While ABS and TCS seek to assist the driver during braking and accelerating manoeuvres, VDC aims to help the driver during critical steering scenarios. When a vehicle attempts to negotiate a turn the VDC system will control wheel speeds to ensure a predictable driving state is maintained while also attempting to provide maximum practical cornering acceleration. In many respects this is a very similar goal to ABS and TCS, and combined, they represent a comprehensive system that ensures vehicle controllability and high performance during severe manoeuvres. Although VDC is the newest and most complex development, each system should be viewed as providing separate but comparable functions for different manoeuvres.
For ABS, the wheel is the controlled element, with wheel acceleration controlled to keep the slip sufficiently small to preserve some amount of lateral force capability. For VDC, however, the vehicle is the controlled element, with vehicle motion controlled to keep any deviation from its nominal motion as small as possible, and to conform with the environmental conditions through the control of wheel slips to gain the required lateral and longitudinal forces and control yaw angles. It does this by using the braking system and engine control to regulate the individual wheel torques, but also utilises additional data input from a steering angle sensor, a yaw rate (d/dt) sensor and a laterally placed accelerometer [14].
Figure 2.33: Dynamic yaw response during cornering [14]
1) Very slow vehicle with no yaw angle, 2) Overpowered vehicle oversteers with very large yaw angle, & 3) Well controlled vehicle at stability limit with small yaw angle
The effect of yaw rate on stability is an important observation, as the sensitivity of yaw moment on vehicle stability, with respect to changes in the steering angle, decreases rapidly as the slip angle of the vehicle increases. In critical cornering manoeuvres it is therefore important to control the yaw rate of the vehicle to correlate to the drive’s desired path, which is determined from the steering angle. At large vehicle slip angles (where the y-slip curve of the tyre is maximum), variation in the steering angle has little effect on the yaw moment, with the result that manoeuvrability is lost in these conditions. VDC attempts to utilise wheel slip control to manage vehicle yaw rate within selected bounds.
Figure 2.34: Functional diagram of VDC [43]
The addition of a yaw rate control does not, however, guarantee stability in all conditions. If the control is used on a slippery road the yaw rate of the vehicle may correspond to the driver’s requested turning rate through the steering wheel, but the vehicle may just be spinning in oversteer, and not following the intended course. In this case, while the yaw rate is controlled correctly, the lateral (cornering) acceleration of the vehicle does not correlate to the driver’s intended path, and it spins off the road. The
addition of the lateral acceleration sensor to the yaw rate sensor eliminates this problem and forms the backbone of the VDC system, shown conceptually in Figure 2.34.
The first task of the VDC controller is to determine the driver’s desired (nominal) path. It does this from the data gathered from the onboard sensors, including driver inputs of steering wheel angle, throttle position and brake pressure, but must also account for unknown variables, such as coefficient of friction, which can affect driving attitude and behaviour. Further, steering wheel angle, vehicle velocity and yaw rate can be used to determine the nominal yaw rate during turns (Eqn 2.2), which is limited by the coefficient of friction of the road (Eqn 2.3). [8, 37]
2 2 1 CH x w x No v v c a v Eqn 2.2where: a = longitudinal distance from front wheels to centre of gravity of vehicle c = longitudinal distance from rear wheels to centre of gravity of vehicle vx = longitudinal vehicle speed vCH= characteristic vehicle velocity
w = angle of steered wheel
x L No v g Eqn 2.3
Once the nominal path is determined, the controller compares it with the actual path of the vehicle, as measured through the wheel speed, yaw rate and lateral acceleration sensors. Any deviations are then sent to the dynamics controller to either brake or accelerate the offending wheel(s) to alter lateral and longitudinal forces and the yaw moment, the dynamics of which are discussed in Figure 2.35.
If the braking slip of the left front tyre is increased by a small amount from an initial value o and if
tyre slip angle is o, then the yaw moment on the car is in a first approximation changed by the following
amount:
w w
B w w S Yw a b d dF b a d dF M cos sin sin cos
Here, changes in the tyre normal force as a result of a change in the tyre longitudinal of lateral force are neglected, as are the changes in the aligning torque on the tyre. Similarly, the lateral and longitudinal forces on the vehicle will be changed by the following amounts: w B w S x d dF d dF F sin cos w B w S y d dF d dF F cos sin
These relations which can be derived for each wheel of the vehicle are extremely non-linear, since the derivatives of the forces are highly dependent on the operating point (o, o) of
the tyre.
The effect of variation in the tyre slip may be explained best by using the figure. This illustration shows the forces FR (=0), FR
(o), FB (o) and FS (o). FR is the resultant tyre force that is
obtained by the vectorial sum of the longitudinal and lateral tyre forces. FR (=0) is the resultant tyre force acting on the free-
rolling tyre and is equal to the lateral force on the tyre that results from the slip angle o.
If the tyre slip is increased to the value o, then the lateral force on the tyre is reduced to the value FS (o).
