Vehicle Dynamic Stability Control and Driving Crisis Analysis Using Fuzzy Logic

ALIREZA BAHARIZADEH Sama Organization (affiliated With Islamic Azad University), Shahrekord Branch, Iran

MAHMOOD FATHY Department of Computer Engineering, Iran University of Science & Technology

MOHSEN DAVOUDI Department of Electrical Engineering, Politecnico di Milano, Milan, Italy

Abstract: - In this paper, we explain the process of designing fuzzy based analyzers which can be installed in a vehicle. These analyzers use some kinds of sensors to determine the crisis of driving situation. This system helps a driver to be aware of the danger of the obstacles, other vehicles on the road, fatigue and environment noises. An alarm massage concentrates the driver attention while s/he is doing something that may distract the attention. A different fuzzy controller using electronically controller of the Brakes/ Steering/ Suspension systems controls the vehicle to avoid the obstacles and also maintain the kinetic balance of the vehicle by mean of dynamic stability analysis. An advantage of this controller is that it doesn’t interfere with the driver’s habit in vehicle control and it resumes functioning only in critical moments. Using various actuators and sensors, we introduce a new approach to detect driving and stability crisis. This makes the proposed fuzzy analyzer a novel one.

Key-Words: - Driving crisis, Fuzzy analysis, Dynamic stability, vehicle control

1 Introduction Ever since the invention of automobiles, research in vehicle safety systems has been an on-going study. Engineers and researchers have been trying to fully understand the dynamic behavior of vehicles as they are subjected to different driving conditions, with different types of the drivers. They want to apply these findings to improve issues such as ride quality and vehicle stability and safety, and to develop innovative designs that will improve vehicle operation [1]. Generally car accidents occur because of high speed, inequality of the road and lack of attention on the part of drivers. Rapid reaction of the driver may cause dynamic problems like rollover and skidding. In this paper we develop two sets of fuzzy analyzers, one to detect driver's consciousness and danger of the obstacles and other neighbor vehicles on the road and the second to

detect dynamic stability crisis while the actuators are activated automatically or manually. We name these two kinds of crisis as external and internal crisis respectively. Dynamic problems occur when the Centre of Gravity (CG) moves outside the perimeter of the vehicle. CG behaviour analysis has a key role to play when investigating vehicle kinetic equilibrium [2]. The proposed system consists of some fuzzy analyzers: Driver consciousness (DC), data accuracy (DA), dynamic stability (DS) and crisis fuzzy analyzers. Sensor #1- 4 prepare information needed for external crisis analysis. The driving crisis signal is made with two crisis signals: 1) external crisis and 2) internal crisis. Figure 1 shows the whole concept of analysis of driving crisis and dynamic stability system.

ISBN: 978-960-6766-57-2 239 ISSN: 1790-5109

9th WSEAS International Conference on FUZZY SYSTEMS (FS’08) which was held in Sofia, Bulgaria

Fig.1. block diagram of driving crisis analysis

The rest of the paper is organized as follows. In the first section we describe the suspension, brake and steering system dynamics, the structure of the fuzzy analyzers is considered in the second section and the last section demonstrates the simulation results. 2 The suspension, brake and steering

system dynamics 2.1 Suspension System Model, Statics and

Dynamics

In dynamic analysis points of view the suspension system is an important part of vehicle. We use a simple full-car suspension model. In this section both statics

and dynamics of the Spring Mass Damper (SMD) system for the simulation are briefly introduced. We consider both the spring pK and the damper pC in the

passive mode. The actuator aF is considered in the

dynamics of the vehicle in this paper [3].

In the full-car model the links between sprung masses are considered to be solid rods (see Figure 2). Then, we can formulate three mechanical equations for pitching, rolling and center of gravity (CG) motion, respectively [4]:

TbodyAAAA

rrAAlAA

prAAfAA

mFFFF

JdFFlFF

JlFFlFF

rrfrlrlfl

rrfrlrlfl

rrrlfrfl

υ

ω

&

&

&

=+++

Ω=+−+

=+−+

)()(

)()(

where rrrlfrfl bbbbbody mmmmm +++= .

