Brake-by-steer concept

Brake-by-steer concept
Department of Precision and Microsystems Engineering
Brake-by-steer concept
Steer-by-wire application with independently actuated wheels
used for stopping a vehicle
Name:
Ing. Bas Jansen
Report no:
Coaches:
ME 10.009
Ir. J.W. Spronck
Ir. E.J.H. de Vries
Dr. A. Reedman (SKF)
Professor:
Specialisation:
Prof. Ir. R.H. Munnig Schmidt
Advanced Mechatronics
Type of report:
Date:
Master Thesis
04 March 2010
Acknowledgments
For this research project I have been working as an intern at the SKF European Research
Centre in Nieuwegein, in the Mechatronics department. SKF provided me with the materials,
test facilities and support to realize the steer-by-wire go-kart. I would like to thank Adam
Reedman, who has been my mentor at SKF, for guiding me through the entire project. I also
would like to thank Frank Sperling, former group leader at SKF, for creating this opportunity to
work on a very interesting and fun project.
I would like to thank Dennis van Raaij and Krijn Wielinga for the substantive feedback on the
content of my report and for the conversations we had which refreshed my mind and made
me continue with the project.
Finally I would like to thank Annelies for the infinite patience when I, again, needed a little
more time to complete my work. But now, it’s done!
iii
iv
Abstract
Throughout the years cars are equipped with more and more convenience and safety
increasing systems. Examples are power steering, Electronic Stability Program and Antilock
Brake System. All these systems improve convenience and safety, but do not have the
flexibility of mechanically decoupled drive-by-wire systems.
Before brake- and steer-by-wire can be accepted they need to be as failsafe as their hydraulic
and mechanical predecessor. This can be achieved by using redundancy. Another method is
proposed here as is brake-by-steer. The braking force, needed to stop the vehicle, is created
by turning the front wheels such that the generated lateral tire force works in the longitudinal
vehicle direction. With this concept the steering system can back-up a failing brake system
without introducing redundant components in the braking system. Visa versa it is possible to
steer the vehicle with uneven distributed brake force [10].
Main goal in this thesis is to investigate the possibility to stop a vehicle by turning the tire
lateral force into the longitudinal vehicle direction. This is done by turning both wheels
extremely in- or outwards. The performance is estimated by setting up a conceptual model
that describes vehicle behaviour under large slip angles. Under these conditions the lateral
tire force is completely saturated. This behaviour is described with simplified non-linear tire
characteristic. The tire model is incorporated in a three wheeled vehicle model, which is an
extension of the frequent used bicycle model.
Two brake-by-steer methods are developed. The first is symmetric toe, where both wheels
are turned in- or outwards. The second is asymmetric toe, where one wheel is turned to the
maximum and the second wheel used for lateral control of the vehicle. The model shows that
the lateral behaviour changes drastically. The steering sensitivity is reduced to nearly zero
and for some regions steering becomes inverted.
The theory is verified on a go-kart that is modified to a steer-by-wire vehicle with independent
steerable front wheels. The mechanical steering system geometry has a large influence on
the vehicle handling. The static and dynamic toe angles influence the lateral vehicle
behaviour. These conventional settings already reveal part of the behaviour of the brake-bysteer concept. The kingpin angles influence the required steering torque. This input is
necessary for the of actuation design of the steer-by-wire system.
The design consists of two wheel actuators and one at the steering wheel to provide a basic
sense of passive force feedback. The required actuator performance is based theoretical
expectations and measurement data from a separate equipped measurement kart. The major
limitation in the mechanical design is the limited space in the small vehicle. A user interface
makes it possible for the driver to switch between steering configurations where he can
manipulate each wheel independent on top of a conventional steering setting. There is no
vehicle state estimator incorporated in the controller. All strange behaviour needs to be
compensated by the driver himself.
The results show that the braking performance of the brake-by-steer concept is approximately
half of what conventional brakes achieve. This may be enough to stop the vehicle in an
emergency situation. Although not successfully measured, the lateral behaviour of the kart did
change to inverted steering. The results differ from the theory where the kart specific steering
system geometry plays a role. These are not described by the model.
In order to make this system work in a car, the relation between steering angle and vehicle
heading has to be restored by implementing a vehicle state estimator in the onboard control
algorithm. The tire model needs improvement on describing the lateral tire forces for extreme
large slip angles.
v
vi
Table of content
Acknowledgments.................................................................................................................. iii
Abstract .................................................................................................................................... v
1
Introduction ...................................................................................................................... 1
1.1
Steering system developments......................................................................... 1
1.1.1
Steering assists....................................................................................... 1
1.1.2
Steer-by-wire........................................................................................... 1
1.1.3
By-wire research and commerce ............................................................ 2
1.2
Problem introduction ......................................................................................... 3
1.2.1
Research goal......................................................................................... 3
1.3
Thesis Outline ..................................................................................................... 3
2
Modelling the Brake-by-Steering system ...................................................................... 5
2.1
Tire model............................................................................................................ 5
2.2
Vehicle model...................................................................................................... 6
2.3
Steering system geometry................................................................................. 7
2.3.1
Static Toe................................................................................................ 7
2.3.2
Dynamic Toe........................................................................................... 8
2.3.3
Kingpin inclination and Caster angle ...................................................... 9
2.4
Brake-by-steering cases .................................................................................. 10
2.4.1
Symmetric toe braking .......................................................................... 10
2.4.2
Asymmetric toe ..................................................................................... 12
2.4.3
Braking performance ............................................................................ 12
2.5
Inverted steering............................................................................................... 13
2.5.1
Lateral and longitudinal vehicle force contributions.............................. 13
2.5.2
Behavior with linear tire model.............................................................. 13
2.5.3
Behavior with non-linear tire model ...................................................... 15
3
Implementation on a Go-Kart ....................................................................................... 17
3.1
Go-kart introduction ......................................................................................... 17
3.1.1
Steering system .................................................................................... 18
3.2
Steering system performance and design requirements ............................. 18
3.2.1
Steering wheel actuation design requirements..................................... 18
3.2.2
Wheel actuation design requirements .................................................. 18
3.2.3
Measured system performance ............................................................ 18
3.3
Electro-Mechanical modifications .................................................................. 19
3.3.1
Steering wheel ...................................................................................... 19
3.3.2
Wheel actuation .................................................................................... 21
3.4
Control algorithm.............................................................................................. 24
3.4.1
Local control loop.................................................................................. 24
3.4.2
Global control loop ................................................................................ 25
3.5
Sensor systems and electrical layout ............................................................ 25
3.5.1
Sensors................................................................................................. 26
3.5.2
Electrical layout..................................................................................... 26
3.6
Control hardware and software....................................................................... 28
3.6.1
CompactRIO hardware ......................................................................... 28
3.6.2
Controller software................................................................................ 28
3.6.3
FPGA software...................................................................................... 30
3.6.4
Offline PC software ............................................................................... 34
4
Results ............................................................................................................................ 35
4.1
Test description ................................................................................................ 35
4.1.1
Test track .............................................................................................. 35
4.1.2
Test cases............................................................................................. 35
4.2
Steering performance....................................................................................... 35
4.2.1
System identification ............................................................................. 36
4.2.2
Tracking error........................................................................................ 36
4.3
Brake-by-steering performance ...................................................................... 37
4.3.1
Maximum measured braking performance ........................................... 37
4.3.2
Estimated performance......................................................................... 37
4.3.3
Lateral vehicle stability.......................................................................... 38
vii
5
6
A.
B.
C.
D.
E.
4.3.4
Asymmetric toe ..................................................................................... 39
Conclusions and recommendations............................................................................ 41
5.1
Brake-by-steer concept.................................................................................... 41
5.2
Recommendations & future work ................................................................... 41
Bibliography ................................................................................................................... 43
Go-Kart dimensions ......................................................................................... 45
Measurement Kart ............................................................................................ 46
a.
Used equipment ................................................................................................ 46
i.
Data acquisition......................................................................................... 46
ii.
Velocity sensor .......................................................................................... 46
iii.
Absolute through shaft angle sensor ........................................................ 46
iv.
Accelerometer ........................................................................................... 46
v.
Force sensors............................................................................................ 46
b.
Measurement kart layout ................................................................................. 47
c.
Measurement kart results ................................................................................ 47
i.
Steering angle range................................................................................. 47
ii.
Steering speed and frequency, hard cornering......................................... 48
iii.
Steering speed and frequency, slalom...................................................... 48
iv.
Steering torques ........................................................................................ 48
v.
Breaking performance............................................................................... 48
vi.
Summary ................................................................................................... 49
Sensor list and layout ...................................................................................... 50
Used materials .................................................................................................. 45
a.
National Instruments ........................................................................................ 53
b.
Maxon Motor ..................................................................................................... 53
Steer-by-wire go-kart ..................................................................................................... 54
viii
List of Figures
Figure 1 Brake-by-steer impression of symmetric toe in ........................................................... 3
Figure 2 Slip angle sign conventions......................................................................................... 5
Figure 3 Tire characteristic, normalized representation ............................................................ 6
Figure 4 Three-wheeled vehicle model ..................................................................................... 7
Figure 5 Toe angle effect on vehicle handling........................................................................... 8
Figure 6 Dynamic toe angles..................................................................................................... 8
Figure 7 Kingpin inclination and Caster angle........................................................................... 9
Figure 8 Steering torque for vertical axle load........................................................................... 9
Figure 9 Torque for frame twisting........................................................................................... 10
Figure 10 Brake-by-steer wheel configuration......................................................................... 11
Figure 11 Pacejka versus piecewise linear tire model for longitudinal force........................... 11
Figure 12 Asymmetric toe........................................................................................................ 12
Figure 13 Braking force over full steering range ..................................................................... 12
Figure 14 Inverted Steering for toe in, lateral vehicle force..................................................... 13
Figure 15 Momentum contribution from longitudinal and lateral vehicle forces, linear tire
model................................................................................................................................ 14
Figure 16 Resultant moment linear tire model ........................................................................ 14
Figure 17 Momentum contribution, longitudinal and lateral vehicle forces, non-linear tire
model................................................................................................................................ 15
Figure 18 Resultant moment non-linear tire model ................................................................. 15
Figure 19 General impression of the go-kart........................................................................... 17
Figure 20 Steering system details ........................................................................................... 18
Figure 21 Steering wheel actuation implementation ............................................................... 20
Figure 22 Motor operating area, steering wheel motor ........................................................... 20
Figure 23 Steering wheel interfaces ........................................................................................ 21
Figure 24 Wheel actuation exploded view (front view)............................................................ 22
Figure 25 Wheel actuation implementation ............................................................................. 22
Figure 26 Front view wheel actuation...................................................................................... 23
Figure 27 Fail safe steering design (top view)......................................................................... 23
Figure 28 Motor operating area, wheel motors ....................................................................... 24
Figure 29 Control system representation ................................................................................ 24
Figure 30 Steering wheel representation ................................................................................ 25
Figure 31 Block scheme of haptic control loop........................................................................ 25
Figure 32 Electrical layout ....................................................................................................... 27
Figure 33 CompactRIO............................................................................................................ 28
Figure 34 State machine of the software structure.................................................................. 29
Figure 35 control scheme and set point selection ................................................................... 30
Figure 36 Test track................................................................................................................. 35
Figure 37 Frequency response of measured and identified system ....................................... 36
Figure 38 Steering angle behaviour on step input (toe in) ...................................................... 36
Figure 39 Braking performance brake-by-steer,...................................................................... 37
Figure 40 Brake force data collection ...................................................................................... 38
Figure 41 Braking performance, wheel positions .................................................................... 38
Figure 42 Inverted steering paths............................................................................................ 39
Figure 43 Go-kart dimensions ................................................................................................. 45
Figure 44 Measurement kart layout......................................................................................... 47
Figure 45 Strain gage and steering angle detail...................................................................... 47
Figure 46 Braking performance reference kart........................................................................ 48
Figure 47 Sensor electronics................................................................................................... 52
Figure 48 Steer-by-wire kart .................................................................................................... 54
Figure 49 Steer-by-wire kart toeing-out ................................................................................... 54
ix
List of Tables
Table 1 Simplified Pacejka coefficients ................................................................................... 12
Table 2 Steering system performance original kart................................................................. 19
Table 3 Sensor list ................................................................................................................... 51
Table 4 Used material CompactRIO........................................................................................ 53
Table 5 Used material MAXON Actuators ............................................................................... 53
x
1
1.1
Introduction
Steering system developments
1.1.1
Steering assists
Throughout the years cars are equipped with convenience increasing systems. Hydraulically
power assisted steering was introduced in the mid twenties of the previous century. Here, the
engine drives a hydraulic pump that provides the power to reduce the steering effort for the
driver. Stronger environmental regulations and awareness and the increasing oil prices
demand the manufacturers to design better energy efficient systems. A solution for this is
electric power steering. This motor will only consume power when power assist is needed
[28].