At the same time a brake force FB (o) is generated. FR (o) is now the resultant tyre force. At the limit of
adhesion between the tyre and the road the absolute values of FR (=0) and FR (o) are approximately
equal. Clearly, increasing the tyre slip then means rotating the resultant tyre force and therefore changing the yaw moment, the lateral force and the longitudinal force on the vehicle.
Figure 2.35: Control of yaw moment and tyre forces with slip [37]
Braking or accelerating any given tyre can be used to control the vehicle slip angle, effectively helping to steer the automobile. By controlling individual wheel slip values, it is possible to significantly aid the driver during cornering manoeuvres. Unfortunately, this can come at a cost of unwanted deceleration or acceleration of the vehicle. It also can cause a lateral deviation from the nominal path, as the ability of the tyres to transmit lateral forces changes with the controlled longitudinal slip. The VDC system must control individual wheel slips to achieve a compromise between these effects, with the overall aims of:
Keeping the driver in control by providing vehicle response similar to normal driving conditions;
Intervening on a ‘smart’ basis and only when needed; and
Emulating the expert driver to assist the average driver in realising the performance potential of the vehicle.
The operation of VDC (which has the same operation as Bosch’s Electronic Stability Program – ESP) will be described through two examples, as illustrated by Bauer et al. [14].
In the first, two vehicles (one with ESP, the other without) initially travel on a high road at high speed and enter a tight corner, as shown in Figure 2.36 and Figure 2.37. It can be seen that the vehicle without ESP soon becomes unstable (oversteer) and departs from its intended course. The vehicle with ESP remains on its intended course by selectively braking individual wheels to increase yaw moment, and thus helping the car to steer through the corner.
Figure 2.36: Vehicle operation on a tight corner without VDC [14]
The second example, shown in Figure 2.38, depicts the potential benefits of ESP when a vehicle is accelerating at its physical limit around a corner of constant radius. On a high (static =1.0) surface and at a corner radius of 100m, the vehicle without ESP reaches its stability limit at 95 km/hr. The result is significant understeer as the slip angle increases rapidly and the driver experiences difficulty keeping the vehicle on course. As the vehicle speed increases further to 97 km/hr, the rear end brakes away and all stability is lost as the vehicle leaves the course. The vehicle with ESP also reaches its stability limit at 95 km/hr, but at this point the ESP reduces engine torque so the limit cannot be exceeded. It also controls wheel torques to help steer the vehicle through the corner, reducing the sensitivity of driver steering inputs. This control results in small deviations from the nominal path that can easily be corrected by the driver.
Figure 2.38: ESP operation when accelerating while cornering [14]
Therfore, VDC can be a significantly aid when driving at the vehicle’s stability limit by controlling individual wheel torques. Further, because VDC reduces oversteer, it has also been observed that vehicle resistance to rollover increases [43]. These advantages show what can be accomplished in vehicle dynamics modelling and control above ABS and TCS by the addition of just three sensors (yaw rate, lateral acceleration and steering angle), and also represent ‘state of the art’ commercially available active control systems.
Future systems can be expected to improve safety and performance even further. As new and existing sensors and data sources are developed to a level where they can be economically installed in mass-produced vehicles, control models will become more accurate and incorporate greater possibilities. These advances include absolute vehicle velocity sensors, chassis attitude sensors (which measure vehicle roll, pitch and yaw),
road surface sensors, traffic monitoring via vision, laser and radar, and driver monitoring, using systems such at BAC and fatigue observers [23, 27]. It also includes Global Positioning System (GPS) information and wireless communication and broadcasting of various scales [44, 45, 46]. In this way, new controllers will be able to gain greater information from their surroundings, including communications with roadside devices and other vehicles, and far greater functionality will result.
On the other hand, control actuator advances also have great scope in improving vehicle safety and performance. Of particular note here is that the slip control method used by all ABS, TCS and VDC systems represents only one of numerous possible controllable parameters. Camber control, for instance, results in significant tyre grip increases beyond what is achievable using simple slip regulation. Other similar possible active actuators include variable spring rate and ride height [25, 43, 47], variable anti-roll bar stiffness, variable damping [47, 48, 49] and variable LSD and differential control [33, 38, 50, 51, 52, 53, 54]. Looking from a wider perspective other anticipated advances in active control, such as “brake by wire”, “throttle by wire” and “steer by wire”, offer greater flexibility from a controller point of view. Here, the mechanical linkages between the driver and the vehicle are replaced with electronic actuators, which give various vehicle controllers scope for fast, accurate and improved control of these parameters and capacity for greater integration between systems [27, 45, 46, 55, 56].
Of further interest is the scope for integrating separate automotive systems for reduced cost and greater functionality, as well as exploring emerging controller architectures and modeling techniques. In addition, performance increases can be realised by deriving additional control possibilities from existing actuators and developing new methods to gain greater information from existing sensors. In this way, greater vehicle performance and safety can be increased with very little additional cost. Road surface prediction is one such parameter that has broad scope in improving stability system performance and, as demonstrated below, has been explored using a wide variety of methods.