These equations lead to the quarter-car links. If some nonlinearities are neglected, a car model describing the impacts of actuators and road irregularities to the vehicle body through the suspension system becomes available.

The dynamics of the SMD system has two important parameters that completely define the dynamics of the SMD system: these are its undamped natural frequency and its damping ratio. The undamped natural frequency, ω, is given by the expression

mk

n′=ω , in radians/sec.

The undamped natural frequency is the frequency at which the mass will oscillate about the zero reference if

Fig.2. Full-car SMD model

ISBN: 978-960-6766-57-2 240 ISSN: 1790-5109

9th WSEAS International Conference on FUZZY SYSTEMS (FS’08) which was held in Sofia, Bulgaria

the mass is pushed down (or pulled up) and then let go. The actuators cause these movements. Theoretically, the oscillation will go on indefinitely since there is nothing to dissipate the original energy stored in the spring at its initial deflection (the spring is assumed to dissipate no energy. Since C=0, the natural frequency is a function only of the mass and the spring rate. As damping is added, frequency ( nω ) tends to reduce with increased C

(that is, If damping is light and oscillatory behavior is occurring) [5]. The method of CG position calculation in this paper is based on the height changes. So rectilinear system is used for height demonstration in the simulation.

2.2. Braking and Cornering Now, we introduce the dynamic forces, which act directly on the car body. In the other words, this description is concerned with load changes during suddenly braking and cornering. To describe how the braking and cornering affect the dynamic load, both influences can be analyzed separately due to the superposition principle [6]. The equations for each wheel are similar; hence equations for the front-left wheel only will be introduced and the others will be easy to derive. The front-left force acting on the wheel is:

leftfrontflfl pitchrollstaticload FFFF ∆+∆+=

In the above:

ddFF

llFF

lKlhmF

lKdhamF

dd

llgmF

lpitchpitch

frollroll

pitchpitch

pcxbodypitch

rollroll

rcybodyroll

rrbodystatic

left

front

fl

⋅∆=∆

⋅∆=∆

Φ⋅+⋅⋅=∆

Φ⋅+⋅⋅=∆

⋅⋅⋅=

υ&

For simplicity it is assumed that the body angle is proportional to horizontal forces. The symbol Φ indicates angle rate and the constants rollK and pitchK are the roll and pitch body stiffness, respectively [6]. The following assumptions are made for the angles:

ghmKhm

ghmKahm

pcbodypitch

xpcbodypitch

rcbodyroll

yrcbodyroll

⋅⋅−

⋅⋅=Φ

⋅⋅−

⋅⋅=Φ

υ&

where 9.8g = m/sec2 is the gravitation force. If these equations are included into the model, a full car model, which is able to simulate car driving with braking and cornering, will be obtained. The model developed above implies the question of how driver commands impact car motion through the Brake and steering wheel, in the lateral direction especially, so that this effect can be included in the model. The main problem is to determine the force acting on each wheel from the road, which impacts the spring and changes the height of the spring. In fact, this force depends mainly on the tire characteristics, which are strongly nonlinear, in particular during skidding. Moreover, even nonlinear tire models are very complicated and, therefore, in most applications a simple linear model is used. The side force acting on the wheels depends not only on the tires and road, but on the car speed too, because a real car must over- or understeer and therefore slip on the front and rear wheels is different and the radius of the curve varies for fixed front wheel angles. Fortunately, if some of these nonlinearities and dependencies are neglected, a relatively simple model of driver’s impact to the lateral behavior of the car can be observed [7]. If the car is cornering at high speed, we should consider over- or understeering behavior of the car. How the car behaves depends on the location of the center of gravity. Consequently, if the wheel angle is fixed, the radius of the curve increases with increasing speed of the car. Then, the radius is:

where K is the understeer gradient defined as:

where xTc is the tire coefficient. These coefficients

depend on the load and the slip of the wheels is nonlinear. If K is positive, then car is understeering and if K is negative, it is oversteering, i.e., the CG is toward the front or toward the rear of the car, respectively. For K equal to zero, the car has neutral steering and the radius is the same as for low speed turning [8]. It is obvious that to obtain an accurate lateral model of

the car responding to the driver’s commands is a very

)11

(rT

f

fT

rN cl

lcl

lFK −=

δυ 2KLR −

=

ISBN: 978-960-6766-57-2 241 ISSN: 1790-5109

9th WSEAS International Conference on FUZZY SYSTEMS (FS’08) which was held in Sofia, Bulgaria

complicated task for the purpose aimed in this paper. Therefore, we use fuzzy logic analysis to cover the

Fig.3. Steering mechanism

imprecision of vehicle dynamics nonlinearities. The simplistic model of vehicle dynamics is introduced only to organize our imagination in order to extract the fuzzy rules correctly. From the vehicle dynamics point of view, acceleration in each direction causes CG movement and change in rollΦ

, pitchΦ . Also dynamic forces on the vehicle influence

the suspension system, with resulting spring height change. Excluding small road disturbances that have no effect on the vehicle’s mass, we can suppose that any changes in vehicle’s dynamic forces will be detected as changes in the height of the springs.

By measuring the height of the springs, we can calculate the CG position and by derivation of the CG movement, the velocity can be calculated. Hence, a sensor that measures this height is an important instrument of the dynamic stability controller [9]. The perimeter in commonly used vehicles is a rectangular shape. Vertices of this rectangle are placed at the wheels. In rollover the perimeter changes and becomes smaller and it depends on the direction of rollover. For the sake of simplification, the three dimensional coordinate (X, Y, Z) in a vehicle is mapped to a two dimensional area (X,Y). Hence, the CG position in space is mapped to a rectangular area on the earth. The line between wheels about which the rollover occurs (inner wheels) is fixed. In the dynamic stability analysis section, we consider two parameters that are changed during vehicle instability: 1) position of the CG with respect to this line, and 2) velocity of the CG toward the line. These two parameters are factors to be considered in creating the fuzzy based controller for improving dynamic stability. The full calculations are mentioned in [10].

3. Driving crisis analysis

In this section we describe Driver consciousness (DC), data accuracy (DA), dynamic stability (DS) and crisis fuzzy analyzers. The structures of these fuzzy analyzers are so similar. We focus on the first, driver consciousness analyzer, and mention the membership functions, fuzzy rules and defuzzification method. Then the remaining analyzers will be briefly discussed. Three parameters (fatigue, amusement and noise) are inputs of the driver consciousness fuzzy analyzer. After fuzzification of inputs, the rules of consciousness detection are applied and the output (DC) is defuzzified using the centre of area method. The driver consciousness fuzzy analyzer designed in the paper consists of 18 rules which are derived from our imagination about logical relationships between parameters effective on driver consciousness. Some samples of these rules are given below [12, 13].

IfRDC :1 (Fatigue is L) and (Amusements is L) and

(Noises is L) then (DC is HH)

IfRDC :2 (Fatigue is M) and (Amusements is L) and

(Noises is L) then (DC is H)

IfRDC :3 (Fatigue is M) and (Amusements is L) and

(Noises is M) then (DC is MH) where low (L), medium (M), High (H) are linguistic values of fuzzy sets for the Fatigue, Amusement and noises [14]. For instance input and output fuzzy sets of "fatigue" are depicted in Figure 4. The fuzzy set of Driver consciousness is: Very Low (LL), Low (L), Low-Medium (LM), Medium (M), Medium-High (MH), High (H) and Very High (HH).

