四轮转向investigation of automatic path tracking control using four-wheel steering vehicle

1、Yaw moment control of four wheel steering vehicle by fuzzy approachR.KazemiDepartment of Mechanical Engineering, K.N.Toosi University of Technology, Tehran, Iran P.O.Box: 16765-3381E-mail:kazemikntu.ac.irM.Keshavarz Bahaghighat Department of Mechanical Engineering, K.N.Toosi University of Technology

2、, Tehran, IranP.O.Box: 16765-3381Email:K.PanahiDepartment of Mechanical Engineering, K.N.Toosi University of Technology, Tehran, Iran P.O.Box: 16765-3381E-mail:considered. In 5four wheel steering system using fuzzyAbstract-In this paper the influence of rear s

3、teering system on stability and manoeuvrability of a vehicle using nonlinear model is investigated. Proposed mathematical model consists of 7-dof vehicle model which nonlinearity of tire characteristics is considered in. Next, based on the nonlinear model, fuzzy control system is developed to improv

4、e the handling and stability of vehicle. The advantages of coordinating four wheel steering system are demonstrated through computer simulations in lane- change manoeuvres for condition of dry road.TSK model is presented.Since 1980s, four wheel steering system has been considered by engineers to inc

5、orporate the concept of control in the area of vehicle dynamic performance. First-generation 4WS transmitted the angle of the front wheels to the rear wheels mechanically by means of a shaft. This assembly adjusts the angle of the front wheels and turns the rear wheels in the same phase as the front

6、 wheels when the steering wheel was turned at a small angle and in the opposite direction when it was turned at a large angle. This provided excellent stability at high speeds when the steering angle was low, and a very small turning circle at low speeds (Sano, Furukawa, & Shiraishi, 1986). In addit

7、ion to the steering angle-responsive system described above, there are various other types of 4WS, including systems which steer the rear wheels in response to the amount of steering force input (Shibahata, Irie, Itoh, & Nakamura, 1986), and systems which steer the rear wheels using the yaw rate as

8、a feedback signal (Inoue, Kawai, Inagaki, Tanaka, & Kawakami, 1991). 6This paper proposes a new method for nonlinear control ofthe four wheel steering system which is based on the fuzzy logic inference system. The goal of this investigation is to coordinate steering to improve vehicle steerability a

9、nd handling. As a consequence of nonlinearity of yaw and lateral characteristics, a fuzzy method is applied to achieve high performance of vehicle in severe manoeuvres. This paper is organized as follows. In section II the equations of mathematical model of the vehicle and tire model are exposed. Th

10、ese equations, then, are used to create a model- based design of vehicle via MATLAB-SIMULINK. In section III the fuzzy logic based control system is presented. In section IV, firstly, to validate the proposed model, the results of open-loop simulation are compared to the experimental results present

11、ed in 7 and then the simulation results of controlled vehicle are illustrated and compared to uncontrolled vehicle simulation results. Finally, the conclusion is proposed in section V.I.INTRODUCTIONIn the recent decades, achieving automotive stability and high performance has continuously been of co

12、nsiderable attention, and many attempts have been done toward improving vehicle security. However, the number of road accidents still significantly remains high. In order to prevent this obstacle, control systems must be developed and installed. One of most important criterion of vehicle handling re

13、fers to the yaw motion that participates as an outstanding factor in automobile stability and manoeuvrability. So as to control yaw motion, so many methods have been considered such as direct yaw moment control (DYC), active front steering (AFS), braking and traction control and also four wheel stee

14、ring system (4WS). Instability of the vehicle typically results from the limitation of the road coefficient of friction which limits the tire forces, in severe manoeuvres. A way to overcome the instability in vehicle relatively is by using of all wheels to steer. The rear wheels can engage in steeri

15、ng system using this method. The control system doesnt interfere in driver command but assists the driver in terms of following the drivers intention. With the proper coordination of 4WS, enhanced improvement might be achieved even in severe conditions and manoeuvres.Integrated control of four wheel

