In the previous section, the driving and steering actuators were discussed.
Apart from the next control steps, a servo control system for the actuators will be proposed in this section. The wheel speeds will be servo controlled to a reference rotational speed and the wheel steering angles will also be servo controlled. A number of reasons will plead for this servo control approach.
After the modeling of chapter 4, it can be proven that the servo controlled system is stable on velocity level. This automatically means the whole sys-tem is detectable, which offers a lot of possibilities for choosing feedback variables. Without the models, this can also be shown by reasoning. If all the wheels have a prescribed velocity and steering angle, they actually do have a prescribed velocity in ATV-fixed x- and y- direction. In total eight speeds while the platform can only have three main velocities. If the wheels do not have matching speeds, some slip will start compensating for this.
Finally, the final velocity can be predicted exactly. Other perturbations will all be dampened out since this is a physical system with dampers in the construction.
The ATV is not a holonomic system. In the case of the ATV this means the vehicle is not able to move sideward directly due to limited steering angles. By driving forward and backwards, this sideward movement can be reached with a detour. This is the reason there are no requirements posed on position level. A certain range of velocities can all be obtained directly be the system however. Acceleration demands again can lead to inadmissible velocities. The acceleration demands can be translated to velocity demands on which level the tracking demands are posed. A time delay in velocity equals the same time delay in acceleration, the same applies for magnitude errors. This makes the velocity a good tracking variable.
Driving the wheels directly by a torque would be a fast way to produce force interaction between the road and tyre. However, when the tyre forces become very high, the saturation region of the tyres can be reached and more slip will result in a lower tyre force. This situation is unstable, and with a constant force, this can result in spinning the wheel up to high speeds. Using a servo control has the advantage of protecting the system from getting in this situation.
2.5 Servo control 13
C ATV C
dw
w
d
i
i
Y u v wi,ref
di,ref
T
di i
.
+
-
+-.
Figure 2.5: Plant H with servo-feedback and new inputs and outputs
The servo control for steering is chosen at a gain of 50. With the actuation at velocity level, the closed loop system from reference steering angle δref and real steering angle δ becomes a first order system. The time constant of this first order system τhydr of 0.02 [s] is typical for this kind of hydraulic systems.
δi+ τhydr˙δi = δi,ref (2.7)
For the driving controller, a single gain Cω of 11, 000 N s/m is chosen. The process of obtaining this value is described in appendix D. It is tuned in such a way that the lateral and longitudinal dynamics have approximately the same response time. A longer response time for longitudinal direction would decrease system performance, while a faster response would increase problems with sensor noise and robustness.
Chapter 3
Literature survey
In the automotive industry, large amounts of research has been done in the field of autonomously guided control as well as in vehicle stability improve-ment. It must be discovered if current control technologies can be applied to the ATV or if a new strategy has to be developed. Therefore, existing control solutions and their belonging models are examined and the goals of each controller design is compared to the ATV control goals. In this chap-ter, the literature results will be summarized while in the following chapters, models belonging to the tyres and the platform will be examined in more detail. Literature related to specific methods and subjects is referred to in the concerning chapters.
3.1 ABS
Anti-lock Braking System, or ABS, has been installed in cars since the eight-ies of the last century. At this moment, most modern cars are equipped with ABS as an important safety system. The reasons for using an ABS system are related to tyre properties. Under normal conditions tyres will generate the maximum braking force under a condition of about 15% slip. With higher slip rates, the braking force will reduce. This might result in an unstable situation where wheel-lock easily occurs and a lower braking force is generated. Another unpleasant phenomenon is that at wheel lock, no lateral forces can be generated and the car will slide rudderless unable to avoid obstacles. The high complexity of this control problem is found in the non-linearity of the tyre, in the uncertainty in tyre parameters in chang-ing drivchang-ing conditions such as icy roads and in difficulties in estimatchang-ing slip 15
rates. Quarter-car models as discussed in section 4.1 are mostly used to describe vehicle dynamics for this kind of control problem, control solutions are tried to be found in rule-based control [7] and fuzzy control [8]. Research in the field of tyre state estimation is also done. A similar approach can also be used for traction control.
In extreme situations, traction control and ABS might help avoiding uncon-trolled slip. However, the above methods do not produce solutions for the automatic guidance of a vehicle. The advantage using quarter-car models, is that longitudinal and lateral dynamics can be well described with relatively simple models. Yaw, pitch and roll effects can evidently not be showed by the model.