Fig.4. input and output fuzzy sets of "fatigue"

ISBN: 978-960-6766-57-2 242 ISSN: 1790-5109

9th WSEAS International Conference on FUZZY SYSTEMS (FS’08) which was held in Sofia, Bulgaria

We use a general form to describe these fuzzy rules [15]:

IfR iDC : (Fatigue is X11) and (Amusements is X21), and

(Noises is X31), then (DC is Y1), i =1… 18 where X11, X21 and X31 are triangle-shaped fuzzy numbers and Y is a fuzzy singleton. Let X and Y be the input and output space, and P, V be arbitrary fuzzy sets in X. Then a fuzzy set, iRVP o],[ in Y, can be determined by each iR . We use the sup-min compositional rule of inference:

)31().21().11( XXXm iiii NAFiDC µµµ= , i= 1...18

where )3(),2(),1( XXX iii NAF

µµµ are membership

functions of Fatigue, Amusement and noises parameters respectively. By using the center of area (centroid) method in the defuzzifier, we can obtain a crisp output DC:

∑

∑

=

=

⋅=

18

1

18

11

i

iDC

i

iiDC

i

i

m

ymDC

where iy1 is the centre of the iDC area. Figure 5 shows

two surfaces of 3-D surfaces of the fuzzy rules considered above. In each surface two of three inputs and the output (DC) are shown. All of the signals have normalized values. Here the rules of remaining fuzzy analyzers are formulized. In a same way a general form is used to describe the fuzzy rules of data accuracy (DA), dynamic stability (DS) and crisis fuzzy analyzers: IfR i

DA : (Network Delay is X12) and (Dust is X22), and (Light is X32), then (DA is Y2), i =1… 20

Fig.5. 3-D surfaces of the fuzzy rules

IfR iDS : (Position is X13) and (Velocity is X23) then

(DS is Y3), i =1… 35

IfR iCrisis : (Sensor1 is X14) and (Sensor2 is X24), and

(Sensor3 is X34), and (Sensor4 is X44), and (DC is X54), and (DA is X64), then (Crisis is Y4), i =1… 35

where ijX are triangle-shaped fuzzy numbers and Y is a

fuzzy singleton. The sup-min compositional rule of inference is used:

)32().22().12( XXXm iiii LDNDiDA

µµµ= , i= 1...20

)22().12( XXm iii VPiDS

µµ= , i= 1...35

)64().54(.

)44().34().24().14(4321

XX

XXXXm

ii

iiiii

DADC

SSSSiCrisis

µµ

µµµµ=

, i= 1...35 where )( ijparameter Xiµ is membership function each

parameter. By using the center of area (centroid) method in the defuzzifier, the crisp outputs can be obtained:

∑

∑

=

=

⋅=

20

1

20

12

i

iDA

i

iiDA

im

ymDA ,

∑

∑

=

=

⋅=

35

1

35

13

i

iDS

i

iiDS

im

ymDS ,

∑

∑

=

=

⋅=

35

1

35

14

i

iCrisis

i

iiCrisis

im

ymCrisis

ISBN: 978-960-6766-57-2 243 ISSN: 1790-5109

9th WSEAS International Conference on FUZZY SYSTEMS (FS’08) which was held in Sofia, Bulgaria

where iii yyy 432 ,, are the centre of the iii CrisisDSDA ,, areas respectively.

Fig.6. sensor #1-4 areas The output of the analyzers which can be seen as Crisis signal in figure1 diagram consists of all parameters mentioned above when proper fuzzy rules are applied. Crisis is a signal that represents the driving critical situation. This signal is the base of actuators. Actuators in this system monitor this signal and act when it is needed. The set of actuators considered in this paper includes the following:

a) an alarm system notifies the driver of driving and instability crisis before they occur,

b) actuators in the suspension change the

damper height.

c) brake by wire system for the cases in which driving crisis is because of obstacles in front of the vehicle.

steer by wire system changes the steering angle if driving crisis is because of the detection of obstacles by

lateral sensors (sensor #2 and sensor #4) (see figure 6). Changing the steering angle can also prevent overturn in vehicles, while it is need to use the steer by wire system for this purpose [7, 11]. The disadvantage of changing the steering angle is that the ordinary trajectory of the car will be changed.