16、 steering and four wheel torque in order to increase vehicle stability has been applied in 1.In 2 cooperation of active front angle and direct yaw moment is introduced. In 3 fuzzy logic control system was applied to the design of combined braking and active front steering. In 4 the effectiveness of

17、coordinating lateral dynamic controller on the vehicle stability has been978-1-4244-1706-3/08/$25.00 2008 IEEE.NOMENCLATUREVehicle mass. Yaw rate.lrl fm rvxFx2FFy 2x 4FLongitudinal velocity. Lateral velocity.Lateral tire force. Longitudinal tire force. Normal tire force.Steer angle.Distance between

18、C.G. and front axle. Distance between C.G. and rear axle. Desired yaw rate.Error between yaw rate and desired value. Wheel base.Distance between tires in same axle.Vehicle mass moment of inertia about z-z axis. Wheel mass moment of inertiaHeight of C.G.Effective radius of each wheel. Angular velocit

19、y of each wheel. Coefficient of friction.Understeer gradient.y 4rvxLxwvVyvyFyixiFzidl flr rde l LwI zIwddrfFFFy3Fx1v xy1yFig. 1. Planar vehicle model.L f ( Fy1 + Fy 2 ) cos d f + ( Fx1 + Fx 2 ) sin d f )- Lr ( Fy 3 + Fy 4 ) cos d r + (Fx3 + Fx 4 ) sin d r )Lw+( F- F ) sin d+ ( F- F ) cos d )y1y 2fx

20、2x1f2L(3)w+( F- F) sin d + (F- F ) cos d )y 3y 4rx 4x 3r2= I z .rRwF x-i T +bi T =aIi wi = (1,.,4)(4)hw ic. g .A.Tire loadRwThe tire force depends apparently on the static force of thewvehicle weight, and the transferred load based on longitudinal and lateral acceleration. Despite the exclusion of t

21、he pitch and roll motions, their effects on the normal tire force as the result of the longitudinal and lateral acceleration are considered. So the tire forces can be stated as below:ik- 0.5 maxhc. g + mlr ayhc.gF= 0.5 mglrVEHICLE DYNAMICS MODELII.z1LmglLL.LwThe 7-DOF vehicle model using nonlinear t

22、ire model has been introduced for controller design. Degrees of freedom consist of longitudinal and lateral motion, rotations of wheels and yaw rate. In this study, the roll and pitch motions of vehicle are neglected due to simplifying the model and also easy-tracking into the equations of motion. T

23、he external forces acting on the vehicle explicitly come to result from the interaction between the road and the tire. Considering thesema hml a hx c. gLr y c.gF= 0.5r -0.5z 2LL.LwF= 0.5 mgl f+ 0.5 maxhc.g + ml f ay hc.gz 3LLL.Lw(5)F= 0.5 mgl f+ 0.5 max hc. g - ml f ay hc.gforces as depicted in Fig.

24、1 the motion equations derived as follow:can bez 4LLL.LwFx1 cosd f + Fx2 cosd f + Fx3 cosdr + Fx4 cosdr- Fy1 sin d f - Fy2 sin d f - Fy3 sin dr - Fy4 sin dr= m (v x - vyr)Longitudinal and lateral forces which are the result of the interface between tire and road friction, depend on the tire slip ang

25、le and also longitudinal slip. According to the Fig.2 slip angle is defined as below:(1)Fy1 cos d f + Fy2 cos d f + Fy3 cos d r + Fy4 cos d r+ Fx1 sin d f + Fx2 sin d f + Fx3 sin dr + Fx4 sin d r= m (v y + vxr)(2)x ui - Rewidu1Rewi uifuiaV= vx11(8)Siui - RewiR w ul fR we iie ivyyL / 2wFig. 2. Side-s

