Research Article Control of Yaw Disturbance Using Fuzzy Logic Based Yaw …downloads.hindawi.com/journals/ijvt/2014/754218.pdf · 2017. 11. 15. · Ko et al. proposed the fuzzy logic

Research ArticleControl of Yaw Disturbance Using Fuzzy Logic Based YawStability Controller

S. Krishna, S. Narayanan, and S. Denis Ashok

School of Mechanical and Building Sciences, VIT University, Vellore 632-014, India

Correspondence should be addressed to S. Krishna; [email protected]

Received 31 August 2013; Accepted 2 December 2013; Published 4 February 2014

Academic Editor: Shinsuke Hara

Copyright © 2014 S. Krishna et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Yaw stability is an important consideration for the vehicle directional stability and handling behavior during emergencymaneuvers.In order tomaintain the desired path of the vehicle, in presence of disturbances due to cross wind, different road conditions, and tiredeflections, a fuzzy logic based yaw stability controller is proposed in this paper. Proposed control system receives yaw rate error,steering angle given by the driver, and side slip angle as inputs, for calculating the additional steering angle as output, formaintainingthe yaw stability of the vehicle. As the side slip angle cannot be measured directly in a vehicle, it was estimated using a model basedKalman observer. A two-degrees-of-freedom vehicle model is considered in the present work.The effect of disturbance on yaw rateand yaw rate error of the vehicle is simulated for sinusoidal, step maneuver and compared with the existing fuzzy control systemwhich uses two inputs such as steering angle and yaw rate. The simulation results show better performance of the proposed fuzzybased yaw controller as compared with existing control system. Proposed fuzzy based yaw stability controller can be implementedin steer-by-wire system for an active front steering of a road vehicle.

1. Introduction

The modern automotive researches are focusing on autono-mous and semiautonomous ground vehicle to improve sta-bility and prevent the vehicles from spinning, drifting out,and rolling over. Yaw stability is one of the most significantaspects of the vehicle safety and yaw stability control canavoid dangerous, undesirable behaviors of the vehicles inextreme maneuvers. Active front steering control is one ofthe most practical approaches for yaw stability control inwhich a correction of steering angle is added to the driver’ssteering input, when the desired yaw rate of the vehiclefluctuates due to external disturbances. Steering actuatedyaw stability control gives maximum benefit with steer-by-wire systems, as mechanical linkages between the steeringwheel and road wheels are replaced with electronic actuators,which motivates easier implementation of active front wheelsteering control based on feedback.

Many research works are focusing on developing yaw sta-bility control systemswith steer-by-wire systems. Ackermann(1994) suggests a steering control system which achievesrobust decoupling of the vehicle’s for yaw stabilization and

(1997) yaw disturbance can also be minimized [1, 2]. Guenc,discusses the robust yaw stability control based on activefront steering for road vehicle and its performance wasverified using hardware in loop simulation [3]. Canale etal. suggest an internal model control and sliding modecontrol approaches for yaw stability control were designedand their performances are verified using simulation studies[4]. Falcone et al. proposed direct yaw moment controlmethod using in wheel motor control for enhancing vehiclestability [5]. Oncu proposed a disturbance observer basedyaw stability controller for light commercial vehicle [6].Nam developed a control system consisting of a steeringangle disturbance observer and proportional integral typetracking controller for robust control of yaw stability of anelectric vehicle [7]. A proportional integral and derivative(PID) control system is developed for yaw stability controlbased on road wheel steer angel as control input. Bianchiet al. proposed an adaptive integrated control system usingactive front steering and rear torque vectoring [8]. Arabi andBehroozi proposed an integrated vehicle dynamics controlsystem based on the combination of active front steering(AFS) and active rear differential (ARD) for yaw rate stability

Hindawi Publishing CorporationInternational Journal of Vehicular TechnologyVolume 2014, Article ID 754218, 10 pageshttp://dx.doi.org/10.1155/2014/754218

2 International Journal of Vehicular Technology

of the vehicle [9]. Hakima and Ameli presented an integratedcontrol approach for four-wheel steering of automotive sys-tem [10]. These control techniques are complex and theimplementation is difficult, as they require coordinated con-trol of vehicle subsystems for performing the desired controlfunction.

