occurring in the cerebellum. The model learns to control the vehicle through experience, provides discontinuous ramp steer inputs to the vehicle, accepts discontinuous input data, and is applicable to all control situations.

The model is implemented on a simple simulation model of a car and learning is accomplished by the use of an explicit driver model which drives the vehicle along a specified trajectory.     

Vehicle Motion Analysis in Relation to Vehicle Safety

The influence of vehicle handling on the possible avoidance of accident situations is discussed. lit is shown that accident reconstruction at present does not provide the necessary information to relate the cause of accidents to the lack of road worthiness of vehicles. It follows that the vehicle behavior in proximity of its performance limit must be determined in order to infer its accident avoidance potential.

The paper presents a review of the state-of-the-art of vehicle modeling, simulation of vehicle maneuvers and full scale testing. The application of the direct method of the stability theory is suggested as a possible means of obtaining performance limit envelopes which are necessary for establishing standards of the performance of vehicles.     

Additional 4WS and Driver Interaction

This investigation is based on a complex 4-wheel vehicle model of a passenger car that includes steering system and drive train. The tyre properties are described for all possible combined longitudinal and lateral slip values and for arbitrary friction conditions. The active part is an additional steering system of all 4 wheels, additionally to the driver's steering wheel angle input. Three control levels are used for the driver model that thereby can follow a given trajectory or avoid an obstacle.

The feedback control of the additional 4 wheel steering is based on an observer which can also have adaptive characteristics. Moreover a virtual vehicle model in a feedforward scheme can provide desired steering characteristics.

To get information for critical situations a cornering manoeuvre with sudden u-split conditions is simulated. Further a similar manoeuvre is used to evaluate the reentry in a high friction area from low friction conditions. And finally the performance of the controller is shown in a severe lane change manoeuvre.     

Dynamic Behaviour of Ore Wagons in Curves at Malmbanan

The transportation of ore can be made more cost efficient by use of bigger and heavier trains. An increase in axle load is thereby wanted. The fleet of ore wagons of today at Malmbanan/Ofotbanan in northern Sweden and Norway has to be updated. It is of interest to find out if it is possible to allow a higher axle load on the track with new wagons

To be able to understand and predict the effects on track wear depending on what type of vehicle that is in use, the contact forces between wheels and rails have to be determined. A computer aided analysis has been made of the dynamic behaviour of three test vehicles equipped with different types of three-piece bogies running at Malmbanan. The vehicles are modelled and their interaction with the track is analysed using the multibody simulation package GENSYS

The simulations show that, even if the axle load is increased from 25 tons to 30 tons and the velocity is increased from 50 km/h to 60 km/h, it is possible to reduce lateral track forces and wear in curves by using a different bogie than the standard three-piece bogie used today.     

Optimization and Performance Enhancement of Active Suspensions for Automobiles under Preview of the Road

The problem of deriving control laws which minimize specified performance indices for a vehicle moving on a rough surface with preview of the surface elevation is considered. The approach is based on linear optimal tracking theory and consequently the system elements are taken to be linear and the performance index is constrained to be of quadratic form.

The ideas of overtaking optimality are applied to the problem in order to achieve a closed form solution for the control. Then, using the control laws derived, computer simulations of performance are conducted and time histories are shown. In the absence of limitations on either processing or actuator speeds, and for cases in which the preview is sufficient to give good control laws, the value of the preview in enhancing vehicle suspension performance is assessed. Comparisons are made with results in the literature.     

Fuzzy Logic Traction Controllers and their Effect on Longitudinal Vehicle Platoon Systems

This paper presents two fuzzy logic traction controllers and investigates their effect on longitudinal platoon systems. A fuzzy logic approach is appealing for traction control because of the nonlinearity and time-varying uncertainty involved in traction control systems

The fuzzy logic traction controllers we present regulate brake torque to control wheel slip, which is the normalized difference between wheel and vehicle speed. One fuzzy controller estimates the peak slip corresponding to the maximum tire-road adhesion coefficient and regulates wheel slip at the peak slip. The controller is attractive because of its ability to maximize acceleration and deceleration regardless of road condition. However, we find through simulations the controller's performance degrades in the presence of time-varying uncertainties. The other fuzzy logic controller regulates wheel slip at any desired value. Through simulations we find the controller robust against changing road conditions and uncertainties. The target slip is predetermined and not necessarily the peak slip for all road conditions. If the target slip is set low, stable acceleration and deceleration is guaranteed, regardless of road condition

We also study the effect of traction control on longitudinal vehicle platoon systems using simulations. The simulations include acceleration and deceleration maneuvers on an icy road. The results indicate traction control may substantially improve longitudinal platoon performance, especially when icy road conditions exist.