Power steering can be made variable in the amount it assists the driver by applying more or
less torque, possibly varying at different speeds. A drawback is that the driver is less
'connected' with the road if high assistance is applied. Also the steering ratio does not change
with increased assistance.
ZF Lenksysteme GmbH solved this problem by making the Active Front Steering system [22]
[30]. A planetary gear is mounted in the steering shaft. The third exit of the gear set is
connected to an electromotor. This system is capable of giving an offset to the steering wheel
angle. It provides fast turning at low speed and a stable wheel movement at high speeds.
Next to the development of steering, the automobiles are equipped with a lot of intelligent
safety systems. An example is the EPS or Electronic Stability Program from Bosch GmbH
[25]. This system takes over part of the control when a vehicle tends to get unstable. With
assist of ABS, the Antilock Brake System and Electronic Brake-force Distribution, EBD, it can
brake individual wheels and prevent the vehicle from spinning out of control or roll over.
All these systems improve convenience and safety but do not have the flexibility of a steer-bywire system where steering wheel and wheels are mechanically decoupled.
1.1.2
Steer-by-wire
By-wire applications are well known in the aviation world. Slowly they now introduce
themselves in automotive designs. The principle behind by-wire is that the mechanical
connection is replaced by sensors and electrical driven actuators. In steer-by-wire a set of
actuators controls the position of the tires and a motor at the steering wheel provides the
driver with the needed force feedback. The program that controls the wheel positions has in
many possibilities to assist the driver or completely overrule the driver intentions without the
limitation of mechanical coupling of each wheel to the steering wheel. This method also brings
cost reduction and design freedom to the car manufacturers. For the driver this means
personalized driving characteristics, increased comfort and safety [18] [20] [21].
Steer-by-wire cars are not yet available for the consumer market as the mechanical coupling
is nowadays mandatory by European law [29]. To become accepted the steer-by-wire needs
to prove itself as failsafe as the mechanical coupled variant. To provide this level of fail safety,
critical drive-by-wire components have a level of redundancy since one broken sensor may
not be the cause of a defective steering system. A solution is to implement components
multiple times, which means back up sensors, communication lines, actuators and a system
that detects faults and switch to secondary systems [26][27].
Two new ideas are proposed here that, without additions, increase the level of safety of a
drive-by-wire vehicle. The first is steer-by-brake, which is steering by uneven distributed brake
force. The principle is similar to skid steer [10]. Here the braking systems can back up a
failing steering system.
The second idea is brake-by-steer. The braking force is created by turning the front wheels
such that the generated lateral tire force works in the longitudinal vehicle direction and stops
1
the vehicle. This can back up a failing braking system. Combining these two in one vehicle,
reduces the level of redundant components in a complete drive-by-wire system.
1.1.3
By-wire research and commerce
That by-wire is inevitable shows by the number of research projects and car manufacturers
that build concept cars. Linköping University has a four wheel independently steered vehicle
Sirius in cooperation with Volvo [4]. Stanford University is already working with their third
generation P1 by-wire vehicle together with many car manufacturers [19]. Looking at the
commercial businesses shows GM with the Hi-Wire proto type, Nissan with the Pivo and
Renault with the Ellypse. Also the car manufacturer suppliers such as SKF, ZF and Delphi
provide steer-by-wire solutions for future cars.
Looking at patents concerning independent steerable wheels and combinations with brake
functionality shows four interesting patents
Michelin patented an "Active toe adjustment apparatus" [9]. Due to the suspension, braking
and accelerating the toe angles of front and rear wheels vary. The active toe is used to assure
perfect Ackermann steering under all conditions. With Michelin's invention the toe can be
adjusted to the desired angle. This invention is, however, not meant to brake by with steering
motion.
Another non-braking system is the patent by Mazda "Rear wheels steering apparatus for
vehicles", where the steerable rear wheels have variable toe angles to increase vehicle
handling and stability [8]. This is the same sort of system as Quadrasteer by Delphi [5].
Interesting of these systems is that they are applied on the rear wheels, which is allowed by
regulations.
ZF Lenksysteme GmbH and Robert Bosch GmbH applied a patent in 2003 where they used a
turned wheel as a parking brake [7]. This is a nice extra feature of the brake-by-steer
principle, but not the intended goal here.
Delphi Technologies Inc. has a patent from 2004 called; "Control of independent steering
actuators to improve vehicle handling and stopping" [6]. In this patent they describe a steering
system that is capable of using a steering motion as a backup for stopping the vehicle.
Results of the braking performance are very limited discussed.
2
1.2
Problem introduction
Figure 1 gives an impression of the brake-by-steer concept. An increasing steering angle will
increase the braking force as the lateral tire force is positioned more into the longitudinal
vehicle direction. The lateral tire force is created by the slip angle that is forced up on the two
tires. A side effect of this wheel configuration is that the lateral vehicle control and stability will
change from what is traditionally expected.
Figure 1 Brake-by-steer impression of symmetric toe in
1.2.1
Research goal
With the given conceptual ideas the research question is formulated as follows:
Is it possible to stop a vehicle with the brake-by-steer concept,
while maintaining steering controllability?
As this idea of braking is relative new, the goal is to set up a conceptual model that can
predict the vehicle behaviour. This model needs independent steerable wheels and deal with
large slip angles. The concept will be verified on a test vehicle. The basis for this vehicle is a
go-kart. This simple structured vehicle lends itself for easy modification and relative safe
operation when the mechanical coupling between steering wheel and wheels is replaced by a
system that allows independent steering of each wheel.
1.3
Thesis Outline
This report continues with the model construction in chapter 2. It describes the tire and
vehicle model and the steering system geometry. After these definitions the model is ready to
deal with the brake-by-steer cases described in the last part of this chapter. Chapter 3
describes how the independent steerable wheels are designed and implemented in the gokart on mechanical, electrical, software and system control levels. Chapter 4 describes the
test cases with the results from test runs and theoretical model. This report ends with the
conclusion and recommendations in Chapter 5.
3
4
2
Modelling the Brake-by-Steering system
This chapter describes the construction of the conceptual vehicle model for the brake-by-steer
method. It starts with section 2.1 about the relation between slip angle and lateral tire force.
This relation is used in the equations of motion for a three wheeled vehicle described in
section 2.2. Section 2.3 deals with the limitations imposed by the steering system geometry.
With the model complete section 2.4 ends this chapter with describing the brake-by-steer
concept. This section looks into the straight forward braking function and the inverted steering
behaviour.
2.1
Tire model
A wheel can be described as an object with no resistance in longitudinal motion, roll, but will
resist movement in lateral direction. This lateral tire force origins from the angular difference
of the tire heading and the actual travelling direction, “V” and “v” in Figure 2 respectively. This
angle is defined as the slip angle α . The used sign convention is displayed in Figure 2.
,u
V
α
x,y
u,v
F
M
– Velocity vector
– Slip angle
– Tire coordinate system
– Local velocities
– Force
– Momentum
,v
Figure 2 Slip angle sign conventions
The slip angle is derived from the vehicle heading and the orientation of the wheel. Since both
the steering angles and the slip angle will be large, these can not be linearized. The slip angle
is defined in Equation 1, where ‘ i ’ can be replaced by left or right wheel.
 vi 

 ui 
α i = δ i + tan −1  −
Equation 1
The relation between the slip angle and lateral force is described by the lateral tire
characteristic, shown in Figure 3. There are many mathematical functions describing the tire
characteristic. For this project it is important how a tire behaves and not why. Empirical tire
models satisfy this need by describing the behavior without physical relation to the tire.
5
1
Lateral tire force (N)
0.8
0.6
Pacejka
Piecewise
0.4
C
0.2
0
0
5
10
15
Slip angle (deg)
Figure 3 Tire characteristic, normalized representation
For a small slip angle the tire stiffness can be seen as a linear function. At larger angles the
grip saturates and stops increasing and even decreases. In the brake-by-steer application
very large slip angles are applied, therefore it is not possible to use only a simple linear
model. The conceptual model build here does not need to describe every detail of tire
dynamics. A simplified model will loose accuracy, but gain in simulation ease [33]. For this
project a simplified derivative of Pacejka’s Magic Formula [23] and the Piecewise linear model
[32] are used. Equation 4 and Equation 3 describe the mentioned lateral force as function of
the slip angle
Flat = C ⋅ α
Linear
Equation 2
 C ⋅ α , for α < α saturate
FLat = 
 Fsaturate , for α ≥ α saturate
Piecewise linear
Equation 3
Flat = d sin ( c tan −1 ( b ⋅ α ) )
Simplified Pacejka
Equation 4
Where for linear and piecewise C is the tire stiffness,
where the force saturates,
α the slip angle, α saturate the slip angle
Fsaturate the maximum force, and for simplified Pacejka; d the
maximum force, c the shape factor and b stiffness factor.
2.2
Vehicle model
Simple vehicle models are described by the so called bicycle or single track model. This
model is valid for vehicles with a low centre of gravity and a limited roll [23]. The go kart
satisfies these requirements. However, the lateral tire forces will, due to the large steering
angles, end up in the longitudinal vehicle direction. Therefore the distance between the two
front wheels has to be taken into account to describe the vehicle handling, as it contributes to
a yaw moment on the vehicle. Adding a second front wheel to the bicycle model gives the
possibility to incorporate this effect in the model. Figure 4 shows the model of the three
wheeled vehicle.
6
VFL
α Left
F yFL
VFR
δ FL
x Left
FyFR
δ FR
α Right
x Right
xi , ui
X
y Left
y Right
X1
t1
Y
VR
Vehicle
Coordinates
yi , vi
Tire
Coordinates
α Re ar
X2
Fy R
Figure 4 Three-wheeled vehicle model
This model is described by the following equations. Here
ui and vi represent the longitudinal
and lateral velocity tire velocities respectively. The yaw speed is defined as r around the Zaxis. [17][23]
m ( v + Vr ) = FyFL cos (δ FL ) + FyFR cos ( δ FR ) + FyR
Equation 5
m ( u − Vr ) = − FyFL sin (δ FL ) − FyFR sin ( δ FR )
Equation 6
(
)
V ≥0
(
Ir = FyFL cos (δ FL ) + FyFR cos (δ FR ) x1 + − FyFL sin (δ FL ) + FyFR sin (δ FR )
+ FyR x2
)
1
2 1
t
Equation 7
This set of differential equations describes the vehicle behaviour on the variable steering
angles δ Left and δ Right and vehicle speed V . All wheels in the model do not brake in a
conventional manner and are not driven. The rear wheel is not steerable.
2.3
Steering system geometry
This section describes the influence of the steering system geometry on vehicle handling.
Normally the left and right wheel are fixed by the mechanical linkage. Since this will disappear
it, is important to know if and how the steer-by-wire system needs to mimic this behaviour.
Next to that, especially the toe angles will reveal the basics on lateral stability as the brakeby-steer manoeuvre is exaggerated adjustable toe.
2.3.1
Static Toe
Static toe refers to the angle the wheels make when the steering wheel is centred. The angle
of the left wheel is equal, but opposite in sign to the right wheel. When the vehicle drives in a
straight line, the created lateral tire forces are in balance. So far there is no difference
between toe in or out. Figure 5A shows these situations.
7
Ftire
A.
Ftire
Ftire
Toe in
Toe out
Fy vehicle
Ftire
Fy vehicle
Fx vehicle
B.
Ftire
Fx vehicle
Track width
+
Ftire
Track width
+
M vehicle
Toe in
M vehicle
Toe out
Figure 5 Toe angle effect on vehicle handling
Differences occur when a steering angle is applied. Figure 5B shows the tire forces when the
driver steers slightly to the left. Both situations have an equal lateral force Fy vehicle and
longitudinal force or drag Fx vehicle . The difference is how the forces contribute to the yaw
moment of the vehicle. In the toe-in situation lateral and longitudinal forces counter act each
other, whereas in the toe-out vehicle they both contribute to a negative yaw moment. This
principle makes vehicles with toe-in stable in straight line driving but sluggish in corners and
toe out nervous in straight line driving and sensitive in cornering [35]
2.3.2
Dynamic Toe
Next to the static toe, there is also dynamic toe. This is the difference in turning rate of left
and right wheel when steering. The most common configuration is positive Ackermann
steering. In a corner the inner wheel describes a smaller circular path than the outer wheel.
To prevent tire scrub at low speeds the wheels are not steered parallel, but the inner wheel is
rotated more such that the perpendiculars of all wheels point at the same point [16].
δ Left
δ Right
Figure 6 Dynamic toe angles
8
Next to this quasi static effect, the difference in steering angle has also a dynamic
component. In a turn part of the vertical load transfers from the inner to the outer vehicle side,
due to centrifugal force. This increased vertical load on the outer tire creates the opportunity
for the tire to bare larger lateral forces than the inner tire. This peak force can be increased if
the slip angle increases. This is achieved by turning in the tire more. This principle is less
common and applied in high slip angle situation, high cornering speeds or low grip roads (dirt
and ice) [34][35][36].