26、lip angle and steering angle.A.Tire modelAs a consequence of the nonlinearity of tire characteristics,v y + l f rthe tire model which is used for this investigation is combined magic formula tire model. The advantage of this tire model aims to the interplay of the lateral force, longitudinal force a

27、nd moreover the self-aligning torque on each other. Lastly, the integrated equations below stand for the tire model 9:a 1 = tan -1 - d f vL+ rwx2v y + l f ra = tan-1 - dFx= F x0G(9)2L fxa v-r wx sinCx x )+ Sx2Fx0 = Dx x - Ex(B kx x - arctan( B kx arctan( B kVx (10)(6)v y - lr ra = tan-1 - dIn these

28、equations, Fx0is longitudinal force for the condition of pure slip, Fx is the longitudinal force for condition of3r L v +w r Gxcombined slip and force:is the weighting function. For lateral2xav y - l f rFy = Gyk Fy 0 + SVyka 4 = tan-1 - d r(11) vLwr -F = D sinC arctan(B a - E (B a - arctan(B a )+ Sx

29、2(12)y 0yyy yxy yy yVyAs in equations above, Fy0 is lateral force for the condition of combined slip. Aligning torque is defined as follow:The prominent factor, that should be deliberated in order to identify longitudinal slip, is to determine the component of the velocity on the wheel center which

30、is definitely parallel to the vertical wheel plan. This factor for each wheel is specified as follow:M z = (M prim z + M z0 + (R0 (Ssz1+ (Ssz 2 (Fy / Fz0 ) Fx ) (13)Where Mz is aligning torque for the condition of combined slip. The complete equations and also constants and symbols are gathered in 9

31、.L u = (v - r ) cos d f + (v+ l r ) sin d fw1xyf2III.CONTROLLER DESIGNLu2= (v +x w r ) cos d + f(v + lyr ) sfin df2A.Fundamental structure of control system.(7)The main goal is to improve handling and stability of vehicle which are directly related to yaw rate and side slip angle values. In this stu

32、dy, due to the nonlinearity of the vehicle model and natural complexity of vehicle dynamics and effectiveness of soft computing paradigms like fuzzy logic method in solving the difficult problems of control of the nonlinear dynamical systems, the fuzzy approach is applied for controller design. The

33、control system is developed to enhance stability and handling of the vehicle by controlling two values of yaw rate error and change in yaw rate error as inputs. Output of the control system is rear steering angle value.Lu = (v -r) cos d + (v - l r ) sin dw3xryrr2Lu = (v +r) cos d + (v - l r )sin dw4

34、xryrr2Finally, longitudinal slip is exclusively obtained as follows:B.Desired modelReference signal used for calculating input values are7:Vxdrd =f(14)kVx 2l +gWhere rdis desired yaw rate, Vx is longitudinal velocity ofvehicle and k is under steering coefficient, d f is front steering angle and l is

35、 wheelbase. Thus outputs of desired model -yaw rate error and change in yaw rate error- are calculated as follows:Fig.5. Change in yaw rate error membership functions.TABLE IRULE BASEe = r - rdesireddesired(14)(15)e = r - rC.Fuzzy controllerDesigned controller is MISO withInference system ofMamdani

36、using implication method of minimum and aggregation method of maximum as follows 10:IF e is ei AND e is e j THEN j is jkmj = min(me , me )(16)(17)IV.SIMULATIONkijeiA. Model validationIn order to evaluate mathematical model of vehicle, simulation result was compared to the real car data. Vehicle para

37、meters and experimental results which have been used are referred to 7.Fig.6 shows the vehicle model yaw rate and lateral acceleration compared to real car data. As it shown, using theWherefor i=1-6 are errors of yaw rate membershipfunctions and e j for j=1-6 are errors of change in yaw ratejkmember

