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This article is based on material first published in ProActive, the official industry newsletter of Lotus Engineering. It is used here with permission.
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This article was first published in 2010.
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Most people with an interest in vehicle dynamics will be familiar with the traditional quest for an ideal balance between conflicting attributes such as ride comfort, response, stability and fuel economy. One emerging technique, called ‘torque vectoring’, is particularly suited to electric vehicles and has the potential to significantly reduce the conflict between two of these attributes - stability and response - while offering the opportunity to enhance the others. It is an area where Lotus has been evaluating and developing new systems and approaches.
Yaw Response
When a driver turns the steering wheel, they expect the vehicle to change direction (ie to “yaw” – the vehicle rotating around a vertical axis). The vehicle does not, however, respond immediately because tyres take time to build up lateral forces. The actual vehicle response may also not be exactly what is required, or expected.
Typically, the vehicle yaw rate response to a rapid steering input is as is shown in this graph.
Particularly at high vehicle speed, after an initial delay period (a fraction of a second) the vehicle yaw rate can overshoot and oscillate before settling on a steady value.
At very high speeds, or if the vehicle’s suspension is poorly tuned, the oscillations can increase and the vehicle can go out of control. Even at lower speeds, the oscillations can make the vehicle feel less stable and the driver may find that they need to make multiple steering adjustments to follow the intended path through a corner.
Conventional vehicle suspension is tuned through bump steer, static settings, etc. to minimise the oscillations and to give a stable response at all vehicle speeds and loading conditions. However, any increase in stability is at the expense of vehicle agility and the vehicle response can become dull.
This can lead to a compromise between vehicle response, stability, ride and fuel consumption. For example, tyre rolling resistance would be reduced if the suspension characteristics could be tuned to reduce tyre scrub.
However, when a vehicle is fitted with a means of independently controlling the drive and braking torques to each wheel (for instance by the use of electric hub motors), there is an opportunity to improve the vehicle yaw response. This is done by increasing the drive torque to the outside wheels, and at the same time creating an effective braking torque to the inside wheels. These drive torques are in addition to the normal drive torques required to control vehicle speed.
This diagram shows drive torques helping the vehicle turn left. This is called Torque Vectoring and is defined as creating a difference in the braking or driving forces at each wheel to generate a yaw moment (torque) with the intention of controlling yaw rate.
The ability to tune yaw behaviour via torque vectoring can potentially eliminate the compromise between response and stability. Suspension characteristics could be tuned to benefit ride and fuel economy; whilst torque vectoring generates the desired response to driver steering inputs.
Maximum Turning Moment (Torque)
Independent of the steered angle of the wheels, a yaw moment is generated when the resultant of the tyre forces is at right angles to a line through the centre of gravity. The resultant force is the combination of lateral and driving/braking forces. The maximum yaw moment (if required) is obtained when the resultant of the tyre forces is at right-angles to a line from the centre of the tyre to the vehicle’s centre of gravity.
As opposed to purely tyre lateral forces, there are two main advantages in using these resultant forces to control vehicle yaw:
To do this the control of the wheel torques needs to consider:
The challenge is how to control the torque to achieve improved yaw response and stability. For example, simply distributing the torque based on steering wheel angle would achieve more yaw response (for the same steering input), but it would not create any improvement in stability. It could even make the vehicle less predictable.
Control Systems
One method to achieve rapid yaw response and improved yaw stability is to use Lotus’s rear steer algorithm which Lotus developed on rear steer vehicles. This approach uses a calculated yaw rate based on forward velocity and steering angle, and monitors the results via a yaw rate feedback sensor.
Taking this ‘feedback’ approach gave the results shown in this graph (click on it to enlarge). The red line shows the standard response and the blue line the response with the active torque vectoring. It can be seen that with the feedback system there is an increase in lateral acceleration and yaw rate, and a quicker initial gradient for yaw rate. The responses are also less oscillatory and more stable.
A limitation to feedback control is that the system relies on measured yaw rate as an input signal. This measured response data will also include ‘noise’ (high frequency waves created by road inputs and general vibration). In order to use the signal, the signal must be filtered. This unfortunately creates a time delay in the signal, and the feedback comes too late.
An alternative approach is to use model-based control. Model-based control does not require any feedback. Instead it uses a mathematical model to predict the required input to the vehicle (in this case driving and braking torques) to achieve a desired yaw rate. The desired yaw rate can be calculated from the turning circle or alternatively it can be what is considered ultimately desirable, defined as a mapping. The input to the model is therefore the desired yaw response of the vehicle (defined from the steering) and the outputs are the drive/ braking torques that are required to achieve the yaw response.
However, since the mathematical model cannot always match the vehicle/road system perfectly, a feedback loop can be included to correct for the difference between the desired yaw response and the actual yaw response.
The complete control system therefore combines the benefits of rapid response from the mathematical model with the feedback providing fine tuning and improving accuracy.
From this graph it can be seen that with the model-based system there is an increase in lateral acceleration, and yaw rate, and a much quicker initial gradient for yaw rate. The yaw response matched the demand. The responses are also less oscillatory and more stable.
Conclusion
Torque vectoring using this approach has the potential to greatly improve response and stability, with the tuning of the control model enabling vehicle behaviour to meet driver expectations. Not only can future electric vehicles have clear environmental advantages, but with the torque vectoring their drive systems allow, they can potentially be both safer and fun to drive.
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