2.3.3
Kingpin inclination and Caster angle
The steering axis of each wheel has a caster angle and a kingpin inclination, see Figure 7.
These angles create arms that together with the lateral tire force and the vertical axle load
contribute to the torque in the steering axis.
ykart
xkart
ytire
ztire
Vehicle coordinates
Tire coordinated
ztire z
kart
zkart
Caster
angle
Kingpin inclination
Rotation path
Rear view
Left wheel
Side view
Left wheel
Rotation path
Rear wheel
Lateral tire force
point of application
Mechanic,
pneumatic trail
Pneumatic trail
Figure 7 Kingpin inclination and Caster angle
The static vertical axle load is part of the vehicle mass. This vertical load is supported by the
front wheel which rotates around a tilted axis. This causes a torque in the steering axis.
Figure 8 shows the relation between the wheel angle and steering torque for the static vertical
load.
15
Right wheel
Left wheel
Sum
steering toqrue (Nm)
10
5
0
-5
-10
-15
-25
-20
-15
-10
-5
0
5
wheel angle delta (deg)
10
15
20
25
Figure 8 Steering torque for vertical axle load
When the front wheels are turned they twist the frame of the kart. The required momentum is
also added as a vertical axle load. Figure 9 show the momentum when the steering wheel is
9
turned and both wheels rotate with the original steering linkage which is near perfect
Ackermann.
600
400
Torque (Nm)
200
0
-200
-400
-600
-80
-60
-40
-20
0
20
Steering angle (deg)
40
60
80
Figure 9 Torque for frame twisting
A third origin of changing vertical load is the load transfer due to lateral and longitudinal
accelerations of the centre of gravity. Since the height of this centre is very low, this effect is
neglected.
The second force which contributes to the steering torque is the lateral tire force. The moment
arm consists of the mechanical trail, which is constant and dependant on the steering system
geometry, and the pneumatic trail which is variable and non-linear for large slip angles. There
are too many uncertainties about the tire - road characteristics that it is not possible to say
anything about the pneumatic trail and estimated lateral tire forces.
The last contributor is the torsional tire friction. This torque relaxes when the tire rolls a certain
distance and plays a large roll at standstill. This torque is also dependent on the tire - road
characteristics which are uncertain.
These torques are transmitted through the steering linkage to the steering wheel in the
driver’s hands. This force sensing is important to be able to drive a vehicle [31][38]. An
experienced driver can feel that the tire grip saturates by the decreasing steering torque in the
hand wheel [24] . When the steering linkage is removed the left and right wheels do not
balance each other and the force sensation does not reach the driver. These phenomena
need to be implemented in the steering control system
2.4
Brake-by-steering cases
Now that the behaviour is defined it is possible to zoom in on the brake-by-steer concept. Two
methods are developed to generate brake force and be able to steer, being symmetric toe
and asymmetric toe braking. Assuming the heading of the vehicle is straightforward it is
possible to state that the steering angle and slip angle are equal.
2.4.1
Symmetric toe braking
By turning in both wheels, the lateral tire force is partly directed into the longitudinal vehicle
direction, creating a brake force. The forces in lateral vehicle direction are in balance. Figure
10 shows the wheel orientations described as symmetric toe in. Symmetric toe-out means
that both wheels point outwards.
10
V
δ Right
δ Left
α Right
α Left
FLatTire
V
FLatTire
FLateral vehicle
Fbrake
Figure 10 Brake-by-steer wheel configuration
The lateral tire force is generated by creating a slip angle. In order to get the lateral tire force
work for a longitudinal vehicle deceleration, the steering angle must be large, since:
Fbrake vehicel =
∑ sin (δ ) ⋅ F
i
Equation 8
Lattire i
i = L, R
But to maintain control of the vehicle in lateral direction the steering angle may not be to
large, since:
Flatvehicle =
∑ cos (δ ) ⋅ F
i
Equation 9
Lattire i
i= L,R
Most tires reach their maximum lateral tire force is below a slip angle of 15 degrees. A quick
calculation shows that at this operating point only 25% of the lateral tire-force is translated
into the longitudinal vehicle direction, see Figure 11. For maximum brake performance the tire
lateral force needs to be completely saturated.
Figure 11 shows the difference between the Pacejka and the piecewise linear tire
characteristic. Multiplying these with the sine of the steering angle, according Equation 8, the
difference is marginal. For cases where the slip angle of the two front wheels is large, it is
possible to use only the saturated part of the piecewise linear function, which is independent
of the slip angle. For the rear wheel it is possible to use a linear relation assuming that the slip
angle remains small.
1
Force (N)
0.8
0.6
0.4
Pacejka
0.2
sinδ ⋅ Piecewise
Piecewise
sinδ ⋅ Pacejka
0
0
10
20
30
40
50
Slip angle (deg)
60
70
80
90
Figure 11 Pacejka versus piecewise linear tire model for longitudinal force
11
2.4.2
Asymmetric toe
Another strategy to be able to brake and steer at the same time is to turn one wheel to its
maximum angle, for the braking force, and use the other for directional changes. The best
orientations would be 90 degrees for the braking wheel and a small angle to correct for lateral
vehicle forces on the other side.
V
V
δ Left
α Left
M+
δ Right
α Right
FLatTire
FLatTire
x1
1
2 1
t
Figure 12 Asymmetric toe
Downside of this method is that only one wheel is braking, which means less performance.
Advantage is that lateral control remains functional.
2.4.3
Braking performance
Figure 13 shows the longitudinal vehicle force over the full range of left and right wheel. The
largest forces are generated when both wheels are at the largest combined steering angles.
Figure 13 Braking force over full steering range
This plot is made with the following values for the tire characteristic of Equation 4.
Coefficient
b
c
d
Value
8 [-]
1.4 [-]
755 [N]
Table 1 Simplified Pacejka coefficients
12
2.5
Inverted steering
The different brake-by-steer cases have their own braking performance, but the lateral forces
are also influenced by these new wheel configurations.
2.5.1
Lateral and longitudinal vehicle force contributions
Figure 14 explains what happens with the lateral vehicle force during a brake-by-steer action
with a symmetric toe angle of 50 degrees while driving straight. If toe-in is applied point “A” is
the left wheel and point “B” the right. At point “1” the lateral vehicle forces are in balance,
there is no lateral movement. When a right-hand turn is initiated the left wheel will move to
“A2” en the right to “B2”. The sum of the lateral forces now points to the left! Steering has
become inverted when looking at the lateral forces. This applies to both toe-in and toe-out.
1000
800
C1
A1
600
A2
Lateral force (N)
400
200
0
-200
-400
B1
-600
B2
-800
-1000
-80
-60
-40
-20
0
20
Slip angle (deg)
40
60
80
Figure 14 Inverted Steering for toe in, lateral vehicle force
Taking the longitudinal forces into account shows how toe-in is different from toe-out. The
same effect as described in section 2.3.1 plays an important role. When applying toe-in the
lateral tire force is partly directed into the longitudinal vehicle direction. The forces of left and
right wheel contribute to an overall vehicle momentum. In toe-out the momentum behaves like
the driver requests, for toe-in the effect is inverted.
2.5.2
Behavior with linear tire model
For the following analysis it is assumed that the initial vehicle heading is straight ahead. The
advantage is that the steering angle is equal to the slip angle and this also implies that the
contribution of the rear tire can be neglected as there is no sideways motion. Another
simplification is the usage of a linear tire model. This can not describe large slip angle
behavior, but makes it easier to understand the responsible parts of the overall momentum.
Equation 9 is build up out of the longitudinal part, described by the sinus and the lateral part,
described by the cosine part.
ΣM vehicle = ( −Cδ L sin (δ L ) + Cδ R sin (δ R ) ) ⋅ 12 LTrack +
( Cδ
L
cos (δ L ) + Cδ R cos (δ R ) ) ⋅ x1
Equation 10
Figure 15 shows the effect over the complete steering range for the longitudinal and lateral
vehicle forces. The top left part describes toe-out, the bottom right toe-in. The colors only
indicate to which direction the front of the vehicles tends to go. There are no actual numbers
assigned, as they make no sense using the linear tire model.
13
The longitudinal force contributes the most if the wheel angle is large, dictated by the sine
function and the linear increasing amplitude. The region where both angles are equal in size
and equal, or opposite, in sign does not contribute to the overall vehicle momentum, indicated
with the dashed line.
The cosine function in the lateral part of Equation 10 is large at low angles but the amplitude
at a large angle. The overall lateral vehicle force is the biggest if the steering angles are
equal in size and sign, as they both work in the same direction. This describes conventional
steering. If the angles are their exact opposites the vehicle remains on a straight line. This is
the neutral line from the top left to bottom right in Figure 15. Two other neutral regions can be
defined where the lateral forces cancel each other out. This is explained by point “C1” and
“B1” in Figure 14. Beyond these lines Figure 15 shows that the lateral vehicle forces react
inverted, for both toe-in and –out.
Longitudinal
Lateral
Figure 15 Momentum contribution from longitudinal and lateral vehicle forces, linear tire
model
Adding the two effects results in Figure 16. it shows that the inverted region is now only seen
in the toe-in region. In the far toe-out region the longitudinal parts of each wheel are equal, a
change in steering angle has a direct effect on the lateral vehicle forces which results in
inverted behavior.
Figure 16 Resultant moment linear tire model
14
2.5.3
Behavior with non-linear tire model
A more realistic behavior is displayed in graph Figure 18. This graph is constructed with the
non-linear tire model from Equation 4 and Equation 9. The lateral tire force will now saturate
which makes the amplitudes of the sine functions in Equation 10 stop increasing and even
decrease for large angles. This means that the longitudinal part has less effect on the overall
momentum.
This shows directly in the longitudinal part of Figure 17 compared to Figure 15.
Longitudinal
Lateral
Figure 17 Momentum contribution, longitudinal and lateral vehicle forces, non-linear tire
model
Adding these two effects results in Figure 18. The neutral regions are again indicated with
dotted lines. Differences are the sharp edges along the lines of δ L , δ L = 0 . The lateral tire
force is now at its maximum at low slip angles even as the conversion to lateral vehicle force.
Any changes in low slip angle region will cause high changes in lateral vehicle force. The
inverted steering range for the toe-in configuration still remains.
Most important difference is the region for toe-out at the top left side. It starts with a small
range where steering is still possible, but after the lateral tire force saturates, the gain,
between steering angle and lateral vehicle force, drops drastically. At large angles the
steering becomes inverted, but with a low sensitivity.
Figure 18 Resultant moment non-linear tire model
15
16
3
Implementation on a Go-Kart
This chapter describes how the brake-by-steer system, with independent actuated wheels, is
implemented in the go-kart. This vehicle will be the test setup to verify the brake-by-steer
concept. It starts with describing the original configuration as the point of departure for the
design. After this, section 3.2 describes the new functional requirements of the steering
system and needed system performance. Section 3.3 will deal with the actuation concepts
where motor choice and transmission design are defined. Section 3.4 looks closer into
controlling the position of the wheels and steering wheel. Section 3.5 describes the sensor
systems for measuring the vehicle state and describes the electrical layout. This controller
hard- and software is described in section 3.6. Photos of the final result of the design are
shown in Appendix E.
3.1
Go-kart introduction
The go-kart that is used for this project is a standard “Sodi GT2” from Sodikart [11]. In general
a kart is a miniaturized version of a car. Specific characteristics of a kart should however be
kept in mind as they differ from passenger cars.
The wheels of the kart are not separately suspended. The flat tube frame of the kart acts as
the suspension by bending and twisting on variable axle load. Other than in conventional
vehicles not all four wheels are always kept on the ground as the deflection of the frame is
very limited.
The fixed rear axle implies that the kart has bad cornering behaviour [13]. This is partly solved
by the effect the kingpin angles introduce [14][15]. The kingpin makes angles in both the Zand Y-plane, kingpin inclination and caster angle respectively, see also section 2.3.3 and
Figure 20. Due to these angles the frame is lifted upwards where the wheel is turned inwards
and visa versa. The overall roll of the front of the kart and the limited frame deflection
decreases the vertical load on the inner rear wheel which decreases the effect of the fixed
rear axle.
The driver can influence this effect by leaning sideways in a corner. His mass makes up
approximately one third of the total mass. In the relative small kart this has a large
contribution to the vehicle behaviour, but is very hard to incorporate in a model and remains
an uncertainty.
Figure 19 shows an impression of the go-kart and the used vehicle coordinate system and
views used in this report. Appendix A shows the detailed dimensions of the go-kart.
