David J. Cole

Predictive and linear quadratic methods for potential application to modelling driver steering control

A brief review of the literature reveals that both predictive control theory and linear quadratic (LQ) control theory have been used to design path-following controllers with preview, but it is not clear how the controllers compare. This article derives optimal linear preview controllers using the two approaches starting from a common state-space description of the vehicle dynamics. The transformation of the controllers from ground-fixed axes to vehicle-fixed axes is discussed. The influences of preview horizon, control horizon and cost function are investigated. For the case of long preview and long control horizons, it is found that the predictive and LQ approaches give identical controllers. The results in this article provide a basis for identifying human steering behaviour from measured data.

Truck suspension design to minimize road damage

The objective of the work described in this paper is to establish guidelines for the design of passive suspensions that cause minimum road damage. An efficient procedure for calculating a realistic measure of road damage (the 95th percentile aggregate fourth power force) in the frequency domain is derived. Simple models of truck vibration are then used to examine the influence of suspension parameters on this road damage criterion and to select optimal values. It is found that to minimize road damage a suspension should have stiffness about one fifth of current air suspensions and damping up to twice that typically provided. The use of an anti-roll bar allows a high roll-over threshold without increasing road damage. It is thought that optimization in the pitch-plane should exclude correlation between the axles, to ensure that the optimized suspension parameters are robust to payload and speed changes. A three-dimensional ‘whole-vehicle’ model of an air suspended articulated vehicle is validated against measured tyre force histories. Optimizing the suspension stiffness and damping results in a 5.8 per cent reduction in road damage by the whole vehicle (averaged over three speeds). This compares with a 40 per cent reduction if the dynamic components of the tyre forces are eliminated completely.

Fundamental Issues in Suspension Design for Heavy Road Vehicles

Heavy road vehicles play an important role in the economy of many countries by providing an efficient means of transporting freight. Such vehicles can also have a significant impact on safety, the infrastructure and the environment. The design of the suspension affects the performance of the vehicle in terms of ride, infrastructure damage, suspension working space, energy consumption, rollover stability, yaw stability, braking and traction. The published literature on suspension design for heavy road vehicles is reviewed. It is found that extensive knowledge exists, but that there are areas where improved understanding is needed. Areas identified as fundamental issues requiring attention include ride discomfort criteria, secondary suspensions, and controllable suspensions. Two issues in particular are examined in detail: suspension tuning and suspension configuration. In the tuning of suspension parameter values for vibration performance, numerical optimisation techniques have been used extensively, but generic tuning strategies have not been widely developed. Modal analysis is proposed as a technique for gaining the insight into vehicle vibration behaviour necessary to enable tuning strategies to be devised. As an example, the technique is applied to the pitch-plane vibration of a tractor-semitrailer. In analyses of new suspension configurations or concepts, comparison with alternative concepts is not always made. Lack of such comparisons makes the selection of an optimum concept difficult. Analysis of alternative concepts using simple mathematical models, and comparison of their performance using common criteria, is advocated for enabling informed selection of an optimum. An example involving two alternative roll control systems is used to demonstrate the issue.

A mathematical model of driver steering control including neuromuscular dynamics

A mathematical driver model is introduced in order to explain the driver steering behavior observed during successive double lane-change maneuvers. The model consists of a linear quadratic regulator path-following controller coupled to a neuromuscular system (NMS). The NMS generates the steering wheel angle demanded by the path-following controller. The model demonstrates that reflex action and muscle cocontraction improve the steer angle control and thus increase the path-following accuracy. Muscle cocontraction does not have the destabilizing effect of reflex action, but there is an energy cost. A cost function is used to calculate optimum values of cocontraction that are similar to those observed in the experiments. The observed reduction in cocontraction with experience of the vehicle is explained by the driver learning to predict the steering torque feedback. The observed robustness of the path-following control to unexpected changes in steering torque feedback arises from the reflex action and cocontraction stiffness of the NMS. The findings contribute to the understanding of driver-vehicle dynamic interaction. Further work is planned to improve the model; the aim is to enable the optimum design of steering feedback early in the vehicle development process.

