# Fuzzy Logic in a Low Speed Cruise-Controlled Automobile by ijcsiseditor

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```									                                                                   (IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 4, July 2010

Fuzzy Logic in a Low Speed Cruise-Controlled
Automobile
Mary Lourde R., Waris Sami Misbah,
Department of Electrical & Electronics Engineering
BITS, Pilani-Dubai, Dubai International Academic City, U.A.E

Abstract — Traffic congestion is a major problem that drivers                MATLAB. It is the most commonly used platform by most
face these days Long rush hours exhibit both mental and                      of the scientific organizations.
physical toll on a driver. This paper describes the design of
cruise control system based on fuzzy logic, in order to reduce                   In order to make the fuzzy logic cruise control system
the workload on a driver during traffic congestion. The                      more realistic, we need to model a commercially available
proposed low speed cruise control system operates by sensing                 car on MATLAB and then integrate the fuzzy cruise control
the speed and headway distance of the preceding vehicle and                  system to the vehicle model. The car chosen for modeling is
controlling the host vehicle’s speed accordingly. The vehicle                Toyota Yaris 2007 Sedan[1]. The reason behind the selection
speed is controlled by controlling throttle and the brakes. The              of this car is the availability of technical information of its
fuzzy logic based cruise controlled vehicle is simulated using               control system.
MATLAB Simulink and the results are presented in this paper.

Keywords - fuzzy logic, cruise control, low speed, and traffic
III.      MODELING OF THE VEHICLE ON MATLAB
congestion.                                                                      The modeling of the vehicle’s drive train and dynamics is
done by mapping on the specifications of a Toyota Yaris
I. INTRODUCTION                                        onto a demonstration model in MATLAB[6]. The automatic
drivetrain model available in SIMULINK is taken as the base
A cruise control system is a general feature found in most               model for the system development.
of the automobiles today. A basic cruise-controlled car
travels at constant speed set by the driver, allowing
automatic movement of the vehicle without the driver
pressing the accelerator. The driver sets the speed as desired
and then the cruise control system maintains that speed by
controlling the throttle of the car. A typical cruise control
system comes with features such as acceleration, coasting
and resume functions.
Since the cruise control system replaces the driver, it must be
able to imitate human behavior. The use of fuzzy logic is an ideal                        Figure 1. Block diagram of basic Drivetrain system
tool for this purpose. Fuzzy logic, which also means imprecise
logic, when applied to system makes it user friendly. A fuzzy                    The inputs to the drive train are the throttle opening and
system involves a set of linguistic rules applied on set of input and
output parameters, in order to control a system.
brake torque. The engine, vehicle dynamics and the
automatic transmission have been modeled using non-linear
Conventional cruise control systems generally operate at                  differential equations. The transmission control unit has been
speeds greater than 40 km/h; mostly used by drivers at                       modeled in STATEFLOW as it involves decision-making
highways. For speed lower than this, the vehicle needs to be                 based on the current state of the vehicle.
controlled manually. A cruise control system that operates at
lower speed is rarely available.                                                 Reference [6] gives the complete details of modeling
equations used by Mathworks to design this drive train. The
complete Drivetrain model used for simulation is shown in
II.       SOFTWARE USED TO SIMULATE THE                                 figure 3 below. The engine subsystem was modified
SYSTEM                                                 according to the engine-torque curve of Toyota Yaris.
The software used for the modeling of the system is                      Default transmission gear ratios were modeled to that of
MATLAB/SIMULINK. It has several toolboxes available                          Toyota Yaris. The shift schedule used by the shift logic block
such as the Fuzzy Logic Toolbox, SIMULINK, Image                             and the vehicle dynamics parameters were modified by the
processing, Simdriveline, SimMechanics, SimScape etc. all                    corresponding Toyota Yaris values. Any subsystem for
of which can be integrated with a control system. This allows                which the corresponding Toyota Yaris specification was not
the user to develop most of the real world conditions in                     available, the default value used by Mathworks has been
retained.

ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 4, July 2010

Figure 2. Complete Drivetrain SIMULINK model used for the simulation [6]

Simulation One

Figure 3. Simulation 1 results of a Toyoto Yaris 2007 automobile under normal running environment

ISSN 1947-5500
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Vol. 8, No. 4, July 2010
vehicle. From the simulation1 results shown in figure 3
IV.       MODEL TESTING OF THE AUTOMOBILE                                    above it is seen that the vehicle speed as well as the engine
The vehicle model is tested for accuracy and compared                      speed closely follows as required by the instruction specified
with the actual operation of Toyota Yaris. Several                             by the throttle profile of the vehicle.
simulations, with various inputs, were carried out to verify                       As we can see from the graph, the vehicle speed reaches
the simulation model of the vehicle of which two set of                        its maximum value of 120 mph, which is the top speed of
results are given below.                                                       Toyota Yaris. The maximum engine rpm reached is 4100,
The vehicle’s throttle profile are selected to simulate the                which is about 100 revolutions less than that of Toyota Yaris.
real time operation of the engine and vehicle speeds and the                   The up shifts take place at 10 mph and 40 mph, which are
gear positions are also observed to verify the working of the                  close to the shift schedule of Toyota Yaris.

Simulation two

Figure 4. Simulation 2 results of the automobile in heavy traffic environment

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Figure 4 shows a typical example of a heavy traffic environment
B. Definition of Input Membership Functions
as the vehicle stays below 10 mph for a major amount of time
during the simulation. The simulation1 is carried out for 300                     Inputs to the fuzzy controller are relative velocity
seconds and the simulation2 is done for 600 secs. In simulation               and the distance between the two vehicles. Therefore,
2, in addition to the throttle profile, the second input brake torque         we need to define membership functions for fuzzy
is also applied. These two simulation results proves the model of             variables relative velocity and relative distance. The
range for the fuzzy variable relative velocity chosen is -
the automobile in the Simulink platform.
10 km/h to +10 km/h. The speed range chosen is the
V.        DESIGN OF THE FUZZY LOGIC CRUISE                            typical range that vehicles travel in a congested traffic
CONTROL SYSTEM                                      situation. The range of relative distance is chosen 0.5 to
2m, which again is the typical range in a congested
The objective of the fuzzy controller is to control the vehicle           traffic situation. Most of the membership functions
in a congested slow moving traffic environment. Therefore, the                chosen in this system are triangular shaped as it has less
design of the fuzzy controller must be based on the variables that            parameters and responds rapidly when compared to
affect the vehicle’s movement in such an environment                          other functions. This helps the inference system, to
make decisions more effectively when compared to
A. Input to the Fuzzy Controller                                              other membership functions. Literature also shows that
In order to control the vehicle longitudinally, a sensor must             most commonly used membership function is triangular
detect a vehicle ahead and provide the distance and relative                  shaped, due to its effectiveness in a real-time
velocity of that vehicle with respect to the host vehicle.                    environment and economic feasibility.
Therefore, a 24 GHz radar sensor can be installed in the vehicle
1)     Relative Velocity
since it has a very short range [7].
The relative velocity fuzzy variable has the
following linguistic values: mildly negative (MN),
an output profile coming from a sensor is assumed and provided
mildly positive (MP), negative (N), positive (P), very
as an input to the fuzzy controller. There are two output profiles
negative (VN), very positive (VP) and null (N). The
from the sensor. They are relative velocity and relative distance
figure 6 below shows the membership function
between two vehicles. The figure below shows two typical
definition for relative velocity.
unfiltered measurement profiles from a sensor [8].

Figure 6. Membership function for Relative Velocity

2)     Relative Distance
The fuzzy variable for relative distance has the
following linguistic values: very very close (VVC), very
close (VC), close (C), Mildly Close (MC), distant (D),
very distant (VD) and very very distant (VVD). The
Figure 5. Output profiles from a radar sensor                  figure 7 below shows the membership definition for
relative distance
It can be observed from the above profiles, that when relative
velocity is positive, the distance between the vehicles increases.
The distance between cars will keep on increasing, as long the
relative velocity is positive. The rate of change of distance varies
the rate of change of relative velocity. When relative velocity
becomes negative, the distance between the vehicles starts
decreasing. Relative distance decreases as long as the relative
velocity remains negative.