4. Simulation Results

In this section we assume an irregular road for the vehicle and run the simulation in MATLAB/Simulink software. The passive suspension spring stiffness is

mNK p 12000= , passive suspension damping coefficient

is m

NsC p 4000= and the rigid mass of the vehicle’s body

is Kg1000 . For the fatigue, amusement, noises, network delay, dust, light and sensor #1-4 we used predefined signals as inputs (see figure 7). These signals practically come from the real sensors. In this simulation after producing crisis signal the activation of actuators can be seen. The dynamic stability and keeping kinetic balance during activation of actuators is also depicted.

Fig.7. predefined signals for fatigue, amusement, noises

0 2 4 6 8 10 12 14 16 18 20

0.4

0.5

0.6

0.7

0.8

0.9

1

Time

Driv

erC

onsc

usne

ss

Fig.8. the output of Driver consciousness fuzzy analyzer

ISBN: 978-960-6766-57-2 244 ISSN: 1790-5109

9th WSEAS International Conference on FUZZY SYSTEMS (FS’08) which was held in Sofia, Bulgaria

The output of Driver consciousness fuzzy analyzer, DC signal, is depicted in figure 8. The output of Data accuracy fuzzy analyzer, DA signal, is depicted in figure9.

0 2 4 6 8 10 12 14 16 18 200.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

0.6

Time

Dat

aAcu

racy

Fig.9. the output of Data accuracy fuzzy analyzer

The signals shown in figure… and figure… depict the crisis and dynamic stability crisis signals respectively. Combination of these signals, driving crisis, is monitored by actuators and alarm system. According to the figure10 the crisis signal has high amplitude from 6S to 17S meaning that in this period of time the situation of driving is dangerous and the alarm is activated and some of the actuators should also be activated according to this situation to reduce the danger of this situation.

0 2 4 6 8 10 12 14 16 18 200.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Time

Cris

is

Fig.10. crisis signal

As shown in figure11, the dynamic stability crisis signal has high amplitude from 6S to 11S that means in this period of time the dynamic instability (like rollover or skidding) may occur so in this period of time we expect the controller to activate proper actuators to keep kinetic balance of vehicle.

0 2 4 6 8 10 12 14 16 18 200.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

Time

Sta

bilit

ySig

nal

Fig.11. dynamic stability crisis signal

So the fuzzy analyzer declares the crisis before occurring.

−0.3−0.2

−0.10

0.10.2

−0.1

0

0.1

0.2

0.30

5

10

15

20

XY

Tim

e

Fig.12. CG position within the perimeter of the vehicle

Figure 12 shows the CG position within the perimeter of the vehicle in the XY plane during the time of simulation (Z axis). This curve shows the CG point didn't go out of perimeter. The width of perimeter is X=2 M and length of perimeter is Y=4 M. the analysis of the CG behavior within the perimeter gives us the danger of rollover and skidding.

Figure14 shows the old heights of the springs

rlrrfrfl AAAA ,,, which there were not any actuator

activated. The new heights of the springs

rlrrfrfl AAAA ,,, are after use of actuators. Between t1 to

t2 the driving crisis is high. So the system reduces the crisis by braking. Figure 13 shows the control signals imposed on brake actuator.

ISBN: 978-960-6766-57-2 245 ISSN: 1790-5109

9th WSEAS International Conference on FUZZY SYSTEMS (FS’08) which was held in Sofia, Bulgaria

The curves of the heights in this case are lower in amplitude in comparison with the previous cases. It means that the height difference between right side of the vehicle (

rrfr AA , ) and left side of the vehicle (rlfl AA , )

is decreased effectively by dynamic stability controller. So the crisis of the rollover and skidding will be decreased while the actuators are activated because of reducing danger of the obstacles.

Fig.14. the effect of dynamic stability control in spring heights Seeing the figure 14 we can observe that the heights of the springs are going to be stabilized. So the fuzzy controller can control the critical situations.