Many researchers have applied fuzzy logic approach fordeveloping active front wheel steering based yaw stabilitycontrol systems. Boada et al. applied fuzzy logic approach fordeveloping a control system tomaintain the targeted values ofyaw rate and side slip angle for a vehicle [11]. Sharif-Ul Hasanand Anwar designed a yaw stability controller of a vehicle viasteer-by-wire system [12]. Ko et al. proposed the fuzzy logicbased yaw stability controller based on the input parameterssuch as yaw rate and steering angle [13]. Goodarzi et al.designed a fuzzy controller based on yaw rate error, side slipangle, and a lateral acceleration of the vehicle for calculatingthe corrected steering angles of the front inner and outerwheels of the vehicle [14]. Ghosh et al. proposed fuzzy logicbased active yaw control algorithm, which receives yaw rateand steering angle as inputs for generating additional steeringangle [15]. Geng et al. used an observer based approach forestimating the body slip angle of a vehicle [16].

This paper presents fuzzy based yaw stability controlsystem which requires three input parameters which areyaw rate error, steering angle, and vehicle body side slipangle of the vehicle, for maintaining yaw rate of the vehicleby generating additional steering angle to the front wheelsof the vehicle. In distinction to the existing methods, theproposed fuzzy control system uses a Kalman filter basedobserver for body side slip angle estimation of the vehiclefor better maintenance of yaw rate error. Simulation resultsare presented for analyzing the performance of proposedapproach.

2. Vehicle Dynamics Model

In the present work, a three-degrees-of-freedom (DOF)vehicle model is considered for analyzing lateral dynamics ofthe vehicle, which is adapted from [1]. The vehicle dynamicsmodel used in present work is shown in Figure 1. This modeldescribes the lateral dynamics such as yaw rate ( 𝜓), lateralacceleration (𝑎𝑦), tire forces on front, and rear wheels.

Lateral acceleration is written as follows:

𝑎𝑦 =𝑦 + 𝑉𝑥

𝜓, (1)

𝑦 refers to acceleration of the vehicle in 𝑌-direction and 𝑉𝑥refers the longitudinal velocity of the vehicle.

The equation of lateral translation motion is

𝑚𝑎𝑦 = 𝑚 (𝑦 + 𝑉𝑥

𝜓) = 𝐹𝑦𝑓 − 𝐹𝑦𝑟. (2)

The terms 𝐹𝑦𝑓 and 𝐹𝑦𝑟 describe the respective tire forces onfront and rear wheels in “𝑌” directions of the vehicle. “𝑚”refers to the mass of vehicle and “𝑉𝑥” refers the longitudinalvelocity of the vehicle. Yaw angle of the vehicle, whichdescribes the orientation of the vehicle, is shown in Figure 2.

Figure 1: 2-DOF vehicle model, [1].

Figure 2: Lateral vehicle dynamics.

The actual yaw moment of the vehicle with externalmoment (𝑀𝑑) due to disturbance is given by

𝐼𝑧𝜓 = 𝑙𝑓𝐹𝑦𝑓 − 𝑙𝑟𝐹𝑦𝑟 +𝑀𝑑. (3)

Lateral tire forces of front and rear wheels of the vehicle areas follows:

𝐹𝑦𝑓 = 2𝐶𝑎𝑓 (𝛿 − 𝜃V𝑓) ,

𝐹𝑦𝑟 = 2𝐶𝑎𝑟 (−𝜃V𝑟) ;

(4)

𝑙𝑓 and 𝑙𝑟 refer to the longitudinal distance from CG to frontand rear tires, respectively, as shown in Figure 1. Here 𝐶𝑎𝑓and𝐶𝑎𝑟 represent the cornered force of front and rear wheels,respectively. 𝜃V𝑓 and 𝜃V𝑟 are the velocity angles of the front andrear tires, respectively.

The 𝜃V𝑓 and 𝜃V𝑟 can be calculated using the followingequations:

tan (𝜃V𝑓) =𝑉𝑦 + 𝑙𝑓

𝜓

𝑉𝑥

,

tan (𝜃V𝑟) =𝑉𝑦 − 𝑙𝑟

𝜓

𝑉𝑥

.