Figure 7. Membership function for relative distance (0.5 - 2 m).

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C. Output of the Fuzzy Controller                                               be formed in order to control the output variables
1) Throttle Control                                                           throttle and brake based on the input variables, relative
velocity and relative distance. A set of 31 rules for
The linguistic values for throttle control are down (D), down              throttle control and another set of 34 rules for brake
very low (DVL), down low (DL) down medium (DM), up (U), up                      control is composed. All the rules are conditional. Table
very low (UVL) up low (UL), up medium (UM) as shown in                          1 shows set of rules for brake control and Table 2
figure 8 below. The throttle control membership functions are                   shows the rule set for throttle control.
classified into two major categories, Up and Down. These two are
further divided into subcategories normal, low, very low and                             TABLE I.       RULE BASE FOR BRAKE CONTROL
medium. This is to enhance the control of the vehicle at different
relative velocities and distances.                                              RD       RS   VN       N      MN         NULL       MP        P         VP
VVC         HRD      VH     -          HRD        L         L         -
VC         VH       H      VH         -          L         L         -
C        -        H      M          -          L         L         VL
MC         -        H      L          -          L         VL        -
D        -        M      M          -          L         NULL      NULL
VD         -        M      M          -          L         NULL      NULL
VVD         -        M      M          NULL       -         NULL      NULL

Figure 8. Membership function for Throttle Control
TABLE II.         RULE BASE FOR THROTTLE CONTROL

Majority of the membership functions cross each other. The                   RD RS            VN   N          MN         NULL       MP        P         VP
membership functions have been made to cross in order to allow                    VVC             D    D          D          NULL       DM        -         -
for smooth transition from one membership function to other,                      VC              DM   DM         DM           -        DM        UVL       -
while the input values are changing. If the cross points are not                   C              -    DM         DL         -          DVL       UVL       -
included, discontinuities might arise in the operation of the                     MC              -    DL         DVL          -        UVL       UL        UM
controller as no rule will be fired at the end of each membership                                      DV
function.                                                                            D            -               DV L        -         UL        UM        U
L
VD             -    -          -           -         UM        U         U
2) Brake Control
VVD             -    -          -           U          -        U         U
Controlling the brake along with the throttle allows better
control of the car. Since the vehicle is assumed to travel in                   E. Defuzzification Method
congested traffic situation, it will be required to stop frequently.                The final output of the fuzzy controller must be a
The linguistic values for the fuzzy variable brake control are no               discrete value. In order to achieve this, a method called
brake (NB), slow brake (SB), medium brake (MB), high brake                      defuzzification must be applied. The centroid method
(HB) and hard brake (HDB). The figure 9 below shows the                         was used to defuzzify the output fuzzy variables, since
membership functions of the brake control                                       all the membership function definition are triangular.
The centroid method makes it easier to defuzzify a
triangular shaped membership function and reduces the
overall computational task allowing the system to
respond effectively

F. Selection of Inference Method
The fuzzy logic toolbox provided in MATLAB has
two inference methods, Mamdani inference method and
the Sugeno method .The Mamdani method is commonly
employed in most of the applications due to the fact that
Figure 9. Membership function for brake control
the Mamdani method gives outputs as fuzzy variables.
Whereas Sugeno method gives linear output. As both the
D. Construction of the Rule Base                                                outputs (throttle and brake) used in this controller are
The construction of rules base determines relation between input                fuzzy variables, Mamdani method is selected for the
and output membership functions. This means that the fuzzy                      inference.
controller will give a certain output depending upon the input
and the rules that are executed. A set of rule guides the fuzzy                 G. Fuzzy Logic Cruise Control System model in
inference system to make decision regarding the control of the                      MATLAB/SIMULINK
output variable. A rule can take three forms conditional,                           The fuzzy logic cruise control system needs to be
unconditional and an assignment. In this system case rules must                 integrated with the vehicle model. The vehicle model

ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 4, July 2010
has throttle opening and brake torque as its inputs. Two fuzzy                  diagram of the Fuzzy Logic Cruise Controlled
controllers are used to control the throttle and brake respectively.            automobile.
Figure 10 shows the complete MATLAB-SIMULINK block