Top View
Side View
Y
Pitch
Roll
Rear View
Yaw
X
Z
Figure 19 General impression of the go-kart
17
3.1.1
Steering system
Figure 20 shows the components of the original steering system. The rotational motion of the
steering shaft is translated via the steering rods to the stub-axle on which the wheels are
attached. This construction is limits the maximum steering angle by the dimensions of the
steering shaft bracket. By decoupling the steering rods this maximum can be increased until
the tires hit the tube frame. The steering shaft bracket provides the Ackermann effect by
applying non-straight angles.
Ackermann angle
King pin
inclination
Caster
angle
Steering shaft
bracket
Figure 20 Steering system details
3.2
Steering system performance and design requirements
This section sets the specifications for the steer-by-wire system with independently actuated
wheels. The steer-by-wire system should provide similar steering as conventional and provide
additional functionality to actuate the wheels independently on driver request.
3.2.1
Steering wheel actuation design requirements
The desired functionality of the steering wheel part is to measure the steering angle of the
steering wheel as a set point for both wheels. Next to this conventional setting, it should be
possible to create additional angle data for each individual wheel to steer them independently.
The second function is to provide a force feedback to the driver to improve drivability [31][38].
The actuator must also indicate the end-stop by an increased feedback force when the
steering wheel reaches its maximum angle. From a safety standpoint of view it is important
that the steering wheel can still rotate, even if there is no power provided to it. And when, in
an error state, the steering wheel actuator counteracts the driver’s intentions.
3.2.2
Wheel actuation design requirements
The main function of the wheel actuation systems is to let the wheels follow the desired set
point created by the steering wheel system. Each wheel has to be actuated independently.
The position data of each wheel is needed to control the system and can be used to provide a
force feedback sense to the driver.
The brake-by-steer concept requires large steering angles. The construction of the kart limits
the maximum wheel angle. This means that the new design needs to provide a construction
to increase the steering angle range.
3.2.3
Measured system performance
The specific performance of the two subsystems is measured in a test setup, described in
detail in appendix B. Table 2 shows the results of how the original kart performs.
18
Item
Maximum range
Measured at
Value
Limited by
Steering wheel
Left wheel
Left wheel
+/-85º
+25, -32º
+35, -55º
Steering wheel typical
Steering wheel extreme
Wheel typical
Wheel extreme
160 º/s
600 º/s
80 º/s
300 º/s
Driver
Steering wheel
1 Hz
Driver
Nominal
Peak
8 Nm
50 Nm
Max
5 Nm
Driver
Front wheels
1200 N
Tire grip
Steering linkage
Tire to frame contact
Turning rate
Steering frequency
Steering torque
Steering wheel torque
Braking force
Table 2 Steering system performance original kart
The goal of the new design is to perform similar to the typical behavior of the original kart. The
required torques have to be extrapolated as the mass of the vehicle will increase by the
added steer-by-wire components.
3.3
Electro-Mechanical modifications
This section describes the electro-mechanical design for the new steering system. It consists
of an actuator-sensor combination and the mechanical transmission from the actuator to the
stub-axle or steering wheel. The guidelines presented in [1] and [2] are used for the motor
selection.
The best design concept is chosen from different drive concepts and actuator types and
worked out in detail. Factors that decide the best design are speed, torque and measuring
requirements, consumed space, suitable transmission and robustness, avoiding irreversible
changes to the kart, time to design, time to implement, costs and fault tolerance. The
following subsections look into the steering wheel design followed by the design for the wheel
actuation.
3.3.1
Steering wheel
3.3.1.1 Sensing and actuation
The angle of the steering shaft is measured with a magnetic absolute encoder ring. This is
mounted directly on the steering shaft which excludes play in the system. Figure 21 shows
the encoder ring when extracted from its encoder house where the actual sensor is mounted
in. The encoder measures the absolute position which avoids calibrating the neutral position
of the steering wheel at each system start.
The feedback force is provided by a brushed DC-motor with gear mounted to it, which is
connected to the steering shaft with a belt transmission. The available motor-gear
combination, at the manufacturer, exceeds the maximal desired torque at the steering wheel.
See Appendix A for the used materials. By limiting the current output of the motor controller,
in the hardware, this torque is limited within safe limits. Figure 22 shows that the operating
point is well within the motor safe operating area.
Both subsystems are mounted on the same support block and replace the original steering
shaft guiding. This makes the design very compact and does not make and irreversible
changes to the original steering system.
19
Steering
wheel
Bearing
houses
Toe handles
Gear
Transmission belt
DC motor
Encoder
Steering
shaft
Support block
Encoder housing
Gas tank
Encoder ring
Figure 21 Steering wheel actuation implementation
Figure 22 shows that the maximum steering rate from Table 2, with a gear ratio of 1:113 this
is approximately 11.000 rpm, does not lie within the safe operating area. The limited allowed
speed is a trade-off in the design.
Continues
operation
Short
operation
term
Driver safety operation area
Figure 22 Motor operating area, steering wheel motor
The belt transmission was quick to design and implement, but has a design flaw. The limited
allowed axial load on the gear exit-shaft, limits the tension in the belt and therefore the
possible transmitted torque is also limited. The additional bearing in the support bracket did
not relief this load enough. A better design would be to support the pulley on the gear shaft on
both sides.
3.3.1.2 Toe lever and user interface
The independent actuation of each wheel is provided by two “toe-wings”. These are two
levers attached to the steering wheel and can be activated while the driver holds the steering
wheel, see Figure 23. The angle of the levers is measured with a potentiometer. With
20
switches on the steering wheel the actuation setting can change from symmetric toe-in and
toe-out, to asymmetric toe of each wheel independently. Other switches and indicators
provide functionality to control the system states, see section 3.6.2 for further details.
Toe wings
EMO button
Switches
Indication LED’s
Figure 23 Steering wheel interfaces
An emergency off button is mounted in the middle of the steering wheel. This will shut down
the complete system when pushed. This is the only safety related part of the steering design.
It is a deliberate choice not to implement any redundant hardware in the system. This makes
the system complex and time to design and implement long. The created risks are accepted.
3.3.2
Wheel actuation
Each wheel has its own individual actuator which is mounted directly to the steering axis, as
shown in Figure 24 and Figure 25. The required speed and torque have a one-to-one
relationship to the motor and gear specifications and makes controlling the motor position
straight-forward. The design has very little moving parts which makes the design robust. And
the motors and transmission are located in a free volume in the kart and to not claim already
taken space. See Appendix A for the used materials.
Additional steering range is created by inserting extension brackets in the brackets that hold
the stub-axle in the original kart, see Figure 24 and Figure 25. This provides design freedom
for the motor–stub-axle interface as it can be designed from scratch and does not interfere
with the original structure of the kart. The extension bracket assembly consists of a number of
plates with filler rings that is bolted to the kart frame. In this way the original orientation of the
steering angle, caster angle and kingpin inclination, is maintained. The front of the kart is
lowered slightly, but has no negative side effect.
21
Encoder
Wheel
DC Motor
Motor-stub
interface
Gear
Extension brackets
Support frame
Bearing
Stub axle
Bearing
Kart frame
Extension brackets
Outwards displacement 40 mm
Angle sensor
Figure 24 Wheel actuation exploded view (front view)
Encoder
DC Motor
Wheel axle
Gear
Motor-stub
interface
Support
frame
Figure 25 Wheel actuation implementation
Figure 26 shows the front view of the actuation system. Each actuator is in line with the king
pin and therefore inclined inside and backwards. An additional absolute angle sensor is
mounted to the bottom of the king pin.
22
Batteries
Actuator
Angle sensor
Figure 26 Front view wheel actuation
There is no safety or fault tolerance build into the wheel system to avoid complexity. It has
been considered to apply a third motor in between the two stub axles where the steering rods
were originally located, as shown in Figure 27. This system, based on the Active toe
adjustment apparatus [9] design, is able to rotate each wheel independent and one of the
motors may fail, without losing functionality.
Figure 27 Fail safe steering design (top view)
Next to available space and applicable linear actuator, a control system, fault detection and
intervention program are required to implement this configuration. This is beyond the initial
goal and will exceed the available time to design.
The safe operating area for the applied motor-gear combination is shown in Figure 28. The
operation point lies within the continues operation area. The short term operating area is
limited by the allowed temperature of the windings. The overloud duration for the chosen
motor is up to one minute in an ambient temperature of 25º C [12]. The steering-by-brake
system will operate in open air, T < 25º C, and under driving wind conditions, therefore the
temperature limit can be stretched.
23
Continues
operation
Short
operation
term
Figure 28 Motor operating area, wheel motors
This combination will not be able to deal with the extreme high peak loads from Table 2. with
a gear ratio of 1:100 this is approximately 6500 rpm. This is a design trade-off. Limiting factor
in the motor selection is the maximum 24 Volt that is supplied from two on board batteries.
More power full, motors require a higher voltage.
3.4
Control algorithm
The control strategy is split up into two parts. The local control algorithm lets the steering
wheel and wheels follow their given set point. The global control algorithm ties the two local
loops together, where the position output of the first is the set point for the second.
3.4.1
Local control loop
3.4.1.1 Wheel actuation
The feedback loop for the wheel positioning is shown in Figure 29. The controller acts on the
position error signal to generate a torque on the wheel. This is added to the sum of all other
external forces, described in section 2.3.3. The vehicle state is however, not implemented in
the real time controller. Advantage would be that the lateral tire forces and changing vertical
axis loads can be estimated and anticipated for, but this would require a sophisticated vehicle
model, which is not created to that extend for the modified go-kart. The applied controller is
modelled as a straight forward closed loop PD control system acting on a second order plant.
The dashed part enclosed by the blue rectangle in Figure 29 Control system representation is
not implemented.
Speed
Steering
set point
Vehicle
angle
+
Controller
Steering
angle
+
+
Wheel
−
Figure 29 Control system representation
The controller parameters are partly based on the theoretical estimated forces coming from
subsection 2.3.3. The actual system is identified with a chirp signal on the actuator. With the
24
wheels on the ground the system shows to be higher than second order. The high frequency
part of the system is not successfully identified.
The input of this system comes from the measured steering signal of the steering wheel. The
measurement kart showed that typical steering behaviour has a steering frequency around 1
Hz. This means that any signal much higher than 1 Hz does not come from the driver and
does not need to be inserted in to the controller.
3.4.1.2 Hand wheel actuation
The hand wheel actuation is implemented as a passive spring-mass-damper system as
shown in Figure 30 Steering wheel representation. A larger displacement from the initial
centre position results in a higher feedback feel. The stiffness of this system, k, is speed
dependent to mimic the effect of increasing lateral tire force at higher speeds. The stiffness
and damping factor for this system are experimentally tuned to a “good” steering feel.
Tactuator
γ steer angle
k (V )
J tot
d
Tdriver
Figure 30 Steering wheel representation
The steering angle of the steering wheel is limited by a simulated end stop. The stiffness of
the feedback force increases stepwise at the limit angle. This is an indication for the driver
that the end of the steering range has been reached.
3.4.2
Global control loop
It was initially indented to create a haptic feedback loop. In this loop, schematic shown in
Figure 31, the displacement made by the driver on the steering wheel is fed to the wheel
actuator. The wheel interacts with the environment, road, and these forces are send back to
the driver. With this feedback feel the driver has additional and essential vehicle information.
Driver
Steering
wheel
Communication
channels
Wheels
Environ
ment
Figure 31 Block scheme of haptic control loop
In conventional vehicles the feedback force reflects the lateral tire forces of the front wheels
and indirect together with vehicle speed the heading of the vehicle. The lateral tire forces in
the brake-by-steer configuration do not have this same relation for steering wheel angle and
vehicle heading. A vehicle state estimator could calculate the vehicle heading on the fly and
reproduce the expected feedback force, but this is not implemented in the system.
The driver needs to act on the unconventional vehicle behaviour, for example the inverted
steering effect.
3.5
Sensor systems and electrical layout
This section describes the complete electrical and software design for the steer-by-wire
system. It consists of a real-time controller that processes and stores the data of the sensors
in the kart and executes the control algorithms. The sensors need to measure position data
25
for the control loops and vehicle parameters to check vehicle behaviour under brake-by-steer
circumstances.
Factors that decide the best design are data processing capacity, number of I/O channels,
sensor accuracy, time to design, time to implement, costs and fault tolerance.
3.5.1
Sensors
The most important sensors are listed here. Table 3 in appendix C displays all applied
sensors.
Steering angle
The steering wheel angle is measured with an absolute magnetic encoder. It is mounted
directly on the steering axis. This sensor is part of a combined sensing bearing unit.
Toe angles
The additional data for the brake-by-steer actuation is implemented in the toe wings. These
levers are mounted on the steering wheel and are connected to a potentiometer. The toe
method can change, by switches on the steering wheel, from toe-in and toe-out, toe left or
right wheel in or toe left or right wheel out.