(5)

The vehicle body side slip angle 𝛽 is one of the importantparameters which gives the information about the chassis

International Journal of Vehicular Technology 3

Driver module

Yaw stability controller (steer-by-wire)

Vehicle dynamics

Desire yaw rate

Externaldisturbance

Given path Hand wheel angle

Yaw rate error

𝛽 Observer

Sideslip angle

Σ

{ ay

𝜓}

Figure 3: Block diagram of proposed yaw stability controller.

direction of the vehicle and it is calculated using the followingequation:

𝛽 = arctan(𝑉𝑦

𝑉𝑥

) . (6)

The rate of desired yaw orientation or yaw rate is defined asfollows:

𝜓des =

𝑉𝑥

𝑙𝑓 + 𝑙𝑟

𝛿. (7)

From the above equation, it can be noticed that the desiredyaw rate depends on steering angle given by the driver,speed of the vehicle. Desired yaw rate provides the expectedvehicle path information; however, due to external dis-turbance such as cross wind, asymmetric friction coeffi-cients on front, and rear tires, there exists an error inthe yaw rate and it can be calculated using the followingequation:

𝑒𝑟 =𝜓 −

𝜓des. (8)

In order to analyze the above vehicle dynamics in timedomain, a state space model for linear bicycle model with𝑥 = [𝛽

𝜓]

𝑇, 𝑦 = [𝑎𝑦𝜓]

𝑇 is used for analyzing yaw rateof the vehicle as given below:

[

𝛽

𝜓

] =

[

[

[

[

[

[

−𝐶𝑎𝑓 − 𝐶𝑎𝑟

𝑚V

−𝐶𝑎𝑓𝑙𝑓 + 𝐶𝑎𝑟𝑙𝑟

𝑚V2− 1

𝐶𝑎𝑟𝑙𝑟 − 𝐶𝑎𝑓𝑙𝑓

𝐼𝑧

−𝐶𝑎𝑓𝑙2

𝑓− 𝐶𝑎𝑟𝑙

2

𝑟

𝐼𝑧V

]

]

]

]

]

]

[

𝛽

𝜓

]

+

[

[

[

[

[

𝐶𝑎𝑓

𝑚V𝐶𝑎𝑓𝑙𝑓

𝐼𝑧

]

]

]

]

]

𝛿 +

[

[

[

[

[

1

𝑚V𝑙

1

𝐼𝑧

]

]

]

]

]

𝑀𝑑,

[

𝑎𝑦

𝜓

] =

[

[

−𝐶𝑎𝑓 − 𝐶𝑎𝑟

𝑚

−𝐶𝑎𝑓𝑙𝑓 + 𝐶𝑎𝑟𝑙𝑟

𝑚V0 1

]

]

[

𝛽

𝜓

]

+

[

[

[

𝐶𝑎𝑓

𝑚

0

]

]

]

𝛿.

(9)

3. Control System Design

The construction of proposed control system is shown inFigure 3. As the desired path of the vehicle depends uponthe steering angle, yaw rate error, and side slip angle, thesethree parameters are taken as inputs to the proposed controlsystem. Measurement of side slip angle is a difficult task;hence, an observer which uses a kalman filter is used in thepresent work. The steer-by-wire system receives the yaw rateof a vehicle using a yaw rate sensor and yaw rate error iscalculated using the actual vehicle model. A correction inthe steering angle is estimated using the fuzzy logic controlsystem,whichwill be applied to the frontwheels of the vehiclefor maintaining the desired path of the vehicle.

The observer model to estimate the side slip angle ofthe vehicle using Kalman filter is discussed in the nextsection.The description about the fuzzy control system, suchas fuzzification, fuzzy rules and inference, defuzzification isdiscussed in the subsequent sub sections.

3.1. Sideslip Angle Observer. Sideslip angle is an importantparameter which is useful for determining the actual stabilitycondition of a vehicle. In this work, a linear observer isused for estimating the sideslip angle because sensors formeasuring side slip angle are more expensive. A model basedKalman filter is used for estimating the sideslip angle valueusing lateral acceleration and yaw rate has input as given in(9). The state equations for the observer are given below:

�� = 𝐴𝑥 + 𝐵𝑢 − 𝐾 (𝑦 − 𝑦) . (10)


−2 −1.5 −1 −0.5 0 0.5 1 1.5 20

0.5

1NB NS Z PS PB

(a) Steering angle

−2 −1.5 −1 −0.5 0 0.5 1 1.5 20

0.5

1 NB NS Z PS PB

(b) Yaw rate error

−4 −3 −2 −1 0 1 2 3 40

0.5

1 Low High

(c) Side slip angle

Figure 4: Membership functions for input variables.