38、ship functions. Andfor k=1-9 are membershipfunctions which represent fuzzy sets assigned to the output by consequent of fuzzy rules.Figs. 3-6, show membership functions of yaw rate error and change in yaw rate error and rear steering angel. Table 1, illustrates general structure of designed rule bas

39、e.Fig.3. Yaw rate error membership functions.Fig.6. Validation of model, initial speed of 80km/hr and input steering angel of 2.25(a) yaw rate comparison (b) lateral acceleration comparison. 7Fig.4. Rear wheel steering angel membership functions.een2n1zp1p2n2P4P3P2P1Zn1P3P2P1ZN1zP2P1ZN1N2p1P1ZN1N2N3

40、p2ZN1N2N3N4vehicle data gathered from 7 and running the simulation with the same condition as described in 7, in Fig.6.a we getaround 2nsdecondbutthethe same pick for yaw ratesimulation test result at the 7thsecond differs about 23percent. it is the same with less difference, for lateral acceleratio

41、n. There is two main causes for this situation, the error in measurement tools which lead the experimental results to show oscillatory characteristics and the road profile which assumed to be perfectly smooth in the simulation.B.Simulation resultsSeries of tests have been carried out on vehicle mode

42、l toevaluate performance of the proposed controller compared to conventional vehicle.Single lane change test was performed, with front steering angel of 0.05 rad and in the condition of dry road (=0.8).Differences of vehicles main response parameters to these maneuvers with and without 4ws controlle

43、r are presented in Figs. 7-10. Compared main parameters are front and rear steering angel, yaw rate, side slip angel, vehicles position and longitudinal velocity. Proposed fuzzy controller clearly demonstrates higher level of performance in handling and maneuverability of vehicle. In Fig.7, the resu

44、lts of the lane change test clearly shows effectiveness of designed control system in stability of the vehicle. As it is depicted in Fig.7 (a), the yaw rate response in controlled model respectfully follows the desired value but uncontrolled model shows unstable behavior in the same condition of the

45、 test. Also, in Fig.8 (b), Yaw rate versus lateral acceleration response is shown for both controlled model and uncontrolled model in which the priority of controlled model can be explicitly considered. Specially in Fig.10 (b), it is obvious that the controlled(b)vehicledemonstratesdesiredbehaviorwh

46、ereastheuncontrolled vehicle completely shows undesired behavior.(c)(a)(d)Fig.7. Vehicle responses in a lane change test, with and without 4ws system. Initial velocity of the vehicle is 80km/hr. (a) desired yaw rate compared to open loop and closed loop yaw rates. (b) Side slip angel. (c) Longitudin

47、al speed. (d) Position of vehicle(a)(b)Fig.8. (a) Front and rear steering angels in a lane-change maneuver (b) Yaw rate value versus lateral acceleration value, initial speed is 80km/hr.aabcdFig.9. (a) Front and rear steering angels in a lane-change maneuver. (b) Desired yaw rate compared to open lo

48、op and closed loop yaw rates. (c) Side slip angel. (d) Vechiles position, initial speed is 120km/hr.abFig.10. Lane-change maneuver , initial speed is 120 km/hr.(a) Longitudinal speed. (b) Yaw rate value versus lateral acceleration.7T.J.Park, C.S.Han, S.H.Lee, “development of electric control unit fo

49、r the rack-actuating-steer-by-wire using the hardware-in-the-loop simulation system,” Elsevier Ltd., Mechatronics, 2005, pp.889-918 T.D.Gillespie, “Fundamentals of vehicle dynamics,” society of automotive engineers, Third printing, 1994H.B.Pacejka, “Tyre and vehicle dynamics,” MPG books ltd, 2002, pp.184-190J. S. R. Jang et al., “Nero-Fuzzy and soft computing,” Englewood Cliffs, NJ: Prentice-Hall, 1997.V.CONCLUSIONIn this paper a four wheel steering system based on controlling vehicles yaw rate was introduced. Considering the nonlinearity and complexity of vehicle and tire