Wheel angle relative
The position of each wheel is measured with the encoder that is mounted on the back of the
actuator. A design concession made here is that the play the gearbox can not be
compensated.
Wheel angle absolute
At system start the relative position data from the encoder is calibrated with the predefined
absolute position. A potentiometer is mounted to the bottom of the kingpin and measures
directly the steering angle of each wheel.
Velocity sensor
The velocity of the kart is measured with an optical sensor. It scans the road passing
underneath and calculates the absolute velocity in longitudinal vehicle velocity. The lateral
velocity of the vehicle is not measured.
Accelerometers
Two accelerometers measure the lateral and longitudinal accelerations. The sensors need to
be mechanically isolated from the frame to prevent the sensors to saturate on the heavy
frame vibration form the engine. The final solution for this was to attach them to the
framework supporting the two batteries
A yaw rate sensor or digital compass that provides the heading information of the vehicle
would be of great value to make an estimate of the complete vehicle state. Yih added a GPS
system to his test vehicle [18]. These sensors, however, are very expensive and not within
budget for this project.
3.5.2
Electrical layout
All sensors receive their power supply from a DC/DC converter. This reduces the 24 Volt from
the double battery pack back to 12 Volt. The motor controllers and the CompactRIO are direct
connected to the 24 Volts. Figure 32 shows the layout of the electrical system of the kart.
Figure 47 in Appendix C shows the detailed connection of each sensor.
26
Figure 32 Electrical layout
27
F1: 40A
DO3 NI 9474
L2
Power Supply
24 V
HeadSwitch
L1
L3
F3: 6.3A
1
2
3
4
5
1
2
3
4
5
A,B,I 12
Encoder
Gnd
Ch I
Ch A
Vcc
Ch B
A,B,I 11
Encoder
Gnd
Ch I
Ch A
Vcc
Ch B
dc - dc Converter
24 - 12 V
+ INput 24V
Gate IN
- INput
AO3 NI9263
COM NI9263
Pin 12
Pin 8
Pin 6
Pin 5
Pin 7
Dsub 1
Pin 12
Pin 3
Pin 1
Pin 4
Pin 2
- OUT
- Sense
+ Sense
+ OUT
Vcc
S18
Gnd
F9: 8A
Vcc
S20
S21
Gnd
Omega2
DI1 NI9423
DatronSwitch
Vcc
S19
Gnd
Omega12
AI14 NI9205
Vcc
S8
Gnd
tau12
AI6 NI9205
Vcc
S3
Gnd
delta12
AI1 NI9205
Vcc
Gnd
Gnd
S11
DI2 NI9423
DI3 NI9423
AI9 NI9205
AI5 NI9205
AI7 NI9205
AI2 NI9205
DCDC indicator
AI8 NI9205
g_lon
Gnd 1
(S16) Vref 2
Vcc 3
S10 4
Shield 5
DI0 NI9423
1
2
3
4
5
Vcc
S7
Gnd
tau11
Vcc
S2
Gnd
delta11
AI0 NI9205
Gnd
(S15)Vref
Vcc
S9
Shield
g_lat
Omega11
NI9411
Vcc
S1
Gnd
alpha
Power Supply
12 V
Vcheck12 S17
AI10 NI9205
Signal
1
2
3
4
1
2
3
4
5
1
2
3
4
Monitor n 7
(S6) Monitor I 8
(14) Ready 9
Gnd 12
+ Set Value
- Set value
Enable
Gnd
1
2
3
4
5
(S5) Monitor I 8
(S13) Ready 9
Gnd 12
+ Set Value
- Set value
Enable
Gnd
Motor Controller 20
Power
+ Motor
- Motor
Ground Safety Earth
+Vcc 24 VDC
Power Ground
Signal
1
2
3
4
1
2
3
4
5
(S4) Monitor I 8
(S12) Ready 9
Gnd 12
+ Set Value
- Set Value
Enable
Gnd
Motor Controller 12
Power
+ Motor
- Motor
Ground Safety Earth
+Vcc 24 VDC
Power Ground
Signal
Motor Controller 11
Power
+ Motor
- Motor
Ground Safety Earth
+Vcc 24 VDC
Power Ground
Diode
AI18 NI9205
AI5 NI9205
AI13 NI9205
AO2 NI9263
COM NI9263
DO2 NI9474
F6: 10A
Motor20
AI4 NI9205
AI12 NI9205
AO1 NI9263
COM NI9263
DO1 NI9474
F5: 20A
Motor12
AI3 NI9205
AI11 NI9205
AO0 NI9263
COM NI9263
DO0 NI9474
F4: 20A
Motor11
AI19 NI9205
Relay 1
Emergency Switch
MC Switch On/Off
{
Dsub3
F8: 6.3A
SP3 MC11
SP3 MC12
SP3 MC20
Gate IN DCDC
LED 1
LED 2
State Indicator LED
nc
SP1 MC11
SP2 MC11
SP1 MC12
SP2 MC12
SP1 MC20
SP2 MC20
P1 CM
P2 CM
S18 Omega11
S19 Omega12
S20 Omega2A
S21 Omega2B
Switch Asym toe
Switch Sym toe
Switch Invert steer
Switch Asym out
F7: 0.35A
A,B,I 12
A,B,I 11
Dsub 1
S1 alpha
S2 delta11
S3 delta12
S4 SP8 MC11
S5 SP8 MC12
S6 SP8 MC20
S7 tau11
S8 tau12
S9 g_lat
S10 g_lon
S11 Datron abs V
S12 SP9 MC11
S13 SP9 MC12
S14 SP9 MC20
S15 Vref
Log file nr.
S17 Vcheck12
Switch Feedback
SP7 MC20
Power Check
Switch Logging
Switch Start button
Free AI
Log file nr.
Switch Off switch
DI0
DI1
DI2
DI3
DI4
DI5
DI6
DI7
NC.
COM
AO0
COM
AO1
COM
AO2
COM
AO3
COM
0
1
2
3
4
5
6
7
8
9
DO0
DO1
DO2
DO3
DO4
DO5
DO6
DO7
Vsup
COM
Digital Output Module
NI cRIO-9474
0
1
2
3
4
5
6
7
Analogue Output Module
NI 9263
0
1
2
3
4
5
6
7
8
9
Digital Input Module
NI cRIO-9423
0 Vsup
1 COM
1 DI0a
2 DI1a
3 DI2a
4 Supply +5 Vout
5 Supply +5 Vout
6 DI3a
7 DI4a
8 DI5a
9 DI0b
10 DI1b
11 DI2b
12 Common COM
13 DI3d
14 DI4b
15 DI5b
Digital input Module TTL
NI cRIO-9411
Analogue Input Module
NI 9205
AI0
AI1
AI2
AI3
AI4
AI5
AI6
AI7
AI8
AI9
AI10
AI11
AI12
AI13
AI14
AI15
AI16
AI17
AI18
AI19
AI20
AI21
AI22 & AI23
AI24-AI29, AI31
AI30
AIS
COM
V1
C
V2
C
Controller
NI cRIO-9004
Externel Power
12V
F11: 0.75A
F3: 0.7A
Secundary Power Switch
3.6
Control hardware and software
This section describes the functionality of each piece of software running on the different
components of the hardware controller. The section is split up in a short description of the
CompactRIO, followed by the software description running on the controller, the FPGA and
the offline PC. The in and output signals are in the software domain.
3.6.1
CompactRIO hardware
The CompactRIO from National Instruments [37] is used as the real-time stand-alone
controller. It is programmed with NI Labview. It is build up with a real-time processor and a
reconfigurable FPGA. It is possible to use different types of I/O cards, which can be inserted
in the I/O bay of the FPGA chassis. For the project a 30 channel analog input card, a six
channel digital TTL input card, a four channel analog output card, a nine channel digital in and
a nine channel digital output card are used. The configuration used is displayed in Figure 33.
Appendix A shows the detailed information of the used materials.
Mains
Analog in
Digital in
Encoder in
Digital out
Analog out
Ethernet
link
Controller
Chassis with FPGA
Figure 33 CompactRIO
The I/O modules are directly connected to the FPGA without a shared bus. The FPGA is also
connected to the controller with a local PCI bus. The variables defined on the FPGA are
available for the controller for manipulation. The program running on the controller and the
one running on the FPGA are downloaded from a PC with the ethernet link.
3.6.2
Controller software
The controller is configured as host of the CompactRIO. On start-up it will open the
connection towards the FPGA for data transfer. Each variable defined in the FPGA code can
be imported to the controller domain and vice versa.
The other tasks of the controller are executing the “state-machine”, execute the data logging
program and performing motion control calculations.
3.6.2.1 State machine
The top level of the software is controlled with a state-machine. During start-up, various
functions are enabled and configured. This is graphically displayed in Figure 34. The main
sequence is described as follows, starting from the green balloon on the top left;
- At power on the steer-by-wire system will be in an “idle” state. Only the CompactRIO
controller is powered and starts running this state-machine program. Herein in
activates the connection towards the FPGA, which makes it possible to use actual
I/O.
28
-
-
-
-
On a push of the start button the electrical system will “Start-up”. The motor controller
are enabled and the DC/DC converter for sensor power supply is enabled.
In the “Check all” state the previous step is checked. All power supplies are checked
and all power amplifiers need to report “status OK”.
In the “Init / Reset” state the system is functional, but not calibrated. The wheel
angles are (re-) calibrated to their zero position. A separate set of controller
parameters, with large integrator gains, moves the wheels to the stored wheel
position with the absolute sensor and sets the zero for the encoder measurements. If
needed the positions can manually be adjusted with the toe levers. It is also possible
to reset the zero position of the steering wheel in this step.
In the “Ready” state all systems are active and calibrated. The software switches to
the operational controller parameter set. Only the encoder data is now used for the
position measurement of the wheels.
During the complete walkthrough of all states and in the final “Ready” state, all critical
functions are monitored. If for example power supplies or motor controllers behave
out of normal, the system will go to an “Error” state. The driver will be notified by the
indication LED’s on the steering wheel. The driver can choose to overrule the error, or
go back to the idle state.
The driver has the opportunity to stop and recalibrate the wheels in the “Ready” state,
via the “Stop” state. In this state the electrical application are shut down, but
calibrated wheel positions are still saved. From this stop state it is also possible to go
to the idle state and shut down the complete system.
Figure 34 State machine of the software structure
3.6.2.2 Data logging
The data packages coming from the FPGA is locally written in the controller on operator
request. The data is saved under a test number which is set in the user interface.
29
3.6.2.3 Motion control
Figure 35 show the control scheme from the steering wheel inputs, to the wheel position
output. The setpoints for each wheel are calculated from the steering wheel angle and the
individual toe lever angles depending on the selected toe mode. In the FPGA these analogue
signals go through a low-pass filter. The steering angle is reformatted to wheel angles and is
corrected with an Ackermann angle. The angle is limited to prevent set-points out of the wheel
angle range. It is also possible to tie an analogue input or software defined variable to the setpoint input of the controller via a switch, which is convenient for analyses purposes.
The controller is a straightforward PD controller with limiting output range to prevent over
current on the motor and amplifier. The wheel positions are calculated in the FPGA and the
value is passed through to the controller where the controller.
Mechanical / electrical hardware
I/O boards FPGA
Controller
Toe lever Left
Sensor
I/O
Gain
Toe lever Right
Sensor
I/O
Gain
+
Sensor
I/O
Position
calculation
I/O
Gain
Ackermann
correction
Switch
Steering
wheel
SW input
I/O boards
+
Controller
I/O
Amplifier
Motor
-
Controller
Position
calculation
I/O
FPGA
I/O boards
Wheel
angle
Sensor
Mechanical / electrical hardware
Figure 35 control scheme and set point selection
3.6.3
FPGA software
The FPGA is used for basic signal import and export. Initially the control loops were built in
the FPGA. But during development of the code this was unpractical as each new feature
requires a full time consuming rebuild of the FPGA code. The following functions with in and
output are executed in the FPGA.
3.6.3.1 Clock
Generate basic clock, used throughout the program to synchronize different functionality.
Inputs
-
Funtion
Clock
30
Outputs
4 kHz Timing Stamp
3.6.3.2 Read in analog input card
Read in all data coming from the analog input card. Each signal is stored as a 16-bit integer.
Due to the lack of digital inputs, some logic digital signals, not timing critical, are fed to the
analog card. A trip hand made trip-level provides the digital behaviour.
Inputs
Timing Stamp
Funtion
Outputs
Read analog input
Steering angle
Wheel angle left
Wheel angle right
Motor current left
Motor current right
Motor current steering wheel
Toe handle angle left
Toe handle angle right
Motor speed steering wheel
Free analog input 1
Free analog input 2
Lateral acceleration
Longitudinal acceleration
Absolute velocity
Status motor controller left wheel
Status motor controller right wheel
Status motor controller steering wheel
Sensor reference voltage
CompactRIO temperature
Status on/off
Status force feedback
Status EMO
Status data logging
Status start button
Status 12 Volt supply
Logfile number
3.6.3.3 Read and process encoder signal
The ‘A’ and ‘B’ signal from the encoders are read in by a dedicated digital TTL encoder card.