The output of the observer is given by the following equation:

𝑥 = [

𝛽

𝜓

] 𝑦 = [

𝑎𝑦

𝜓

] . (11)

The model for determining Kalman gain (𝐾) [16] is shownbelow:

𝐾 =

[

[

[

[

[

[

[

[𝐶

𝑎𝑓𝑙

𝑓− 𝐶

𝑎𝑟𝑙

𝑟] 2 (𝜆

1𝜆

2) 𝐼

𝑧

(4𝐶

𝑎𝑓𝐶

𝑎𝑟) (𝑙

2)

− 1

1

V

−𝜆

1− 𝜆

2

𝑚[𝐶

𝑎𝑓𝑙

2

𝑓+ 𝐶

𝑎𝑟𝑙

2

𝑟]

[𝐶

𝑎𝑓𝑙

𝑓− 𝐶

𝑎𝑟𝑙

𝑟] 𝐼

𝑧

]

]

]

]

]

]

]

, (12)

in which 𝜆1 and 𝜆2 are the assigned pole values of theobserver.

3.2. Fuzzification. Proposed fuzzy control system with threeinputs and one output is developed. The input variable,side slip angle is fuzzified to have two fuzzy sets, namely,Low and High. The steering angle and yaw rate error arefuzzified into five fuzzy sets: negative big (NB), negative small(NS), zero (Z), positive small (PS), and positive big (PB).The output variable, steering correction angle is fuzzifiedto have eleven fuzzy sets: (NB, NMH, NM, NMS, NS, Z,PS, PMS, PM, PMH, PB), where NMH and PMH representNegativeMediumHigh andPositiveMediumHigh.NMS andPMS represent Negative Medium Small, Positive MediumSmall. NM and PM represent Negative Medium and PositiveMedium. Membership functions for the input and outputvariables of the fuzzy control system are shown in Figures 4and 5, respectively.

−2 −1.5 −1 −0.5 0 0.5 1 1.5 20

0.5

1NH NMH NM NMS NS Z PS PMS PM PMH PB

Figure 5: Membership functions for the output variable: correctionangle.

3.3. Fuzzy Rules. For the given input values of steering angle,side slip angle, and yaw rate error, fuzzy ruleswere formulatedfor inferring the output correction angle to the front wheelusing steer-by-wire system. By using fuzzy theory, proposedfuzzy control system uses Mamdani fuzzy inference system,which is characterized by the following fuzzy rules as shownin Table 1.

4. Simulation Results and Analysis

Performance of the proposed fuzzy control system is com-pared with the existing fuzzy control system, which uses onlytwo inputs such as steering angle of the front wheel andyaw rate error [15]. A simulation study was conducted usingSimulink inMatlab for sinusoidal and step steeringmaneuver(in Figure 6) with the external disturbance (in Figure 7),which can be caused by asymmetric friction coefficients at theleft and right tires.The simulation results are presented for thedifferent vehicle speeds such as 10m/s and 30m/s.The vehicle


−15

−10

−5

0

5

10

15

20Steering wheel angle (deg) versus time

0 1 2 3 4 5 6 7 8 9 10−20

(a) Sinusoidal input

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25Steering wheel angle (deg) versus time

(b) Step input

Figure 6: Steering inputs.

parameters used for the computer simulations are given inTable 2.

4.1. Sinusoidal Maneuver. A sinusoidal steering input can beassociatedwith a slalom test, which is performed for assessingthe yaw roll stability of a vehicle. Figures 8 and 9 show thecomparison of vehicle responses for the yaw rate and yaw rateerror of the vehicle during sinusoidalmaneuver. It is observedthat the yaw rate error and amplitude of disturbance aremuchlesser for the proposed control system than the existingmodeland uncontrolled vehicle. The proposed fuzzy controller

0 1 2 3 4 5 6 7 8 9 10−100

0100200300400500600700800900

Time (s)

Figure 7: External disturbance.

Table 1: Fuzzy interference rule.

Side slipangle Steering angle Yaw rate error

NB NS Z PS PB

Low

NB NS NS Z PB PBNS NMS NMS Z PMH PMHZ NM NM Z PM PMPS NMH NMH Z PMS PMSPB NH NH Z PS PS

High

NB NH NH Z PS PSNS NMH NMH Z PMS PMSZ NM NM NS PMS PMSPS NMS NMS NS NS NSPB NS NS NS NS NS

Table 2: Vehicle parameters.

Vehicle mass (𝑚) 1663KgYaw moment of inertia (𝐼

𝑧) 2704Kgm2

Distance from front axle to CG (𝑙𝑓) 1.1437m

Distance from rear axle to CG (𝑙𝑟) 1.431m

Wheel base (𝑙) 2.56mFront tyre cornering stiffness (𝐶

𝑎𝑓) 63946N/rad

Rear tyre cornering stiffness (𝐶𝑎𝑟) 55040N/rad

Vehicle speed (V) 10m/s and 30m/s

was performing better in both low speed and high speed.It means that vehicle with the proposed controlled systemfollows the desired path much closer than the uncontrolledvehicle.