5. Conclusion

In this paper, an approach has been introduced for combining the obstacle avoidance and keeping internal dynamic stability in the vehicles. The main objective of

the paper has been to give a direction on how to analyze the driving crisis and dynamic stability. Fuzzy analyzers in this system use sensors and various actuators to detect driving crisis, avoid obstacles and prevent dynamic instability in critical situations. A demonstration in the Matlab/Simulink environment has been developed to demonstrate how the proposed fuzzy analyzers perform only in critical situations while it doesn’t interfere with ordinary driving. This idea can be developed in different types of the vehicles or even some kinds of robots. References:

[1] Dr. Laszlo Palkovics Director of Advanced Engineering, Identification and Control Problems in Vehicle System Design,Knorr-Bremse Publication, 1991

[2] Eric J. Rossetter , A Study of Lateral Vehicle Control under a `Virtual' Force Framework, Department of Mechanical Engineering, Stanford, California 94305-4021.

[3] Frederic Mastronardi, Marco Fenoglio, Vehicle Dynamics with Real Time Damper Systems, FIAT Auto Chassis Department, 1992.

[4] Mark D. Donahue, Implementation of an Active Suspension, Preview Controller for Improved Ride Comfort, Department of Mechanical Engineering, Boston University, 1998

[5] William F. Milliken, Douglas L. Milliken, Race Car Vehicle Dynamics, SAE International, ISBN: 1-56091-526-9

[6] Takahide Hagiwara Sergey, An application of a smart control suspension system for a passenger car based on soft computing, Mechanical Engineering, Stanford university, 1998.

[7] Christopher D. Gadda, Incorporating a Model of Vehicle Dynamics in a Diagnostic System for Steer-

Fig.13. the control signals imposed on brake actuators

ISBN: 978-960-6766-57-2 246 ISSN: 1790-5109

9th WSEAS International Conference on FUZZY SYSTEMS (FS’08) which was held in Sofia, Bulgaria

By-Wire Vehicles, Dept. of Mechanical Engineering, Stanford, California 94305-4021, AVEC ’04.

[8] Eric J. Rossetter, J. Christian Gerdes, Performance Guarantees for hazard based lateral vehicle control, Department of Mechanical Engineering Stanford University, Stanford, California 94305-4021, Copyright by ASME.

[9] Harry Lewellyn, Center of Gravity, Academic Publ., Ecological 4Wheeling Adventures REPRINT, Boston, 1994.

[10] Mohsen Davoudi, M. B. Menhaj, Mehdi Davoudi, A Fuzzy Based Vehicle Dynamic Stability Control (FDSC), SAE Commercial Vehicle Engineering Congress & Exhibition 2006, USA.

[11] Kenneth R. Buckholtz, Use of Fuzzy Logic in Wheel Slip Assignment: Yaw Rate Control with Sideslip Angle Limitation, Delphi Automotive Systems, Vehicle Dynamics and Simulation 2002 (SP–1656).

[12] B. G. Buchanan, E. H. Shortlire, Rule-Based Expert Systems, Addison-Wesley, Reading, MA, Menlo Park, CA, 1984.

[13] V. Novak, I. Per¯ lieva, J. Mo·cko·r, Mathematical principles of fuzzy logic, Kluwer Academic Publ., Boston/Dordrecht, 1999.

[14] V. Kreinovich, G. C. Mouzouris, H. T. Nguyen, Fuzzy rule based modeling as a universal approximation tool, In: H. T. Nguyen, M. Sugeno (eds.), Fuzzy Systems: Modeling and Control, Kluwer, Boston, MA, 1998, pp. 135195.

[15] Piero P. Bonissone, Fuzzy Logic and Soft Computing: Technology Development and Applications, General Electric CRD, Schenectady NY 12309, USA.

ISBN: 978-960-6766-57-2 247 ISSN: 1790-5109

9th WSEAS International Conference on FUZZY SYSTEMS (FS’08) which was held in Sofia, Bulgaria