Control Algorithms for Active Cab Suspensions on Agricultural Tractors

This paper describes active agricultural tractor cab suspensions based on optimal control theory. Control algorithms based on time invariant state feedback and on adaptive control are developed and studied. The influence of different observers and measurement noise levels on the vibration damping capacity are studied as well as the power consumption for the suspensions.

The principle for the adaptive algorithm is based on the parameters in the penalty matrices being varied so that the resulting controller always strives to make optimum use of available travel space. The feedback and observer gains are also changed depending on the characteristics of the vehicle's frame movements.

The results show that it is possible to design an effective active suspension, but that the choice of feedback gains must be dependent on the surface characteristics to reach satisfactory vibration damping performance.     

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.     

Random Vehicle Vibrations as Effected by Dry Friction in Wheel Suspensions

The changes of vibration comfort and stability of vehicles as effected by the value of frictional force generated in laminated springs are discussed and the probability of departure of the tyres from the ground is described.

A partly automated analogue computer simulation being equivalent to a great number of highway experiments was applied in the study.

The computer model was excited by several stochastic roadprofile - analogue signals generated by filters from the wide-band random signal of a digital noise generator.     

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.     

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.     

Survey of Wheel—Rail Rolling Contact Theory

This paper describes the theory of frictional rolling contact as far as it is significant for the wheel-rail system. It is divided into two parts.

The first part, mostly non-mathematical, contains a historical survey from the times of Carter and Fromm (1926) to the present day, in which all aspects of rolling contact theory are discussed. Included are a quantitative account of the results of Hertz theory (Section 3), and a table of the creepage and spin coefficients.

The second part gives a present day account of the simplified theory (Section 4), and of the exact linear and non-linear theory (Section 5).

The paper closes with some recommendations for future research, of which the most pressing is a thorough investigation of the accuracy of simplified theory.     

Optimal Linear Preview Control of Active Vehicle Suspension

The problem of linear preview control of vehicle suspension is considered as a continuous time stochastic optimal control problem. In the proposed approach minimal a priori information about the road irregularities is assumed and measurement errors are taken into account. It is shown that estimation and control issues can be decoupled. The problem formulation and the analytical solution are given in a general form and hence they apply to other problems in which the system disturbances are unknown a priori, even in a stochastic sense, but some preview information is possible.

The solution is applied to a two-degree-of-freedom (2-DOF) vehicle model. The effects of preview information on ride comfort, road holding, working space of the suspension and power requirements are examined in time and frequency domains. The results show that the greatest potential is for improving road holding properties. This effect could not have been observed in previous studies based on a 1-DOF vehicle model. It is also demonstrated that the presence of preview drastically reduces power requirements, thus relieving the performance versus actuator power dilemma.     

Off-Road Vehicle Dynamics

Recent developments in off-road vehicle dynamics are reviewed. Progress on this topic and the application of new techniques to the particular problemsassociated with off-road operation tend to lag behind practices established for road vehicles.

The factor which limits further progress is the lack ofappropriate off-road tyre data, in particular, on vibrational and lateral force generation characteristics. Also, a long term study should be aimed at understanding the dynamic behaviour of tyres on yielding surfaces.     

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.     

Berechnung des extremen Lenk- und Bremsverhaltens von Sattelkraftfahrzeugen

Simulation of Steering and Braking Behaviour of Tractor-Semitrailer Vehicles in Extreme Situations

This paper deals with the simulation of the behaviour of tractor-semitrailer vehicles at braking on wet, slippery road surface. The nonlinear model used for the computation enables to simulate extreme situations at wheel locking and swerving

The instabilities during braking such as jackknifing and trailer swing as well as non steerability are investigated. Straightline braking shows the influence of cornering on the behaviour during braking in a turn.     

Handling Characteristics of Car-Trailer Systems; A State-of-the-Art Survey

Work relevant to the state of the art as regards passenger cars towing trailers is referenced and reviewed. Not only included is the very limited amount of work specifically dealing with passenger cars towing trailers, but also reviewed is the much larger body of work having a bearing on car-trailer systems. Topics included are aerodynamic forces, tire forces, the compliance concept, relevant work on vehicles without trailers, vehicles with trailers, and the role of the driver. The types of stability problems exhibited by car-trailer systems are discussed.

The state of the art as regards ability to predict vehicle response to specific steering inputs is shown to be fairly advanced. Recent significant advances include the appearance of experimental data useful for validating theoretical models. However, the state of the art as regards definition of what constitute desirable handling characteristics is still at a primitive stage, largely because of a lack of understanding of the roles played by drivers as part of the vehicle -driver - environment systems.

Throughout the review an effort was made to point out topic areas where it is likely that significant future contributions to the state of the art can be made. These areas are reviewed in the conclusions.     

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.     

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.     

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.     

Schwingungsuntersuchungen an einer Pkw-Karosserie

(Title: Investigations into the vibrations of an automobile body)

The numerical treatment of the lower elastic vibrations of a motorcar body is presented. The displacement method has been found to be an effective technique for this calculation. When idealising the structure it is tried to show the lower boundary for the subdivision of the structure, with which satisfying results can be obtained.

The presented results show, that the calculation of the vibration characteristics of a car body is possible with relatively simple model structures. But it must be pointed out that the model structure has to be constructed considering requirements made upon the results. For the calculation of the four lower vibration modes the car body is idealised with beam and triangular elements. By this method the stiffness and mass matrices arc derived. The distributed mass is simply condensed to mass points in the nodes of the structure. Together with the stiffness matrix the mass matrix is reduced to a practical size for the final computation of the eigenvalues and cigenmodes.     

A Theory of Wheelset Forces for Two Point Contact Between Wheel and Rail

This paper describes a quasistatic theory of wheelset forces for an important practical case of the wheelset rolling when one of the wheels touches the rail in two contact zones. One of these zones lies on the tread and the other on the wheel flange. For such contact the specific problem of finding the distribution of forces between the tread and flange arises. The simultaneous frictional rolling contact problems for both contact zones have been described with Kalker×apos;s non-linear theory and wheelset equilibrium equations.

The numerical results presented are for an individual wheelset on straight track, the distribution of forces being described for a wide range of loading conditions. The influence of steering on the distribution of forces has also been presented.

This theory can be easily extended for quasistatic curving of railway vehicles and may assist wear studies for vehicles with worn wheels.     

Preview Estimation and Control for (Semi-) Active Suspensions

An active suspension with preview is tested for rounded pulses and a stochastic road surface, and is compared to a passive suspension. The spectacular performance improvement obtained for a step function as road surface is not achieved but the improvement is still significant. The frequency response of the active suspension is determined for comparison with some suspension systems found in literature

An observer to reconstruct the preview information is presented. No model of the road surface is needed. From simulations, it appears that the observer reconstructs both deterministic and stochastic road surfaces satisfactory. However, the influence of measurement noise is not reduced sufficiently.     

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.     

Railway Vehicle Active Suspensions

This paper reviews the state-of-the-art of active suspensions for use on railway vehicles. The primary focus of the paper is on ride quality control, both vertical and lateral, and on lateral stability control.

The section on theoretical considerations summarizes the results of a one-degree of freedom optimization and then investigates analytically the use of active suspensions for lateral ride and stability augmentation. It is shown that separate control structures using different measurements and actuator actions are very effective in controlling both ride quality and stability.

A section on a survey ofcurrent activities reviews published research on active railway suspension work around the world.

Finally a concluding section indicates future trends in active suspension applications.