4.2. Step Maneuver. The step input has been used to sim-ulate conditions similar to the straight line cornering test.Responses for the yaw rate, side slip angle, and yaw rate errorof proposed model are compared with the existing approachand uncontrolled vehicles for step steering input as shownin Figures 10 and 11. As in the previous case of sinusoidalsteering input, the vehicle with the proposed control systembehaves in a stable manner at low speed and high speed with


0 1 2 3 4 5 6 7 8 9 10−20

−15

−10

−5

0

5

10

15

20Yaw rate (deg/s) versus time (s)

Proposed approach/1Existing approach/1Without controller/1Reference

(a) Yaw rate

−6

−4

−2

0

2

4

6

8 Yaw rate error (deg/s) versus time (s)

0 1 2 3 4 5 6 7 8 9 10−8

Proposed approach/3Existing approach/3Without controller/3

(b) Yaw rate error

−2

−1

0

1

2

3Side slip angle (deg) versus time

0 1 2 3 4 5 6 7 8 9 10−3


(c) Estimated sideslip angle

Figure 8: Vehicle response for sinusoidal input with external disturbance for 10m/s.


0 1 2 3 4 5 6 7 8 9 10−25

−20

−15

−10

−5

0

5

10

15

20



(a) Yaw rate

0 1 2 3 4 5 6 7 8 9 10−10

−8

−6

−4

−2

0

2

4

6

8

10Yaw rate error (deg/s) versus time (s)


(b) Yaw rate error

0 1 2 3 4 5 6 7 8 9 10−8

−6

−4

−2

0

2

4

6

8Side slip angle (deg) versus time



Figure 9: Vehicle response for sinusoidal input with external disturbance for 30m/s.

low yaw rate error and effect of disturbance as compared withthe uncontrolled vehicle. Also the responses to yaw rate of

vehicle with the proposed control system is closer to referenceas shown in Figure 11(a).


0 1 2 3 4 5 6 7 8 9 100

5

10

15

20



(a) Yaw rate

0 1 2 3 4 5 6 7 8 9 10−1

0

1

2

3

4

5

6

7



(b) Yaw rate error

0 1 2 3 4 5 6 7 8 9 10−0.5

0

0.5

1

1.5

2

2.5

3

3.5Side slip angle (deg) versus time



Figure 10: Vehicle response for step input with external disturbance for 10m/s.

5. Conclusion

This paper proposes a fuzzy logic based yaw stability con-troller for active front steering of the vehicle. Proposedcontrol system takes steering angle, yaw rate error, side slip

angle as inputs and estimates the additional steering angle tobe applied to the front wheel of the vehicle for maintainingyaw stability of the vehicle.Mathematicalmodel for the lateraldynamics of vehicle is derived for determining the yaw rateerror of the vehicle. A linear observer model is used for


0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25



(a) Yaw rate

0 1 2 3 4 5 6 7 8 9 10−2

0

2

4

6

8



(b) Yaw rate error

0 1 2 3 4 5 6 7 8 9 10−1

0

1

2

3

4

5

6

7

8

9 Side slip angle (deg) versus time



Figure 11: Vehicle response for step input with external disturbance for 30m/s.

estimating the side slip angle of the vehicle. The performanceof the proposed fuzzy based yaw stability control system hasbeen evaluated using computer simulations with sinusoidaland step input maneuver. Simulation results show that the

proposed system has smaller yaw rate error and maintainthe stability of the vehicle under disturbance conditionalso, as compared with the existing model and uncontrolledvehicle.


Nomenclature

𝑎𝑦: Lateral acceleration𝐹𝑦𝑓: Lateral tire force on front wheels𝑉𝑥: Longitudinal velocity𝐹𝑦𝑟: Lateral tire force on rear wheels𝑉𝑦: Lateral velocity𝑙𝑓: Longitudinal distance from CG to front tires𝑚: Mass of the vehicle𝑙𝑟: Longitudinal distance from CG to rear tires𝐼𝑧: Yaw moment of inertia of vehicle𝐶𝑎𝑓: Cornering stiffness of front tires𝜓: Yaw angle of vehicle𝐶𝑎𝑟: Cornering stiffness of rear tires𝜓: Yaw velocity of vehicle𝜃V𝑓: Velocity angle of front tires𝛿: Road wheel angle𝜃V𝑟: Velocity angle of rear tires𝑀𝑑: External Disturbance.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of the paper.