The pulses from the encoder are counted and processed to position data. The motor position
data needs a 32-bits integer to for storage.
Inputs
Time Stamp
Funtion
Read Encoder signal
Outputs
Rear wheel speed
Front left wheel speed
Front right wheel speed
Left wheel motor position
Right wheel motor position
3.6.3.4 Read digital inputs
The digital input signals exist of the status of the toe selection switches on the steering wheel.
Inputs
Time Stamp
Funtion
Read Digital input
31
Outputs
Status asymetric toe switch
Status symetric toe switch
Status inverted steering switch
Status toe-in / toe-out switch
3.6.3.5 Write digital outputs
The digital outputs are used to enable electrical components in the system. the second
function is to control the LED’s on the steering wheel to provide the driver with the needed
feedback on the system state.
Inputs
Funtion
Time Stamp
Enable motor controller left
wheel
Enable motor controller right
wheel
Enable
motor
controller
steering wheel
Enable dc/dc converter
Enable LED 1
Enable LED 2
Enable LED 3
Free digital out
Write digital
output
Outputs
-
3.6.3.6 Write analog outputs
The calculated setpoints for the motor controller are fed directly to the analog output card.
The fourth output is connected to a analog Volt meter. This display gives a speed indication to
the driver while driving.
Inputs
Timestamp
Setpoint left wheel controller
Setpoint right wheel controller
Setpoint
steering
wheel
controller
Velocity out
Funtion
Write Analog out
Outputs
-
3.6.3.7 Wheel position calibration
This calibration loop provides the functionality to reset the home position of the steering
wheel. This angle is measured with an absolute sensor, which means this is only required
after dis- and reassembling the steering unit.
The second calibration is required each time the system is has been shut down. The control
of the wheel position is done with the relative encoder signals. These are zeroed with the
stored absolute angle measurement of the potentiometers. It is possible for the driver to
adjust the angle with the two toe handles to vary the offset or correct the initial angle.
Inputs
Steering wheel angle
Left wheel angle
Right wheel angle
Start reset signal
Left wheel home angle analog
Right wheel home angle
analog
Funtion
Position calibration
32
Outputs
Steering wheel angle ofsett
Left wheel home angle
Right wheel home angle
3.6.3.8 Toe mode selection and execution
The two levers on the steering wheel are used to steer the wheel independent from each
other. The different modes; toe in, toe out, symmetric or asymmetric, are selected with
switches on the steering wheel. This function calculates the toe angle that is superimposed on
the steering angle set-point from the steering wheel. After each shutdown, or manual reset,
the home position of the handles is stored.
Inputs
Toe handle angle left
Toe handle angle right
Status toe-in / toe-out switch
Reset toe handle angles
Funtion
Position calibration
Outputs
Steering wheel angle ofsett
Left wheel home angle
Right wheel home angle
Toe angle setpoint left
Toe angle setpoint right
Toe mode status
Toe handle offset angle left
Toe handle offset angle right
3.6.3.9 System monitoring
During operation the status of the motion controller and the level of the main 24 Volt supply
are monitored. The maximum duration of an over current of the motor / amplifier is also
monitored.
Inputs
Time stamp
Enable motor controller left
wheel
Enable motor controller right
wheel
Enable motor controller steering
wheel
Setpoint left wheel controller
Setpoint right wheel controller
Setpoint
steering
wheel
controller
Status motor controller left
wheel
Status motor controller right
wheel
Status motor controller steering
wheel
Max overcurrent dureation
Status 24 Volt supply
Funtion
System monitoring
33
Outputs
Max motor current exceeded signal
Status motor controller left wheel
Status motor controller right wheel
Status motor controller steering
wheel
3.6.3.10
Data logging
Some signals are combined into one big array. This data is transferred by Direct Memory
Access to onboard memory of the controller. There are 18 variables of 16 bit arrays and 3
arrays of each 32 bits, being the time stamp and two wheel positions.
Inputs
Funtion
Timing Stamp
Steering angle
Wheel angle left
Wheel angle right
Motor current left
Motor current right
Motor current steering wheel
Toe handle angle left
Toe handle angle right
Lateral acceleration
Longitudinal acceleration
Absolute velocity
Sensor reference voltage
Logfile number
DMA Cycle time
ADC Cycle time
Rear wheel speed
Front left wheel speed
Front right wheel speed
Left wheel motor position
Right wheel motor position
3.6.4
Data logging
Outputs
-
Offline PC software
The offline PC is only used to retrieve the logging data which is stored on the controller. It
opens an FTP connection to the CompactRIO and gets the data file, unwrap it and stores it as
a comma separated file on a local directory.
34
4
4.1
Results
Test description
4.1.1
Test track
The tests are performed on the test track described by Figure 36. It consists of two rings
connected by a straight lane of 90 meters.
Figure 36 Test track
All braking tests are performed on the straight road of the test track.
4.1.2
Test cases
The following test cases generate the experimental data, to verify the design, measure real
braking performance and to get a better understanding of how the lateral stability is influenced
by the unconventional wheel setting.
Test set-up, design verification
1. Verify the steering system performance
Braking performance
2. What is the maximum measured braking performance
Run a series of test and get the highest value.
3. How does this relate to the original kart
compare this number with the maximum measured braking performance of the
conventional braking system. The changed mass and vertical axle load have to be
taken into account.
4. What is the performance over the full range?
What are unexpected results
Does it match the theory
Lateral behaviour
5. What happens to the lateral movement when toeing?
Is there a difference between toe in and toe out?
What happens when toeing asymmetric
Do expected phenomena occur (inverse steering)
4.2
Steering performance
This section describes how well the design performs in the go-kart.
35
4.2.1
System identification
The transfer function is derived from the gain part of the bode plot and displays the relation
between steering angle input and wheel position output of the closed loop system. Figure 37
only shows data from the left wheel.
Gain (dB)
50
Measured system
Identified system
0
-50
-100
0
10
1
2
10
Frequency (Hz)
10
Coherence
1
0.5
0
0
10
1
2
10
Frequency (Hz)
10
Figure 37 Frequency response of measured and identified system
4.2.2
Tracking error
Figure 38 shows how well the wheels follow the set points. The setpoint, in this case, is build
up out of the toe handle output with superimposed to that the steering angle position. This is
needed to keep the kart on track as the lateral behaviour becomes unpredictable.
60
Setpoint
Measured
Error
Steering angle
50
Angle (deg)
40
30
20
10
0
-10
0
1
2
3
4
5
Time (sec)
6
7
8
9
Figure 38 Steering angle behaviour on step input (toe in)
The set point rises in 0.15 seconds to its maximum value. After this event it takes 0.7 second
for the wheel to settle below an error smaller than one degree from the steady state error. The
steady state error is ~ 3 degrees, which comes down to an error of ~ 6%.
The steady state error can be eliminated by an improved integrator action or with better
system estimation in the feed forward part of the controller. An error this size is, however,
easy to compensate by the driver.
36
4.3
Brake-by-steering performance
4.3.1
Maximum measured braking performance
Figure 39 shows the deceleration profile when the kart performs a brake-by-steer action. In
this case the wheel positions are 50 and -60 degrees. The two red lines, solid and dashed,
2
represent the acceleration in m/s . The solid line is the derivative of the velocity signal and the
dashed the measured signal from the accelerometer. The delay in the accelerometer signal is
caused by the electronic filter applied in the measurement system. The very gentle
deceleration after the peak velocity is the rolling resistance and air drag of the kart.
10
Velocity
(m/s)
Acceleration (m/s 2)
Brake Force (kN)
8
6
(Various)
4
2
0
-2
-4
-6
0
1
2
3
4
Time (sec)
5
6
7
Figure 39 Braking performance brake-by-steer,
The maximum deceleration is approximately 5 m/s2. Taking the total moving mass in account
the braking force generated by the toed wheels is 1.3 kN. This is the maximum value in the
measurement series. Compared to the reference data measured with the conventional kart,
the deceleration is almost equal, see appendix B.
The difference between the two set ups is the increased vertical axle load. The steer-by-wire
kart is significant heavier on the front than its conventional counterpart. Taking this into
account shows the difference in maximum braking performance.
Fbrake 1300 N
=
= 0.90
Fz
1450 N z
F
1200 N
: brake =
= 1.35
Fz
889 N z
Brake-by-steer performance:
Equation 11
Reference performance
Equation 12
From this standpoint the brake-by-steer performance is 67% of the conventional maximum
braking performance when braking with two wheels.
Trying to compare this to a real car gives the following rough estimate. In passenger cars the
brake force distribution is about ⅔ to ⅓ for front and back respectively. This brings the braking
performance for the brake-by-steer concept, if it was applied on a car, to 50% of the
conventional braking system.
4.3.2
Estimated performance
Figure 40 displays a collection of brake performances. The effective toe angle is the
summation of both left and right absolute toe angle. Through the data point runs a red dashed
fitted and a solid blue estimated result.
37
0
Toe in
Toe out
One wheel
Theoreticle data
Fitted data
-0.2
Brake force (kN)
-0.4
-0.6
-0.8
-1
-1.2
-1.4
-1.6
0
20
40
60
80
100
120
Effective toe angle (deg)
140
160
180
Figure 40 Brake force data collection
The data points follow the expected theoretical trend. The main cause for differences is the
speed dependent factor which is not separated for the different points. Figure 39 shows that a
decreasing speed causes an increase in the deceleration. Another effect that explains the
variation is the tire and road condition which varies for the different measurements.
4.3.3
Lateral vehicle stability
Figure 41 shows the wheel angles belonging to the deceleration profile of Figure 39. This
figure shows that the path of the kart in not straight. A sudden lateral motion occurs, for which
the driver compensates with correctional steering.
60
Left Wheel
(deg)
Right Wheel (deg)
Steering angle (deg)
40
Lateral accel*10(m/s 2)
(Various)
20
0
-20
-40
-60
-80
0
1
2
3
4
Time (sec)
5
6
7
Figure 41 Braking performance, wheel positions
The theory predicted large ranges where steering would be inverted. The inverted steering did
occur during the tests but this phenomenon has not been successfully recorded. It appeared
that the region is much smaller than the theory tells. During the few seconds it takes to
decelerate to zero speed this specific wheel position has to be found and hold, and the
vehicle has to be controlled, while the steering switches between regular and inverted
steering. The engine of the kart does not have enough power to push through the brake force
of the front wheel to prolong the test period.
38
-0.06
-0.04
-0.04
-0.02
-0.02
0
Y [m]
Y [m]
Figure 42A shows the theoretical behavior for toe-in. The graph shows the driven path of the
vehicle in X- and Y-direction. The blue, red and green lines correspond to a symmetric toe
angle of 30, 40 and 50 degrees respectively. Each setting is plotted five times with a steering
angle increase of two degrees in positive, right, direction. Figure 42B shows the same for
symmetric toe-out and with 40, 50 and 60 degrees for the blue, red and green line.
0
0.02
0.02
0.04
0.04
0.06
0.06
0
0.2
0.4
0.6
0.8
1
0.08
1.2
X [m]
A: Toe-in
0
0.1
0.2
0.3
0.4
0.5
X [m]
0.6
0.7
B: Toe-out
Figure 42 Inverted steering paths
The smallest toe setting behaves normal, steering to the right results in a movement to the
right. The middle setting is the turning point to inverted steering. The vehicle responds very
little to a steering input. The largest toe angles result in inverted steering. The brake force
increases with increasing toe angles which results in decreased path length.
4.3.4
Asymmetric toe
The asymmetric toe variant has shown not be very successful during the experiments with the
go-kart.
If one wheel is turned outwards the vertical load on the tire increases and it gains more grip
than the wheel that points straightforward. The lateral force is too large to compensate for the
straight wheel. It is impossible to drive in a straight line with the steer-by-wire kart; it will
always make a turn. The kart reacts very aggressive on this steering maneuver. The rear
wheels loose grip making the kart uncontrollable.
The change of the vertical axle load is not implemented in the model. Therefore this effect
was not predicted.
The opposite of this effect happens when toeing in. Now the toed wheel has less grip than the
straight wheel which decreases the braking performance of the already reduced brake force.
39
0.8
40
5
5.1
Conclusions and recommendations
Brake-by-steer concept
The brake-by-steer concept has shown that it can be a back-up system for failing brakes.
Although the maximum performance is much lower compared to conventional braking, it may
be enough to stop the vehicle in an emergency situation.
The focus in this report is on braking while driving on a straight line. The best braking
performance is achieved with symmetric toe method. There is no difference between toe-in
and toe-out on the braking performance.