Figure 10. Complete MATLAB/SIMULINK model of the Fuzzy Logic Cruise Control System

1000 lb-ft and throttle is reduced to about 1%. Both the
VI.      SIMULATION OF THE FUZZY LOGIC                             relative velocity and relative distance remain constant during
CRUISE CONTROL SYSTEM                                  the next 200s and so does the brake torque and throttle. We
can observe that during this period of 200s that the vehicle
A. Simulation3 - Low speed cruise control system case i                 speed remains zero. Therefore, it can concluded during this
The fuzzy logic cruise control system simulation is                    period, the vehicles are at a stop. This is a typical situation of
simulated for thirty minutes with the assumed profile for                  vehicles being stuck in a heavy traffic environment. The
relative velocity and relative distance as shown in figure 11.             cruise control system has successfully detected the vehicle
The throttle position, brake torque and vehicle speed are the              approaching the preceding vehicle and brings the vehicle to
output variables observed. Initally as the relative velocity and           stop when the minimum distance is reached.
distance increase, the speed of the vehicle increases. An
At 800s, as both the relative velocity and distance begin
increase in throttle opening and the lowering of the brake can
to rise,the throttle increases and the brake torque is lowered
be observed. At 100s, relative velocity begins to decrease,
allowing the car to acclerate and maintain constant speed for
however the relative distance still increases, although at a
about 200s.Then as relative velocity and distance increase to
lower rate. This is due to the fact that relative distance will
a higher value, we see a further rise in throttle value and
increase as long as the relative velocity is positive. The
lowering of brake. During the final stage of the simulation,
relative distance starts to decrease the moment, relative
the relative velocity and distance begin to decrease and
velocity crosses the zero mark. The throttle is reduced and
therefore the cruise control system lowers the throttle and
the brake torque applied increases as the relative velocity and
increases the brake in order to adjust the speed of the vehicle.
relative distance and consequently, we see a decrease in
Finally, as the vehicle approaches the preceding vehicle, a
vehicle speed. The vehicle speed continues to decrease
drop in the throttle and an increase in the brake torque can be
further as relative velocity increases in the negative direction.
seen, which bring the vehicle to a stop.
At 600s, the relative velocity becomes zero and the
relative distance reaches its minimum value. Therefore, the
fuzzy cruise control system increases the brake torque to

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During the simulation, we observe that vehicle speed                         velocity and relative distance. The fuzzy controller takes into
remains constant for a certain period, even though both the                      account the degree of change in both the relative velocity and
relative velocity and distance are varying. This is because of                   the distance. This condition can be observed in the following
the fuzzy logic controller being assigned rules to maintain a                    simulations as well.
certain speed of the vehicle for a certain range of relative
B. Simulation4 –Low speed cruise control system case ii
In the intial phase of simulation, the vehicle speed
increases as the both realtive velocity and distance increase.
A further rise in vehicle speed(16 km/h at about 200s) is
observed as shown in the figure 12 when relative velocity
and distance increase further. During this period appropriate
changes made by the fuzzy logic controller, can be observed,
vehicle speed. The vehicle speed remains constant for about
next 600s.
At 400s, the relative velocity reaches zero and the
relative distance reaches the maximum value (2m) Both of
them remain at that value for the next 200s. During this
period, the both the throttle and brake torque remain the
same and so does the vehicle speed. This is sitaution, where
both the vehicles move at constant speed and headway
distance. The fuzzy logic controller has managed to detect
this and has responded correctly.
At 800s, the relative velocity decreases negative and
subsequently the relative distance alos begins to decrease.
Therefore, we see a drop in the throttle and an increase in the
brake torque applied. The vehicle speed, thereby decreases to
5.80 km/h and remains at this speed until the the relative
velocity crossed the zero. As mentioned in the analysis of the
previous simulation, the vehicle speed remains the same even
though both relative velocity and distance decrease. The
reason being the same as metioned earlier.
In the final phase, the vehicle speed increases as both the
relative velocity and distance increase. Appropriate changes
in throttle and brake can be observed during this period.
Discontinous spikes in the throttle and brake graphs can
be observed whenever the relative velocity crosses the zero
the mark. This reason behind this is that no rule is executed
by the fuzzy controller at that very instant. However, this
does not have an effect on the vehicle speed,since the time
span for which these discontuinities occur is negligible.