References

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[2] J. Ackermann and T. Bunte, “Yaw disturbance attenuation byrobust decoupling of car steering,” Control Engineering Practice,vol. 5, no. 8, pp. 1131–1136, 1997.

[3] B. A. Guenc, L. Guvenc, and S. Karaman, “Robust yaw stabilitycontroller design and hardware-in-the-loop testing for a roadvehicle,” IEEE Transactions on Vehicular Technology, vol. 58, no.2, pp. 555–571, 2009.

[4] M. Canale, L. Fagiano, A. Ferrara, and C. Vecchio, “Vehicleyaw control via second-order sliding-mode technique,” IEEETransactions on Industrial Electronics, vol. 55, no. 11, pp. 3908–3916, 2008.

[5] P. Falcone, F. Borrelli, J. Asgari, H. E. Tseng, and D. Hrovat,“Predictive active steering control for autonomous vehiclesystems,” IEEE Transactions on Control Systems Technology, vol.15, no. 3, pp. 566–580, 2007.

[6] S.Oncu, S. Karaman, L. Guvenc et al., “Robust yaw stability con-troller design for a light commercial vehicle using a hardware inthe loop steering test rig,” in Proceedings of the IEEE IntelligentVehicles Symposium, pp. 852–859, June 2007.

[7] K. Nam, S. OH, H. Fujimoto, and Y. Hori, “Robust yaw stabilitycontrol for electric vehicles based on active front steeringcontrol through a steer-by-wire system,” International Journalof Automotive Technology, vol. 13, no. 7, pp. 1169–1176, 2012.

[8] D. Bianchi, A. Borri, M. D. Di Benedetto, S. Di Gennaro, and G.Burgio, “Adaptive integrated vehicle control using active frontsteering and rear torque vectoring,” International Journal ofVehicle Autonomous Systems, vol. 8, no. 2–4, pp. 85–105, 2010.

[9] S. Arabi and M. Behroozi, “Design of an integrated active frontsteering and active rear differential controller using fuzzy logic

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[10] A. Hakima and S. Ameli, “Improvement of vehicle handling byan integrated control systemof fourwheel steering andESPwithfuzzy logic approach,” in Proceedings of the 2nd InternationalConference on Mechanical and Electrical Technology (ICMET’10), pp. 738–744, September 2010.

[11] B. L. Boada, M. J. L. Boada, and V. Dıaz, “Fuzzy-logic appliedto yaw moment control for vehicle stability,” Vehicle SystemDynamics, vol. 43, no. 10, pp. 753–770, 2005.

[12] M. Sharif-Ul Hasan and S. Anwar, “Yaw stability controlsystem for an automobile via steer-by-wire,” in Proceedings ofthe 4th International Conference on Electrical and ComputerEngineering (ICECE ’06), pp. 345–348, December 2006.

[13] S.-J. Ko, J.-J. Kim, and J.-J. Lee, “Yaw stabilization of a vehicleby yaw stability controller based on fuzzy logic,” in Proceedingsof the 8th Symposium on Advanced Intelligent System (ISIS ’07),Sokcho-city, Republic of Korea, 2007.

[14] A. Goodarzi, S. Arabi, and E. Esmailzadeh, “Design of anintegrated AFS/ACD control system to enhance 4WD vehiclesdynamics and stability,” in Proceedings of the InternationalDesign Engineering Technical Conferences and Computers andInformation in Engineering Conference (IDETC/CIE ’10), pp.307–314, can, August 2010.

[15] S. Ghosh, A. Deb, M. Mahala, M. Tanbakuchi, and M.Makowski, “Active yaw control of a vehicle using fuzzy logicalgorithm,” SAE International, 2012-01-0229.

[16] C.Geng, T.Uchida, andY.Hori, “Body slip angle estimation andcontrol for electric vehicle with in-wheelmotors,” inProceedingsof the 33rd Annual Conference of the IEEE Industrial ElectronicsSociety (IECON ’07), pp. 351–355, November 2007.

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Research Article Control of Yaw Disturbance Using Fuzzy Logic Based Yaw …downloads.hindawi.com/journals/ijvt/2014/754218.pdf · 2017. 11. 15. · Ko et al. proposed the fuzzy logic