The difference between the two symmetric settings is on the lateral behavior when trying to
make a turn or make small steering corrections.
At toe in, steering becomes inverted for part of the steering range. This makes the steering
ratio change from its original setting to negative values as function of the toe-angle. The
control used algorithm does not compensate for this behavior which makes it challenging for
the driver to maintain control over the vehicle. The theory shows this effect and during the
tests this effect occurred, but it is not successfully captured in measurement data.
When toe-out is applied the vehicle reacts very aggressively to a steering input. This is
contrary to what the theory predicts. This is can be explained by the go-kart specific
suspension system of the front wheels. The kingpin angles together with the limited frame
deflection vary the vertical axle load of the steerable wheels. The inner wheel will have a
significantly higher load than the outer. This changes the saturation of the lateral tire force in
the tire characteristic such that the inner wheel generates higher lateral forces. While making
a turn the inner wheel is turned out the most and dictates the vehicle behavior.
Asymmetric toe is presented, by theory, as a way to brake with less performance but maintain
lateral control over the vehicle with one wheel. The same effect as described for the
symmetric toe modes changes the expected behavior. The wheel that is turned inwards
looses vertical load. This reduces the lateral tire force and longitudinal vehicle force. Toeingout with one wheel results in an unintended steering motion, instead of just a braking.
Therefore this configuration was left out of the further tests.
5.2
Recommendations & future work
With this project the basic concept of brake-by-steer has been proven. In order to make this
system work in a car, the relation between steering angle and vehicle heading has to be
restored. This means that the vehicle model has to be embedded into the steer-by-wire
system and calculate real-time how to position the wheels to generate the needed brake force
and follow the steering input from the driver as he expects. There will always be a trade of
between the braking performance and the lateral control of the vehicle. Further research on
how to position the wheels to reach the optimum between these two is needed.
The tire models used here are strong simplifications of actual tire behavior. What needs to
implemented in the future model is more precisely how tires behave under extreme large slip
angles at high speeds. The simplified Pacejka and piecewise linear model are not capable of
doing this very accurately.
The steer-by-wire go-kart has been a good test vehicle to proof the brake-by-steer concept.
The small vehicle was easy to adapt. However the available space was very limited. This
resulted in the positioning of the electronics box and heavy batteries right on top of the front
axle. This changed the vehicle behavior and demanded significantly more effort for the
steering motors. Although there was not an easy alternative, this has been a design choice
that will not be made again.
There were features in the mechanical construction of the kart that influence the vehicle
dynamics such that it is hard to extrapolate the results to a passenger car. A follow up test
41
bed should be a conventional car. Interesting to point out is that the ‘P1’ prototype vehicle of
Stanford University [19] has independent steerable wheels, but there was no references
found of brake-by-steering there.
42
6
Bibliography
[1]
Prof. Dr. Ir. Compter, J.C., “Mechatronics - Introduction to electromechanics”. Philips
Centre for Industrial Technology, October 2000.
[2]
“Spec a Motor”, http://www.specamotor.com/. Accessed September 2009.
[3]
Beckman, B., “Kart Steering, Physical Forces and Setup - Theory and Practice”.
http://www.karting.co.uk/KandK/Tech/KartSetup.html, 2002. Accessed September
2006.
[4]
Degerman, P., Wiker, N., “Analysis and Design of a Redundant X-by-Wire Control
System Implemented on the Volvo Sirius2001 Concept Car”, Master Thesis,
Linköping University, 2003.
[5]
“Delphi QUADRASTEER System Application Expands Onto Additional GM Truck and
SUV Models”. Delphi press release, February 2002.
[6]
Demerly J.D., "Control of independent steering actuators to improve vehicle stability
and stopping". Unites States Patent, US6.719.087B2. Delphi Technologies Inc., April
2004
[7]
Budaker et al., "Fremdkraft-oder Servolenkung". Offenlegungsschrift Int.Cl.
B62D6/00, ZF
LenksystemeGmbH and Robert Bosch GmbH, July 2003.
[8]
Kondo, T. and Yamamoto, T., "Rear wheels steering apparatus for vehicles". Unites
States Patent, 4.786.006. Mazda Motor Corporation, November 1988
[9]
Miller G.R. and Couratier J.P., "Active toe adjustment apparatus". Unites States
Patent, 5.143.400. Michelin Recherche et Technique, September 1992.
[10]
Den Boer, M. and Van der Lijn, D., “Study on brake-by-wire and implemtation on a
Go-kart”. Bachelor thesis at Hogeschool van Utrecht and SKF Nieuwegein, May
2006
[11]
Sodikart, http://www.sodikart.com
[12]
Maxon motor, http://www.maxonmotor.com
[13]
Amato, T., et al, “Handling behaviour of racing karts”. SAE paper nr. 2002-01-2179,
July 2002
[14]
Vitale, E. et al, "A lumped parameters model for the analysis of kart dynamics”, 7th
International Conference ATA, Florence, 2001
[15]
Ponzo, C. and Renzi, F., “Parametric multi-body analysis of kart dynamics“. Technical
paper for students and young engineers, Fisita world automotive congress,
Barcalona, February 2004.
[16]
“Ackermann Steering Geometry“, Wikipedia The free encyclopaedia
http://en.wikipedia.org/wiki/Ackermann_steering_geometry. Accessed May 2009.
[17]
Rill, G., “Vehicle dynamics”, Lecture Notes, Regensburg University of Applied
Sciences, March 2009
[18]
Yih, P., “Steer by-wire: Implications for vehicle handling and safety”. Ph.D.
dissertation, University of Stanford, 2005.
[19]
Dynamic Design Lab, Stanford University http://ddl.stanford.edu/. Accessed
September 2009
[20]
Bretz, E.A., “By-wire cars turn the corner”. Automotive Electronics, IEEE Spectrum,
April 2001
[21]
“Vehicle of the future here now“. Evolution - the business and technology magazine
from SKF, www.SKF.com, Nr. 4 November 2002
43
[22]
W. Klier, G. Reimann and W. Reinelt, “Concept and Functionality of the Active Front
Steering System“, SAE paper 2004-21-0073, 2004
[23]
De Vries, E., “Vehicle dynamics A’, lecture notes course wb3404 - Vehicle dynamicsA“, March 2002
[24]
Smith, N.D., “Understanding parameters influencing tire modelling“. Colorado State
University, Formula SAE Platform, 2004
[25]
Liebemann, E. K., Meder, K., Schuh, J., Nenninger, G. “Safety and Performance
Enhancement: The Bosch Electronic Stability Control (ESP) “. Proceedings - 19th
International Technical Conference on the Enhanced Safety of Vehicles, Washington,
D.C., June, 2005
[26]
Christopher, D. G., Shad M. L., J. Christian. “Eliminating the Need for Sensor
Redundancy in Diagnostic Systems for Steer-by-Wire Vehicles“. SAE Paper Number:
20062976, August 2006.
[27]
Juan R. Pimentel, “An Architecture for a Safety-Critical Steer-by-Wire System“, SAE
paper 2004-01-0714, January 2004
[28]
Noguchi, M., “Trends and Future Prospects Regarding Steering System Technology“.
Koyo Engineering Journal English Edition No. 159E, 2001.
[29]
De Raad van de Europese Gemeenschappen, 'Richtlijn 92/62/EEG van de Commisie
van 2 juli 1992 betreffende aanpassing aan de vooruitgang van de techniek van
Richtlijn 70/311/EEG van de Raad betreffende de stuurinrichting van motorvoertuigen
en aanhangwagens daarvan' 2 July 1999
[30]
ZF Aktivlenkung für Pkw der Mittel und Oberklasse. Product information ZFLenksysteme
[31]
Toffin, D. et al., "Influence of steering wheel torque feedback in a dynamic driving
simulator". Renault – Technical Centre for Simulation, Renault Technocentre and
Laboratoire de Physiologie de la Perception et de l'Action, CNRS – Collège de
France
[32]
Narby, E., “Modeling and Estimation of Dynamic Tire Properties“. Thesis report,
Department of Electrical Engineering, Linköping University, February 2006.
[33]
Beckman B., “The Physics of racing“. http://phors.locost7.info/files/Beckman__The_Physics_of_Racing.pdf, reformatted April 2008. Accessed September 2009
[34]
“Ackermann Explained (Part 1)“. Racecar engineering, IPC Media, Vol. 11 nr.6, June
2001
[35]
“Ackermann Explained (Part 2)“. Racecar engineering, IPC Media, Vol. nr. 7, July
2001
[36]
“Ackermann Explained (Part 3)“. Racecar engineering, IPC Media, Vol. nr. 8, August
2001
[37]
National Instruments, CompactRIO http://www.ni.com/compactrio/. Accessed
September 2009
[38]
Cole, D., “Steering Feedback”. ATZ Autotechnology 002008 Volume 8
44
A. Go-Kart dimensions
501 N
708 N
measurement point
centre of garvity
kart weight = 1322 N
539 N
706 N
638 N
745 N
centre of garvity
kart plus driver weight = 1975 N
centre of garvity
by-wire kart weight = 1962 N
centre of garvity
by-wire kart plus driver weight = 2687 N
centre of garvity heigth = 247 mm
by-wire kart, no driver
Original front axle
Extended front axle
363 N
677 N
422 N
559 N
224 N
591 N
597 N
676 N
Figure 43 Go-kart dimensions
45
B.
a.
Measurement Kart
Used equipment
The measurement kart is used to identify the performance of the steering system and vehicle
behavior as a point of departure for the design and as a reference for the brake-by-steer
system. This appendix shows the used materials, the layout and results.
i.
USB Data acquisition
Data acquisition
Description
Type
Product name
DT9804-EC-I-BNC-16SE
Analogue inputs
16 SE
Input resolution
16 bit
Throughput
100 kHz
http://www.datatranslation.com/products/dataacquisition/usb/dt9800-ec-i.asp
ii.
Velocity sensor
Measures
Type
Range
Sensitivity
Supplier
Velocity
Optical analogue
0 – 400 km/h
25 mV/km/h
Datron
Dartron is an optical absolute velocity sensor used in the automotive branch. It measures the
speed of the road passing underneath.
http://www.corrsys-datron.com/optical_sensors.htm
iii.
Absolute through shaft angle sensor
Measures
Type
Range
Sensitivity
Supplier
SKF
Angle
Through shaft magnetic ring 0-360°
11 mV/°
This sensor provides the absolute steering angle of the steering wheel. The angle of the
wheels is derived from this. The sensor is part of a combined bearing sensor system.
http://www.skf.com/portal/skf_rev/home/products?contentId=079776#Label4
iv.
Accelerometer
Measures
Type
Acceleration
Accelerometer
In house (SKF) build custom sensing system.
Range
+/- 5 g
Sensitivity
400 mV/g
Supplier
SKF
v.
Force sensors
Measures
Type
Range
Sensitivity
Supplier
Force
Strain gage
-35.5 N/V
SKF
Force
Strain gage
-21.9 N/V
SKF
In house (SKF) build custom sensing system. The steering torque is not measured directly at
the steering wheel and wheels. Instead the forces are measured with strain gages in the
steering rods.
46
b.
Measurement kart layout
Data acquisition
Angle sensor
Datron
Accelerometer
Strain gages
Figure 44 Measurement kart layout
Angle sensor
Strain gages
Figure 45 Strain gage and steering angle detail
c.
Measurement kart results
i.
Steering angle range
The maximum wheel angles are 32 degrees for the inner wheel and 25 for the outer wheel.
The difference is caused by mechanical linkage that mimics the Ackermann effect.
47
ii.
Steering speed and frequency, hard cornering
The maximum rotation speed of the steering wheel is 300 degrees per second. The angle
made is 50 degrees (from -25 to +25), resulting in a maximum steering frequency of 1 Hz.
During this aggressive driving test the rear wheels of the kart broke away. This is the point
where the tires physically limit the performance of the kart.
iii.
Steering speed and frequency, slalom
The slalom test gives also information about the bandwidth of the steering rate that can be
made with the go kart. The biggest amplitude is at the frequency the slalom is executed. The
peak-peak value of the slalom is 45 degrees, at a frequency of 0.95 Hz.
iv.
Steering torques
Static load
The static load is around 5 Nm when the wheels are pointing forwards. Turned, the torque
goes up to 16 Nm. The difference between the two can be seen as an indication for the
torque at the steering wheel. Precondition is that there are no additional lateral forces on the
tires
Quasi static load
During a ride the forces are around the 8 Nm at the wheels and 5 Nm at the steering wheel
during steady state circular path driving.
Dynamic load
During a test run with continues fast changing steering angles the torque is between the 25
and 30 Nm. In the sharp turns in the test track the torques spike to values of 50 Nm.
v.
Breaking performance
The maximum braking performance is 1.2 kN for the two front wheels. The graph is shown
below.