C. Simulation5 – Low speed cruise control system case iii
As the simulation begins, the vehicle acclerates as both
relative velocity and distance increase. Further changes in
vehicle speed can be observed as relative velocity and
distance continue to increase. The fuzzy logic controller has
adjusted to vary the throttle and brake appropriately to raise
the vehicle speed. The results are shown in the figure 13.
The vehicle speed begins to decrease at 300s due to the
realtive velocity crossing the zero mark. To lower the vehicle
the speed the fuzzy controller has increased the brake torque
and has simulatanouelsy lowered the throttle. As the relative
velocity and distance continue to decrease, we can observe
the further decrease of throttle and increase of brake torque
Figure 11. Simulation3- Low speed cruise controlled system case i             in order to lower the vehicle speed.

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The vehicle speed rises again the moment the relative                            In the last phase of the simulation, the throttle is lowered
velocity crosses the zero mark at 600s. The fuzzy controller                     and the brake torque is increased, since relative velocity
the varies the throttle and the brake torque to bring about this                 becomes negative and the vehicles starts approaching each
change in vehicle speed.                                                         other. The vehicle decelerates to about 1km/h at the end of
the simulation. The fuzzy controller has effectively managed
to control the vehicle appropriately throughout the
simulation.

Figure 12. Simulation 4 –Low speed cruise control system case ii                  Figure 13. Simulation 5 –Low speed cruise control system case iii

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D. Simulation 6 –Low speed cruise control system case iv                         E.   Simulation7 – Switching of cruise control system to
The vehicle initally accelerates to 7.86 km/h as relative                                      manual mode
velocity and distance increases and moves at constant speed                      This simulation is performed in order to demonstrate that
for another 70s. Then vehicle speed further increases to 16                      the cruise control system can be switched to manual mode
km/h at 100s. Throttle and brake response during this period                     whenever the driver wishes to take over the control of the
can be seen in figure 14. The throttle and brake remain the                      vehicle.
same till the vehicle remains at this speed

Figure 14. Simulation 6 – Low speed cruise control system case iv

At 225s, relative velocity crosses the zero mark and the
vehicle speed begins to decrease. The throttle is lowered
further and brake increases in order to lower the vehicle
speed further. At 275s, the relative velocity remains constant
and therefore, the brake and throttle remain constant. Hence,
it can be concluded that the fuzzy controller has responded                     Figure 15. Simulation 7 – Switching of cruise control system to manual mode
appropriately when relative velocity is constant.
The vehicle intially responds to the changes in the
Finally, the vehicle speed begins to increase as the                         relative velocity and distance as it is being controlled. The
relative velocity crosses the zero mark. Appropriate changes                     driver applies the brakes at 150s, as the manual brake graph
in the throttle and brake torque can be observed from the                        shown in figure 15. The same brake profile can be seen in
figure 14.                                                                       brake torque graph. For the next 150s, we can observe from

ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 4, July 2010
the brake torque graph, that the brake torque profile remains          enhanced to a real time system by extending the model of the
the same as the manual brake profile. This shows that the              automobile with feed back sensors appropriately on
vehicle is being controlled by the driver. A similar                   MATLAB. This will enable the movement of the vehicle in
observation can also be made with respect to throttle graph.           any direction required when simulating the vehicle.
This switching of control of the vehicle is performed by               A complete VRML (virtual reality machine language)
adding a switch to the output of the fuzzy logic brake                 model for an urban traffic environment shall be designed.
controller and manual brake. The switch has a control input            This will allow testing of the vehicle in a congested traffic
and two data input port. The control input allows the first            enviroment. The 3D traffic environment will require several
input, if it is above zero. The brake input has been given both        external variables such as detection of traffic lights,
as the control input and the first input. The fuzzy logic brake        pedestrians, intersections along with the movement of the
controller output is given as the second input to the switch.          vehicle in the congested traffic environment.
The moment the driver presses the brake pedal, and the brake
torque increases above zero, the fuzzy logic controller                    The fuzzy logic system must be able to incorporate the
connection to the vehicle is cut off by the switch and it              environmental conditions when the vehicle is moving in the
allows the manual brake input to the vehicle and hence the             above 3D model. The VRML realm builder along with the
control of the vehicle is switched to the manual mode. A               virtual reality toolbox allows the connection of the fuzzy
similar method is applied for the throttle input.                      cruise control system to the 3D system. This will make the
testing of the system more realistic.
VII. CONCLUSION AND FUTURE WORK
ACKNOWLEDGEMENTS
In this project a Fuzzy logic controlled low speed cruise
control system is designed successfully and extensive                     I would like to express my sincere gratitude to Dr. M.
simulation is carried out to test the results..The basis of the        Ramachandran – Director, Bits Pilani, Dubai for granting me
design of this control system was to control the vehicle in a          an opportunity to perform this project in the college
congested traffic situation.The inputs to vehicle model are            environment and use its resources. I would also like to thank
the throttle and brake. Therefore, two separate fuzzy logic            my thesis guide Dr.Mary Lourde R for her constant guidance
controllers were modeled to control these vehicle actuators.           and support, which has helped me in making this project.
To control the throttle, a set of 33 rules were constructed and
to control the brake, a set 35 rules were constructed. As both                                     REFERENCES
these control variables are fuzzy variables, Mamdani                   [1]  Toyota Yaris Sedan Specification , www.thecarconnection.com
Inference method is chosen to give the output. Two different                2007 Toyota Yaris 4dr Sedan Auto S (Natl)
fuzzy controllers for brake and throttle are used to have                   http://www.thecarconnection.com/specifications/toyota_yaris_2007_4
better control over the vehicle, by allowing them to operate                dr-sdn-auto-s-se_performance-specs
independently.                                                         [2] R. Garcia et al., “Frontal and Lateral Control for Unmanned Vehicles
in Urban Tracks,”IEEE Intelligent Vehicle Symp. (IV2002), vol.2,
In order to maintain a safe distance between the                        IEEE Press, 2002, pp. 583–588.
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vehicles. The sensor profile of these variables were assumed           [4] M.A. Sotelo et al., “Vehicle Fuzzy Driving Based on DGPS and
from a research report [8]. Using the basis of this profile,                Vision,” Proc. 9th Int’l Fuzzy Systems Assoc., Springer, 2001,
different input relative velocity and distance profiles were                pp.1472–1477.
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control system operates well to control the vehicle                    [6] Using Simulink and Stateflow in Automotive Applications, www
effectively based on different input profiles provided to the               mathworks.com Modeling an Automatic Transmission Controller
system.The fuzzy cruise control system completely controls                  http://www.mathworks.com/products/simulink/demos.html?file=/prod
the vehicle without the intervention of the driver. The                     ucts/demos/shipping/simulink/sldemo_autotrans.html
maximum speed that the vehicle reaches when the cruise                 [7] K. Naab et al., “Stop and Go Cruise Control”, “International Journal
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speed range of vehicles moving in a congested traffic                       Fusion for Automated Vehicle Control" (April 1, 2004). California
situation.This leads to the conclusion that the fuzzy logic                 Partners for Advanced Transit and Highways (PATH)
system is able to control the vehicle very well in a low speed         [9] Fancher et al.,“Intelligent Cruise Control Field Operational Test (Final
heavy traffic environment. Moreover, a switching function                   Report)”,University of Michigan Transportation Research Institute
has been attached to the system which allows the driver to                  (1998).
take over the operation simply by pressing the brake or the            [10] Ing. Ondřej Láník, “Fuzzy Logic Vehicle Intelligent Cruise Control
throttle without any difficulties.                                          Simulation”, Czech Technical University in Prague, Faculty of
Mechanical Engineering,Technická 4, CZ – 166 07 Praha 6, Czech
The drivetrain model used in this system is a very basic                Republic.
one and the vehicle can be controlled in the longitudinal              [11] Micheal Klotz, Rohling H, “24 Ghz for Automotive applications”,
direction only. This low speed cruise control system can be                 Journal of Telecommunications and Technology, April 2001, pp 11-
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