Jos Darling

Control of a hydropneumatic active suspension based on a non-linear quarter-car model

Abstract It is extremely difficult to maintain simultaneously a high standard of ride, handling, and body control in a vehicle with a conventional passive suspension. However, it is well known that active suspensions provide a possible solution to this problem, albeit with additional cost and weight. This paper describes the design and analysis of a hydropneumatic slow active suspension. The design is based on hydropneumatic suspension components taken from a commercial system. A non-linear quarter-car model is developed, which includes a gas strut model developed in a previous study and a non-linear dynamic flow control valve model. A hybrid control strategy is proposed for the disturbance rejection and self-levelling requirements. The disturbance rejection control is based on limited state feedbacks and the linear quadratic method plus a Kalman filter that is used to optimize the performance index. The self-levelling control employs a proportional, integral, and derivative (PID) control strategy. Practical issues, such as power consumption, controller robustness, and valve dynamics, are also investigated in this paper. Simulations show that the proposed system has good performance and robustness.

Lateral dynamics simulations of a three-wheeled tilting vehicle

A novel tilting three-wheeled vehicle was developed at the University of Bath as part of a project funded by the European Union. The space and weight savings provided by this type of vehicle could be a solution to the pollution and congestion problems seen in urban environments. The direct tilt control method originally implemented on the prototype was shown to perform well in the steady state, but rapid transients were shown to lead potentially to rollover instability. To investigate this phenomenon and to design an improved controller, a multi-body model was combined with a lateral dynamics single-track model to predict both the steady-state behaviour and the transient behaviour. With this model, it was possible to obtain an accurate representation of the kinematic and dynamic roll motions of the vehicle and the resultant weight transfer across the rear axle, together with the lateral dynamics of the vehicle. The simple lateral dynamics model provided an easily understood physical representation of the system which can often be hidden in a complex multi-body model. This paper presents the development of the model and its validation against data from static and dynamic tests.

Combined steering–direct tilt control for the enhancement of narrow tilting vehicle stability

Narrow tilting vehicles offer an opportunity to reduce both traffic congestion and carbon emissions by having a small road footprint, a low weight and a small frontal area. Their narrow track requires that they tilt into corners to maintain stability; this may be achieved by means of an automated tilt control system. Automated tilt control systems can be classed as steering tilt control in which active control of the front-wheel steering angle is used to maintain stability, direct tilt control in which some form of actuator is used to exert a moment between the tilting part(s) of the vehicle and non-tilting part(s), or a combination of the two, namely steering–direct tilt control. Combined steering–direct tilt control systems have the potential to offer improved performance as, unlike steering tilt control systems, they are effective at low speeds while offering superior transient roll stability to direct tilt control systems. This paper details the implementation of a steering direct tilt control system on a prototype narrow tilting vehicle and presents experimental results which demonstrate a 36% reduction in load transfer from the inside wheel to the outside wheel during a ramp-steering manoeuvre when compared with a direct tilt control system.

Path Following Performance of Narrow Tilting Vehicles Equipped With Active Steering

Narrow Tilting Vehicles offer an opportunity to reduce both traffic congestion and carbon emissions by having a small road footprint, low weight, and a small frontal area. Their narrow width requires that they tilt into corners to maintain stability; this may be achieved by means of an automated tilting system. Automated tilt control systems can be classed as Steering Tilt Control (STC) in which active control of the front wheel steer angle is used to maintain stability, Direct Tilt Control (DTC) in which some form of actuator is used to exert a moment between the tilting part(s) of the vehicle and a non-tilting base, or a combination of the two (SDTC). Combined SDTC systems have the potential to offer improved performance as, unlike STC systems, they are effective at low speeds whilst offering superior transient roll stability to DTC systems. However, alterations to the front wheel steer angle made by STC and SDTC systems may result in unwanted deviations from the driver’s intended path.This paper uses multi-body simulations of a three-wheeled Narrow Tilting Vehicle performing an emergency lane change manoeuvre to show that the path followed by a SDTC equipped vehicle in response to a given series of steer inputs differs significantly from that followed by a DTC equipped vehicle. It is also shown that by using a revised series of steer inputs, a vehicle equipped with SDTC is able to successfully follow a similar path to one equipped with DTC, and that the roll stability of the vehicle is not unduly compromised. Finally, the influence of higher DTC system gains on the SDTC system is considered. It is shown that the result is a small improvement in the vehicle’s path following response at the expense of a small reduction in vehicle roll stability.Copyright