Force Control of a Semi-Active Damper

SUMMARY Two strategies are investigated for controlling a semi-active damper to track a prescribed force demand signal: (i) ‘open loop’ control, using a model of the damping force versus velocity characteristics; and (ii) force feedback (closed loop) control. The damping characteristics and switching transients of a prototype damper were measured, and used to develop a mathematical model of the dynamics of the damper. The two control strategies were investigated using an idealised (constant velocity) test. Their performance was also simulated and measured under realistic operating conditions using the Hardware-in-the-Loop testing method. Open loop damper control was generally found to give superior performance to force feedback control, due to its smaller phase lag at high frequencies.

Performance of a Semi-Active Damper for Heavy Vehicles

This paper describes the development, modeling, and testing of a prototype, continuously variable semi-active damper for heavy vehicles. A simple proportional valve is used to generate the variable damping coefficient and the detrimental effects of the oil flow forces acting on the valve spool are studied. The force tracking performance of the damper is then examined under simple input conditions. The compliance of the hydraulic fluid is found to have a strong influence on the response of the damper. The performance of the prototype damper is investigated under realistic operating conditions using a Hardware-in-the-Loop (HiL) test rig, with a single wheel station vehicle model. The prototype damper displays a time lag of approximately 20 ms between the demanded and achieved damping force. The semi-active suspension is found to be most effective in reducing the vehicle body motion relative to the performance of an optimum passive suspension.

Optimal roll control of a single-unit lorry

Lateral acceleration control and linear quadratic regulator (LQR) theory are used to design active roll control systems for heavy goods vehicles. The suspension consists of a limited bandwidth hydraulic actuator in series with an anti-roll bar. The procedure used to determine suitable controller gains is described. The simulation results show that roll control of a single-unit lorry requires an actuator bandwidth of 6 Hz and mean power of approximately 17 kW for a ‘worst case’ random steering input. The static roll-over threshold of this vehicle is increased by 66 per cent when compared with the same vehicle with passive suspensions and the r.m.s. lateral load transfer is reduced by 34 per cent for a typical random steering input.

Dynamic properties of a driver's arms holding a steering wheel:

Abstract Advances in automotive steering technology are motivating improved understanding of the dynamic interaction between the driver and the vehicle. This paper describes a method for identifying the dynamic properties of a drivers arms holding a steering wheel that is subjected to random torque disturbances. Data from eight test subjects are reported. A single-degree-of-freedom linear mass-damper-spring model is found to fit well to the measured torque-angle transfer functions at frequencies up to about 6 Hz. The effect of the driver opposing a steady offset torque and the effect of the driver co-contracting the muscles are investigated. Both actions are found to increase the stiffness and damping of the arms. The results contribute information about dynamic properties of the neuromuscular system in one of the most common human-machine interactions. The findings are relevant to the development of mathematical models of vehicle-driver dynamic interaction.

Spatial Repeatability of Dynamic Tyre Forces Generated by Heavy Vehicles

Road damage due to heavy vehicles is thought to be dependent on the extent to which lorries in normal traffic apply peak forces to the same locations along the road. A validated vehicle simulation is used to simulate 37 leaf-sprung articulated vehicles with parametric variations typical of vehicles in one weight class in the highway vehicle fleet. The spatial distribution of tyre forces generated by each vehicle is compared with the distribution generated by a reference vehicle, and the conditions are established for which repeated heavy loading occurs at specific points along the road. It is estimated that approximately two-thirds of vehicles in this class (a large proportion of all heavy vehicles) may contribute to a repeated pattern of road loading. It is concluded that dynamic tyre forces are a significant factor influencing road damage, compared to other factors such as tyre configuration and axle spacing.

Active Roll Control of Articulated Vehicles

SUMMARY This paper describes an investigation into active roll control of articulated vehicles. The objective is to minimise lateral load transfer using anti-roll bars incorporating low bandwidth hydraulic actuators. Results from handling tests performed on an articulated vehicle are used to validate a nonlinear yaw/roll model of the vehicle. The methodology used to design lateral acceleration controllers for vehicles equipped with active anti-roll bars is developed using a simplified linear articulated vehicle model. The hardware limitations and power consumption requirements of the active elements are studied. The controller is then implemented in the validated articulated vehicle model to evaluate the performance of an articulated lorry with active anti-roll bars. The simulation results demonstrate the possibility of a significant improvement in transient roll performance of the vehicle, using a relatively low power system (10 kW), with low bandwidth actuators (5 Hz).