Department of Mechanical Engineering

Vehicle dynamics PhD theses

The dynamics and control of a three-wheeled tilting vehicle

Auguste van Poelgeest, 2011


The objective of this study was to develop a new Steer Tilt Control (STC) algorithm inspired by real driver behaviour and to test it in simulation with an experimentally validated non-linear vehicle model.

In order to develop an exhaustive simulation model of the vehicle and to process experimental data correctly, a large number of modelling aspects were taken into consideration. The objective of the study was to identify the unique kinematics of a three-wheeled tilting vehicle and determine the importance of the kinematic effects on the vehicle system. In order to fully understand this unique class of vehicle, the effect of the driver's mass on the vehicle inertias and the effect of the tilting on the vehicle's yaw inertia were considered. A wide-ranging expression for the driver's perceived acceleration was derived and the roll dynamics of the non-tilting part of the three-wheeled tilting vehicle assembly were modelled. The steering torque of the vehicle was fully analysed and, using the simulation model, methods to model the effect of a crosswind on the vehicle, to test the effect of driving up or downhill, and to determine the effect of road camber on the vehicle dynamics were considered.

To create a better understanding of the control task, road experiments were carried out using an instrumented tilting three-wheeler to investigate the driver steer inputs necessary to both balance the vehicle and follow a fixed trajectory. The experimental results demonstrated that the drivers' steering inputs varied even though they had to complete identical tasks. This result confirmed that there are multiple ways to control the roll of the vehicle. The results also showed that the tilt angle always led the steering angle and for a transient manoeuvre, the tilt angle was larger than the balanced tilt angle at the start of the manoeuvre and smaller than the balanced angle at the end of the manoeuvre. The next step in the investigation was the development of a comprehensive non-linear dynamics model of a tilting three-wheeler including a tyre model and a driver model. A new method was developed to estimate the parameters of a Magic Formula Tyre model using the road testing data. The vehicle and tyre model were validated using data from a range of test runs.

The importance of a driver in the loop was recognised and the elements of a driver trajectory-tracking model were studied. The aim was to develop a driver model that demonstrated good tracking and some similarity to real driver behaviour. The final model used the yaw rate demand to determine an anticipatory control steer angle and the current heading error and the vehicle’s lateral position error measured in the vehicle's local axis system to make small steering adjustments.

The STC method based on Proportional Integral Derivative (PID) control was tested with the vehicle model to determine its performance with the non-linear dynamics and the driver in the loop. It was shown that the driver model had the tendency to act against the STC and that the two could only act simultaneously for a very limited range of demand trajectory and velocity combinations. The crosswind, hill driving, and road camber models were combined with the vehicle simulation without a driver but with the PID based STC. The simulations showed that these environmental factors made the control task significantly more difficult. More importantly, it showed that these factors demanded an increased number of vehicle states to be fed back to the controller.

A new algorithm for STC was developed using the full vehicle and driver model. One of the criteria was that the control algorithm had to be realizable in practice. The resulting controller was a logic algorithm that would choose an action based on the steering angle and velocity and the vehicle speed with online gain adjustment based on direction and order of magnitude of the perceived acceleration. The basis of the control was adjustment of the driver's steering input and it was shown that the vehicle's deviation from the driver's intended path was minimal.

Dynamics and control of a tilting three-wheeled vehicle

Johan Berote, 2010


Narrow commuter vehicles have attracted considerable interest in recent years as a means of reducing congestion and emissions in the urban environment. In order for these vehicles to provide similar levels of safety as bigger passenger vehicles, they must be relatively tall and fully enclosed. Due to the tall and narrow nature of the vehicle, they are prone to rolling over during cornering. To prevent this from happening, it is necessary to tilt the vehicle into the turn in order to compensate for the moment due to the lateral force generated by the tyres. The success of this type of vehicle depends primarily on the control strategy used to tilt the vehicle. Although a number of theoretical models have been developed outlining possible tilt control strategies, experimental data is scarce.

CLEVER is a direct tilt controlled three-wheel prototype vehicle that was developed at the University of Bath as part of an EU funded project. The current control strategy utilises measurements of speed and steer to predict the lateral acceleration and hence the tilting angle required to balance the vehicle during cornering. The cabin of the vehicle is then tilted to the desired angle using two hydraulic actuators. Although the vehicle performs well in steady state, transient dynamics have been shown to lead to instability and ultimately roll-over of the vehicle.

The aim of the work presented here is to create an understanding of the dynamics that lead to the transient state instability and design a control method which will improve the handling characteristics of the vehicle and prevent dangerous transients. In order to study the vehicle's dynamics and test the new control system, a full multi-body model is developed using the SimMechanics software package. The model is validated using data from numerous experimental tests performed with the prototype vehicle. Using the full vehicle model, it is possible to analyse the scenarios that could lead to the transient-state roll-over of the vehicle, creating a good understanding of the dynamics that lead to these potentially dangerous situations. Taking these dynamics into account, a lateral dynamics optimisation study is performed which proves the necessity for independent control of the tilting mechanism and the lateral acceleration, confirming the need for combined steer and direct tilt control. The new control system is then developed using a linearised model in order to optimise the controller in the frequency domain and is tested using the non-linear multi-body model. A simple combined control approach is presented and shown to significantly reduce transient roll moments, resulting in a much safer and more predictable handling characteristic.

Although a number of control strategies have been proven successful in simulation by other researchers, these relied on complex switching strategies and weighting functions to switch between steer tilt control and direct tilt control and often required numerous sensor inputs. The system proposed by the author combines both steer and tilt control concurrently, using the driver steering input and vehicle speed as the only input parameters. The simplified principle of the control strategy is anticipated to facilitate implementation in a prototype vehicle.


A study of gas suspension systems for off-road vehicles

Anil Patel, 2010


This thesis describes computer simulation and experimental studies undertaken to investigate the operational performance of a hydro-pneumatic suspension strut. The research was supported by Horstman Defence Systems Limited (HDSL) who, amongst other things, design and build suspension units for heavy off road vehicles. Of primary interest were the gas dynamics and the damper pack behaviour for a particular type of HDSL strut used on multi-wheeled military vehicles.

A computer model was developed for the strut that represented the expansion and compression of nitrogen gas using ideal gas laws based on user defined polytropic indices. The model was validated using experimental test data provided by HDSL. Although it was possible by the appropriate selection of the indices in the model to obtain similar trends to the experimental test data, it was considered that there was scope to improve the model by accounting for the heat exchange between the nitrogen gas and the surrounding.

As it was not possible to test an actual strut at the University, a study was undertaken using a hydraulic actuator and a piston type accumulator to represent the strut. By attaching the actuator to one corner of a four-poster vehicle test rig within the Department of Mechanical Engineering, a series of tests were conducted that allowed the accumulator gas pressure and temperature to be determined using different gas compression and expansion scenarios. The data obtained from these tests was used to validate a new model that accounted for heat transfer when estimating the gas pressure and temperature when the gas was subjected to step compession and expansion changes. The agreement obtained between the model and the test rig was much improved compared with the original polytropic approach.

Further development was undertaken to obtain a general purpose version of the model that could be applied to any compression or expansion cycle applied to the gas. The revised gas model was added to the strut model and its performance validated using experimental test data providedby HDSL. A sensitivity analysis undertaken on the revised model indicated that small variations in the values taken for the gas pre-charge pressure and temperature had a large effect on the predicted pressure responses. Good agreement was achieved when the predicted responses were compared to the experimental results obtained from a sinewave and a ramp test.

A feasibility study on the practicality of predicting the pressure flow characteristic of a Belleville washer type damper was undertaken. For this study a simple arrangement was used which only considered flow in a single direction through the damper pack. With the aid of CFD analysis a working model was produced which accurately predicted the damping characteristic. A full body model was developed for an 8-wheeled vehicle to investigate the possibility of using interconnecting pipework between the struts fitted at each wheel to reduce the vertical accelerations acting on the vehicle. Although some interconnection arrangements produced lower accelerations than the original unconnected system, the level of improvement was not considered to be sufficient to warrant the added complexity involved.

The model developed for the full vehicle was used to investigate whether high or low damping results in a minimal temperature rise in the strut body. It was found that both resulted in minimal temperature gains, however, a high damping rate reduced the ride comfort and a low rate increased the likelyhood of the strut hitting its endstops.


Semi-active control strategies to reduce road damage in vehicles

Georgios Tsampardoukas, 2007


The EU countries spend millions of Euros every year on road maintenance and pavement resurfacing. About half the cost is due to heavy duty vehicles which cause road damage due to high vehicle mass and vibrations. For that reason, the set up of the vehicle plays an important role in road damage reduction.

Controllable dampers (magneto-rheological dampers) are employed to manage the motion of the vehicle. Novel semi-active control algorithms such as hybrid balance, skyhook and ground hook control strategies are proposed, to improve ride and to reduce the road damage due to vehicle motion. A novel approach is proposed to examine the effect of the tyre loads applied to the pavement model.

These control algorithms are employed on quarter car model, passenger vehicle and heavy articulated vehicle examining the frequency response and the response on a random profile in order to assess the effect of each control algorithm. Additionally, a novel mechanical model is proposed to describe the motion of the human occupants due to vehicle motion including ride and handling. Extensive work is performed in terms of handling manoeuvres for both passenger and heavy articulated vehicles. The effect of each semi-active control algorithm is carefully examined in respect to roll over especially for the heavy articulated vehicles.

Practical considerations such as the robustness of the hybrid balance control algorithm and malfunction scenarios such as the loose wire of the MR damper are also studied. The effects of these malfunctions are examined in terms of ride and handling for both passenger and heavy articulated vehicle.

It is hoped that this study provides an overview of the effect of several semi-active control algorithm based on closed loop control in terms of ride, handling and road damage for both passenger and heavy articulated vehicles.


Development of active tilt control for a three-wheeled vehicle

Benjamin Drew, 2007


The CLEVER Project was a European Union funded research project to design and develop a low emission alternative vehicle for city environments, which aimed to combine the comfort and safety of a conventional car with the small road footprint and high efficiency of a motorcycle. The project comprised nine industrial companies and academic institutions from across Europe who collaborated to prove the concept. The project resulted in the construction of five prototypes: three were used for crash testing, one was used for chassis development, and one was a show vehicle.

This thesis focuses on the design, development and testing of the novel tilting system that was the focus of the research at the University of Bath. The role of the chassis of CLEVER is to provide safe and predictable handling while satisfying the requirements of the project. Due to the narrow wheel track, the CLEVER vehicle needs to bank into corners in a similar manner to a motorcycle to maintain stability. The requirement of car-like controls necessitates an active, automatic tilting system.

The two primary components of the tilting chassis are an active control system, which controls an actuation system that performs the tilting action. While previous work includes modelling and simulation of active control systems, none have taken the steps to develop an actuation system with which to tilt a vehicle, and none have developed a system appropriate for a serious means of transport. Through evaluation and assessment of simulation and modelling work for both the active control system and the hydraulic actuation system, the tilting system was developed. Following detailed design work of the chassis systems, a development prototype was constructed, including the implementation of the tilting system in hardware. The vehicle achieves the targets of the project with the results showing an acceptable correlation with the simulation work.

It is proved that a tilting three-wheeled vehicle with one front wheel and a cabin that tilts, which uses direct tilt control as its tilting strategy, can achieve a balanced cornering condition. Good results for steady state handling were achieved, however, as predicted in the simulation work, transient performance is limited. A high control gain value required to provide fast response also increases the moment applied between the upright rear unit and the tilting cabin. Aggressive steering inputs from the driver allows the vehicle to generate cornering force significantly before the tilting system reaches the balanced point, leading to a dangerous condition and possible rollover.

While the CLEVER vehicle offers a tangible glimpse of an alternative vehicle concept, which has achieved very positive public attention, further work, including the investigation of alternative control strategies and more sophisticated control, is required to enable the concept to succeed.


Characterisation of steering feel

Manfred Harrer, 2007


The steering feel and handling characteristics of a vehicle are vital factors in determining the overall driving pleasure. Time-consuming and expensive development is required by the vehicle manufacturer before this quality can be achieved and improved. Due to a lack of reliable links between subjective assessments and vehicle measurements, the tuning process still relies primarily on subjective assessments by test drivers.

In order to improve the understanding and enable the prediction of steering feel, a methodology to describe steering feel objectively is required. Therefore the scope of this work lies on the development of such methodology, in order to identify reliable relationships between subjective assessments and objective parameters derived out of vehicle measurements.

Twenty-five cars, separated into five vehicle segments were analysed. To attain consistent subjective assessments, a new questionnaire has been formulated and, with the use of experienced test drivers, reliable subjective assessments have been achieved. Furthermore, a brand-typical steering feel was identified. A new transformation method for the subjective assessments has been developed to meet the requirements of the performed regression analyses. Various open-loop vehicle tests were performed, with the help of a steering robot, to attain high quality measurements. Automated analyses algorithms were developed to ensure an efficient and consistent data processing. Therefore, a large number of high-quality, objective parameters were derived from the vehicle measurements.

Simple, dummy and multi regression analyses have been carried out to detect valid links between the objective parameters and the subjective assessments. All valid regression results were examined with the help of further statistical tests and a practical knowledge of vehicle handling, which consequently led to the selection of the final results. These results constitute the required relationships between the subjective and objective assessments, from which target areas for objective parameters are drawn. The assessment criteria “Steering wheel torque”, “Centre feel”, “Steering precision” and “Steering friction” are vehicle segment independent, while the criteria “Steering response” and “Steering wheel angle demand” are vehicle segment dependent.

The objective parameters for steering wheel torque gradients and the corresponding vehicle response gradients have been found to be most important in describing on-centre steering feel in an objective way.


Chassis design and dynamics of a tilting three-wheeled vehicle

Matthew Barker, 2006


The CLEVER pro ject was funded by the European Union to prove the concept of a low emission tilting three wheeled vehicle for use in urban environments as a serious means of private transport. The CLEVER vehicle was designed from scratch by a consortium of nine Eurpoean partners, representing a true European effort, and encompassing qualities common to any successful automotive concept.

This thesis investigates the fundamentals of chassis design and dynamics to prove the possibility of a safe vehicle with a similar driving characteristic to a conventional car, and within a limited envelope particularly constrained by styling and dimensions. Previous attempts at tilting vehicles have not encompassed a scientific methodology to correctly identify the necessary chassis features associated with combining tilting and non-tilting axles.

The CLEVER chassis uses simple mechanical features which were designed to obtain correct functionality from calculated responses. Steady state cornering calculations were performed to match kinematic features with tyre and suspension properties whilst maintaining the required steering response. The calculations were extended to qualitatively examine limiting driving conditions in steady and dynamic states. A prototype vehicle was constructed and tested, and these results have shown a good correlation with mathematical predictions. The effects of the rear suspension on vehicle body roll were examined in detail, and it is shown that much attention needs to be payed to this area of chassis dynamics to simultaneously obtain a good tilting response and driver comfort.

It is proved that the concept of narrow wheeltrack 1F1T tilting vehicles offers the ability to maintain a balanced cornering condition. However the vehicle is limited during transient manoeuvres and has a high likelihood of rollover. Improvements to the vehicle to reduce this tendency are presented, ultimately at the expense of yaw response speed. Suggestions are also made to further improve the driver feel.

It is concluded that 1F1T tilting vehicles offer an alternative transport concept, but the level of their success is limited by fundamental chassis dynamics and the necessity of stability systems to prevent dangerous conditions arising during normal driving.


Interaction of vehicle and steering system regarding on-centre handling

Peter Pfeffer, 2006


With modern vehicles, safety and driving pleasure are most important features. A good steering feel is obligatory for these requirements. Beside the overall vehicle response, steering wheel torque is an absolutely crucial feedback to the driver in the “driver-controls-vehicle-road” control loop. As investigation has shown, steering wheel torque is the fastest channel to trigger reaction of the human driver.

A simulation model has been developed and validated to model the generated steering wheel torque of the vehicle and steering system, especially for on-centre driving. For the vehicle a generic model has been developed which includes body roll and elastokinematics. The steering system is implemented with a newly developed advanced friction model for the steering rack and seals. The hydraulic system is modelled with consideration of time lags due to fluid inertia and compliance. The steering valve is modelled physically based on its geometry. Then, it is shown how this highly complex steering model can be reduced to a simplified model suitable for vehicle handling simulation without neglecting the major influence factors.

Through the clever implementation of the simplified steering system in the vehicle model a very fast computation time is achieved, i.e. integration stepsize of 1ms. The combined model was validated successfully with on-centre driving manoeuvres like micro weave test, step input or straight ahead driving. It was also demonstrated that the combined model reacts to minor vehicle setup alterations in the same way as the measurements.

This validated combined simulation model was used to investigate the steering response and steering wheel torque in on-centre driving. To interpret the effects on steering feel, two subcategories were chosen, namely centre feel and steering response. It showed that a lower steering ratio, a stiffer torsion bar and a higher tyre cornering stiffness can improve both and vice versa. The higher trail generates a highly improved centre feel at the expense of the steering response. Increased steering friction at the rack reduces the steering response and an increased column friction diminishes the centre feel. The change in road friction coefficient leads to a change in the pneumatic trail and so in the aligning torque at the front wheel. It has shown that the steering wheel torque is affected more strongly and faster than lateral acceleration or the yaw rate. This stresses the great importance of steering wheel torque as information source to the driver.