Development of a Steer Tilt Controller for a Three Wheeled Tilting Vehicle

A three wheeled tilting vehicle called CLEVER was developed at the University of Bath. The tilt mechanism of this vehicle consisted of two hydraulic actuators that tilted the cabin in response to the driving conditions. Although this system was reliable, it had high power requirements, so a different method was needed. One way in which such a vehicle could be tilted was using the same principle that a motorcycle rider applies to tilt his bike, namely countersteer. This type of tilt control was expected to reduce the power required to lean. First, the vehicle and a basic steer controller were modelled. The simulations showed that the steer controller balanced the vehicle well, but deviated significantly from the intended path. A controller that could combine both the balance and the path following function was required. A good controller for this task is clearly the driver, so a pilot study was launched where the steering inputs of various drivers were measured. This study was carried out using a three wheeled tilting moped. The results of this study showed that the frequency of the steering inputs depended on the driver’s experience and the more experienced the driver, the lower the frequency of steer input for a given manoeuvre. The steady state manoeuvre showed that all drivers achieved a lean angle depending on the speed and turning radius in compliance with the theory. The countersteer was difficult to determine, because the drivers shifted their weight to aid the tilting. This indicated that countersteer is dependent on the driver and the driving conditions. However, a correlation between the countersteer and the countersteer rate was found, showing that either little countersteer could be applied for a short time, or a lot of countersteer could be applied for a short time. Another correlation was found between the countersteer rate and the maximum tilt acceleration, where the larger the countersteer rate, the larger the tilt acceleration. Since the tilt acceleration was related to the lateral acceleration, these correlations could aid the development of a steer tilt controller.Copyright

Modelling of a Novel Gas Strut Using Neural Networks

The strut is one of the most important components in a vehicle suspension system. Since it is highly non-linear it is difficult to predict its performance characteristics using a physical mathematical model. However, neural networks have been successfully used as universal ‘black-box’ models in the identification and control of non-linear systems. This approach has been used to model a novel gas strut and the neural network was trained with experimental data obtained in the laboratory from simulated road profiles. The results obtained from the neural network demonstrated good agreement with the experimental results over a wide range of operation conditions. In contrast a linearised mathematical model using least square estimates of system parameters was shown to perform badly due to the highly non-linear nature of the system. A quarter car mathematical model was developed to predict strut behavior. It was shown that the two models produced different predictions of ride performance and it was argued that the neural network was preferable as it included the effects of non-linearities. Although the neural network model does not provide a good understanding of the physical behavior of the strut it is a useful tool for assessing vehicle ride and NVH performance due to its good computational efficiency and accuracy.Copyright

Non-linear modelling of a gas strut used in ground vehicle suspensions

Gas struts are widely used in vehicle suspensions. However, they are highly non-linear and conventional linear models are not sufficient to describe their complex behaviour. In this paper, two non-linear gas strut models with different modelling approaches are presented. One is based on grey-box methods using the modular dynamic simulation package Bathfp, where both physical parameters and experimental data are used to model the strut. The other uses black-box methods in Matlab, where artificial neural networks are employed and experimental data are used to train the model. Simulation studies demonstrate that the neural network model is more suitable for real road vehicle simulations, whereas the Bathfp model is more appropriate for detailed system dynamics analysis, especially iso-frequency studies. Since the Bathfp model is able to predict the strut performance when certain parameters in the system are changed and can be easily integrated into different vehicle models, it is a useful design tool for both strut manufacturers and automotive original equipment manufacturers.

Friction compensation using Coulomb friction model with zero velocity crossing estimator for a force controlled model in the loop suspension test rig

This paper presents a method of friction compensation for a linear electric motor in a model in the loop suspension test rig. The suspension consists of a numerically modeled spring and damper, with inputs of suspension motion. The linear motor is force controlled using a force sensor to track the output of the numerical model. The method uses a Coulomb friction model and applies a feedforward step signal when velocity zero crossing occurs. Velocity zero crossing estimation is achieved using an algorithm based on measured feedback velocity and force. Experimental results indicate reduction of force tracking error caused by Coulomb friction leading to improved test rig accuracy.

Friction compensation for a force controlled electric actuator with unknown sinusoidal disturbance motion

This paper presents a method of friction compensation for a linear electric motor subjected to unknown sinusoidal disturbance motions. The method uses a Coulomb friction model and applies a feedforward step signal when velocity zero crossing occurs. Velocity zero crossing estimation is achieved using an algorithm based on measured feedback velocity and force.

Computational Simulation for Predicting Flow Through a Belleville Washer Damper Unit

A Belleville washer can be best described as a non flat washer with a conical shape and a uniform cross section. They are also known as disk springs and as the name suggests they are often utilised for their load bearing capabilities. Due to their compactness along the axis of loading and a wide range of attainable load-deflection characteristics they are an attractive alternative to conventional springs. Though Belleville washers are primarily used for their load bearing capabilities, they can also be used to build a damping device; which in turn can be used as part of a suspension system. The non linear deflection of the spring makes it difficult to predict the resulting pressure-flow characteristic and as a result the damper pack is built either by an experienced operative or by a trial and improvement method. Without an analytical tool to predict the behaviour a designer cannot exploit the full functionality of this type of spring. The intension of this paper is to present research undertaken to develop a correlation which describes the pressure drop required for various flow rates when using Belleville washers as damping elements. Using existing load-deflection theory an initial model was developed to relate load with pressure and deflection with flow area which could be used to estimate flow rate. The solutions from a computer simulation showed similar trends to those found in the experimental study, but they estimated smaller pressure drops for a given flow rate. It was postulated that the exit velocity of the fluid created a region of low pressure which tended to close the opening and thus increase the pressure drop. This hypothesis was examined and confirmed with a computational fluid dynamic simulation and the results were used to modify the existing model. Analysis of the new model showed good agreement with the experimental study.Copyright