Measurement data
10
Velocity
(m/s)
Acceleration (m/s 2)
Brake Force (kN)
8
6
(various)
4
2
0
-2
-4
-6
0
1
2
3
4
5
Time [s]
Figure 46 Braking performance reference kart
48
6
7
vi.
Summary
Parameter
Nominal torque
Peak torque
Nominal speed
Max. rotating speed
Steering frequency
Braking performance
Vertical load change front wheels
Value
10
50
64 / 10.7
175.9 / 29.3
1
1.2
300 N
49
Unit
Nm
Nm
˚/s / rpm
˚/s / rpm
Hz
kN
/rad
C.
Sensor list and layout
The table below shows all used sensors in the steer-by-wire kart, their function, configuration and supplier.
Module
I/O
DIN
Function name
Description and Supplier
nr.
I/O
Signal
config
min / zero / max
Sensitivity
Supply
Voltage
Current
AI0
1
Handwheel angle
Absolute through shaft analog manetic senor, [SKF]
±5V
0.5 / 2.5 / 4.5V
11.1
mV / degree
12 V
35 mA
AI1
AI2
AI3
2
3
4
Front left steering angle
Front right steering angle
Monitor I Amplifier [11]
Conductive plastic potentiometer, model 357, [VISHAY]
Conductive plastic potentiometer, model 357, [VISHAY]
Amplifier ADS 50/10, [MAXON]
± 10 V
± 10 V
± 10 V
2.88 / 4.95 / 7.01 V
6.72 / 4.70 / 2.67 V
-10 / 0 / 10V
35.2
32.1
-0.4
mV / degree
mV / degree
V/A
12 V
12 V
24 V
10 mA
10 mA
AI4
Analogue AI5
IN
AI6
NI 9205 AI7
AI8
AI9
AI14
AI10
AI11
AI12
AI13
AI15
AI16
5
6
7
8
9
10
15
11
12
13
14
16
17
Monitor I Amplifier [12]
Monitor I Amplifier [20]
Toe Wing 1
Toe Wing 2
Lateral acceleration
Longitudinal acceleration
Zero G reference
Absolute longitudinal speed
Ready Status MC11
Ready Status MC12
Ready Status MC20
Log file number
Check V12
Amplifier ADS 50/10, [MAXON]
Amplifier ADS 50/5, [MAXON]
21 mm Cermet Potentiometer, CP21, [PIHER]
21 mm Cermet Potentiometer, CP21, [PIHER]
Acceleromter Model 3145 - 005, [ICSensors]
Acceleromter Model 3145 - 005, [ICSensors]
Acceleromter Model 3145 - 005, [ICSensors]
Optical speed sensor DLS-1, [CORRSYS - DATRON]
Amplifier ADS 50/10, [MAXON]
Amplifier ADS 50/10, [MAXON]
Amplifier ADS 50/5, [MAXON]
Thumbwheel switch 180011G [Eeco]
DC-DC converter 100W, VI-221 EW, [VICOR]
± 10 V
± 10 V
±5V
±1V
±5V
±5V
±5V
± 10 V
± 10 V
± 10 V
± 10 V
± 10 V
± 10 V
-10 / 0 / 10V
-10 / 0 / 10V
1.00 / 0 V
0.87 / 0 V
0.5 / 2.5 / 4.5 V
0.5 / 2.5 / 4.5 V
2.5 V
0…10 V
on = 0 V, off = 10 V
on = 0 V, off = 10 V
on = 0 V, off = 10 V
high / low , 0 / 10V
ok = 10 V, error = 0 V
-0.4
-0.8
4.14
4.14
400
400
V/A
V/A
V/deg
V/deg
mV / degree
mV / degree
24 V
24 V
12 V
12 V
12 V
12 V
0.12 mA
0.12 mA
5 mA
5 mA
25
mV / km/h
12 V
2.5 A
12 V
8.2 mA
AI17
18
Switch Feedback
± 10 V
on = 0 V, off = 10 V
AI18
19
Monitor n Amplifier [20]
Amplifier ADS 50/5, [MAXON]
± 10 V
-10 / 0 / 10V
AI19
AI20
AI21
AI22
AI23
AI24
AI25
AI26
20
MC Power checking
Switch Logging
Switch Start Button
AI22
AI23
Log file number
Log file number
Log file number
Battery G40s, 12 V, 38Ah/20h, [Exide]
Switch SPDT, 'no', [C&K]
Switch SPDT, 'no', [C&K]
± 10 V
± 10 V
± 10 V
± 10 V
± 10 V
± 10 V
± 10 V
± 10 V
0 / 8.16 V
on = 0 V, off = 10 V
on = 0 V, off = 10 V
Thumbwheel switch 180011G [Eeco]
Thumbwheel switch 180011G [Eeco]
Thumbwheel switch 180011G [Eeco]
50
high / low , 0 / 10V
high / low , 0 / 10V
high / low , 0 / 10V
24 V
1.47 V / V
24 V
12 V
12 V
1 mA
AI27
AI28
AI29
AI30
AI31
Log file number
Log file number
Log file number
Off switch
Thumbwheel switch 180011G [Eeco]
Thumbwheel switch 180011G [Eeco]
Thumbwheel switch 180011G [Eeco]
Switch SPST, [C&K]
± 10 V
± 10 V
± 10 V
± 10 V
high / low , 0 / 10V
high / low , 0 / 10V
high / low , 0 / 10V
high / low , 0 / 10V
± 10 V
high / low , 0 / 10V
Log file number
Thumbwheel switch 180011G [Eeco]
DI0
21
Front left wheel speed
Digital ferrite ring, RV-BMB-6209/080SA [SKF]
DI1
Digital DI2
IN
DI3
NI 9423 DI4
DI5
DI6
22
23
24
25
26
27
Front right wheel speed
Unipolar Hall-effect sensor, SS411A, [Honeywell]
Rear axle speed
Sensor bearing BMB-6206/064S2/EA002A, [SKF]
256 CPT, 64 poles, quad
Switch - Toe selection modes
Switch - Toe selection modes
Switch - speed dependent FB
Switch DPCO, [C&K]
Switch DPCO, [C&K]
Switch DPDT, [C&K]
DI7
28
Digital
IN
DI0a
t/m
subD
12 V
10 mA
10 mA
20 mA
20 mA
on = 12 V, off = 0 V
on = 12 V, off = 0 V
on = 12 V, off = 0 V
12 V
12 V
12 V
12 V
12 V
12 V
160 CPT, 80 poles, single
Switch - Toe selection, asym
Switch DPCO, [C&K]
on = 12 V, off = 0 V
12 V
Front left motor rotation
HEDL-5540 with RS-422 (EIA-422) line driver
500 CPT, qudrature
5V
4 mA
Front right motor rotation
HEDL-5540 with RS-422 (EIA-422) line driver
500 CPT, qudrature
5V
4 mA
NI 9411 DI5b
Analogue AO0
32
Motor Control signal 11
-10 / 0 / 10 V
AO1
34
Motor Control signal 12
-10 / 0 / 10 V
NI 9263 AO2
36
Motor Control signal 2
-10 / 0 / 10 V
AO3
38
Variable analogue output
0 / 10 V
DO0
41
Enable MC11
1' = [Usup]V, '0' = [0 - 2.5]V
24 V
1.6 mA
DO1
Digital DO2
OUT DO3
NI 9474 DO4
DO5
DO6
42
43
44
45
46
47
Enable MC12
Enable MC20
Enable DC/DC
LED 1
LED 2
State indicator LED
1' = [Usup]V, '0' = [0 - 2.5]V
1' = [Usup]V, '0' = [0 - 2.5]V
0' = on, '1' = off
0' = on, '1' = off
0' = on, '1' = off
0' = on, '1' = off
24 V
25 V
24 V
24 V
24 V
24 V
1.6 mA
1.6 mA
75 µA
12 mA
12 mA
12 mA
DO7
48
nc.
OUT
Table 3 Sensor list
51
The following figure shows the detailed electronics of each individual sensor.
Vcc = 12 V
1
S_gamma
3
Vcc 24 V
NI-9205
0
MC and EM Switch
AI0
External power supply
24V
Vcc = 12 V
R = 22k
2
Motor Encoder [11]
U = 2.9 V
AI SENSE
R2 = 100k
AI19 NI9205
NI-9205
S_delta11
0.5 ... 4.5 V
11.1 mV / degree
35 mA
C1 = 30e-6F
Vcc 2
ch A 6
ch B 8
R = 3k
AI1
C2 = 0.1e-6F
I = 10 mA
AI SENSE
0...10 V
.... mV / degree
12 mA
R1 = 200 Ohm
Vout
cRIO -9411
DI1a
DI2a
GND
0 / 2.88 V
9.6 mA
+5V
Reg
DI0a
ch I 9
0
Vcc = 12 V
Dsub
COM
TTL 2-channel
500 CPT
20 mA per channel max
10 V
R2 = 1 kOhm
Vcc 12 V
NI-9205
S_delta11
External power supply
24V
AI1
Vcc = 12 V
0
Motor Encoder [12]
MC11
MC12
MC20
C2 = 0.1e-6F
C1 = 30e-6F
9
AI SENSE
R2 = 100k
NI-9205
S_delta11
AI11 NI9205 for MC11
AI12 NI9205 for MC12
AI13 NI9205 for MC20
0
1
AI1
Vcc = 12 V
I = 1.2 mA
C1 = 30e-6F
C2 = 0.1e-6F
'0' = 10 V
'1' = 0V
Lateral acceleration
AI2
4700 pf
C2 = 0.1e-6F
1500 pf
dc - dc Converter
24 - 12 V
- INput 24V
0
AI SENSE
4700uf
Vcc
Vref
NI-9205
cRIO -9411
DI4a
DI5a
COM
TTL 2-channel
500 CPT
20 mA per channel max
Vcc = 12 V
R1 = 5k6 Ω
Gate IN
1500pf
Vcc = 12 V
10k
0.5...4.5 V
400 mV / g
5 mA
BC107B
NI-9423
4700pf
AI SENSE
Dsub2
+5V
Reg
DI3a
- OUT
- Sense
+ Sense
+ OUT
+ INput
AI14
AI11
0...10 V
29.4 mV / degree
10 mA
Vout
GND
NI-9205
S_delta12
Dsub
I = 0.2 mA
AI SENSE
0...10 V
.... mV / degree
12 mA
C1 = 30e-6F
ch I 9
GND
R = 50k
0
R1 = 200 ohm
R2 = 1 kohm
Vcc 2
ch A 6
ch B 8
R = 10k
0...10 V
29.4 mV / degree
10 mA
VSignal > 11 V
Sensor
DI0
COM
1.2 mA
GND
330k
NI-9474 DO3
BC107
0...24 V
7.3e-2 mA
'0' = on, '1' = off
Vcc = 12 V
= 100 kΩ
=
Switch 1
Switch 2
DI5 NI9423
DI4 NI9423
160 CPT
2.1 mA
longitudinal accelereation
Vcc
DI6 NI9423
AI7 NI9423
Vref
Switch 3
NI-9205
Vcc = 12 V
AI15
NI-9205
Vcheck
AI12
R1 = 470
Vcc = 12 V
DI7 NI9423
AI SENSE
Check V12 = 8.16V
0.5...4.5 V
400 mV / g
5 mA
AI16
R1 = 5k6 Ω
BC107B
NI-9423
R2 = 1k
V Signal > 11 V
Sensor
DI1
COM
GND
0 / 8.16 V
8.2 mA
NI-9205
160 CPT
2.1 mA
Vcc = 12 V GND
AI11
Vcc = 12 V
AI SENSE
R1 - 850 Ω
R1 - 850 Ω
0...10 V
400 mV / km/h
6000 mA
Sensor
NI-9423
Signal B
Signal A
DI2
Sensor
DI3
GND
256 CPT
14 mA per channel
Figure 47 Sensor electronics
52
COM
D.
a.
Used materials
National Instruments
Description
CompactRIO Controller
CompactRIO Chassis
Analogue input module
Digital input module
Digital input module
Analogue output module
Type
NI cRIO-9004
NI cRIO-9102
NI-9205
cRIO-9423
cRIO-9411
NI-9263
Table 4 Used material CompactRIO
b.
Maxon Motor
Description
Wheel motor
Gear
Digital encoder
4-Q-DC Servo amplifier
Type
F2260.885-51.216-200
GP62 110505
HEDS 5540
ADS 50/10
Steering wheel motor + gear
Digital encoder
4-Q-DC Servo amplifier
RE36 24V, GP42C
HEDL 55
ADS 50/5
Table 5 Used material MAXON Actuators
53
E.
Steer-by-wire go-kart
Steering wheel actuator
Speed indicator
Speed sensor
Electronics box
Batteries
Wheel actuator
Figure 48 Steer-by-wire kart
Figure 49 Steer-by-wire kart toeing-out
54
55
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement