The Dynamics and Control of a Three-Wheeled Tilting Vehicle

  • Auguste Van Poelgeest

Student thesis: Doctoral ThesisPhD


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 inertia’s 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 as 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.
Date of Award1 Jan 2011
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorJos Darling (Supervisor) & Kevin Edge (Supervisor)


  • control systems
  • computer modelling
  • vehicle dynamics

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