Vehicle Handling Improvement with Steer-by-Wire System Using Hardware in the Loop Method

Transcription

1 Vehicle Hanling Improvement with Steer-by-Wire System Using Harware in the Loop Metho V. avoosi*, R. Kazemi an S. M. Hosseini Department of Mechanical Engineering K.N.oosi University of echnology, ehran, Iran ABSRAC In this paper, a control algorithm for improving vehicle hanling has been propose by applying correction angle to the steere wheel, base on the optimal an aaptive theory using Simulink MALAB software. A 4DOF moel with nonlinear tire an SBW subsystem is presente using harware in the loop metho. Since some space variables cannot be measure, an estimator is use to extract the measurable variables from the simulate moel an convert them to the require variables of the controller. hese variables are transmitte to the controller an then it aopts itself with new conitions an applies the best moification on the steering. he results reveal that the propose controller can significantly improve vehicle hanling uring severe maneuvers. Keywors: Hanling; vehicle; steer-by-wire; controller; harware in the loop metho. 1. Introuction he automobile inustry is currently working on new Drive-By-Wire (DBW) systems in which mechanical an hyraulic subsystems, such as steering, braking an suspension, are being replace by electronic actuators, controllers, an sensors. he benefits of applying electronic technology, like DBW systems, are clear: improve overall performance an riving convenience reuce power consumption an significantly enhance passenger safety. Steer-by-wire systems are a relatively new evelopment compare to the traitional mechanical, hyraulic, or electric steering systems that are currently use for motor vehicles. In Steer-By-Wire (SBW) systems, a part of the DBW, the conventional mechanical interface between the steering wheel an the front wheels is replace with electronic actuators. he elimination of parts, such as the steering column, gear box an hyraulic pump, provies avantages incluing saving energy, ecreasing noise an vibration, reucing weight an removing environmentally hazarous hyraulic fluis. Moreover, in front-en collisions, the anger of a river being crushe is reuce because there is no steering column [1-]. here are several main steering function requirements for a steer-by-wire system: (1) Directional control an wheel synchronization: Directional control is the basic requirement for vehicle steering systems, incluing steer-by-wire systems. It is require that roa wheels follow the river s input comman from the steering wheel an the possible input commans from the supervisory vehicle control systems accoring to vehicle ynamics requirements. he roa wheels shoul maintain synchronization with the steering wheels in real time without bias, offset, or time elay. () Ajustable variable steering feel: he steering feel provies information on the force (or torque) at the roa wheel tire-roa surface contact an varies epening on roa conitions. his force/torque information shoul be fe backe to the steering wheel to prouce steering wheel torque that can be felt by the vehicle river. he vehicle river relies on the steering feel to sense the force of roa wheel tire-roa surface contact an maintain control of the vehicle. hus, steering feel has been becoming one of most important vehicle attributes to maintain vehicle irectional control an stability. In a steer-by-wire system, it is require to generate Journal of Applie Research an echnology 769

2 not only a familiar steering feel to the vehicle river just as in the conventional steering wheel systems with mechanical connection, but also ajustable variable artificial steering feels. (3) Ajustable steering wheel return capability: he steering wheel shoul return automatically to the wheel center or a preefine angle if the hans of vehicle river leave the steering wheel. he return rates of the steering wheel can be ajuste base on the vehicle spee. (4) Variable steering ratio: he steering ratio is a ratio between steering wheel angle an roa wheel angle. It is typically fixe aroun 16 to one in conventional steering wheel systems. A variable ratio permits a significant improvement in hanling performance an vehicle ynamics. It can be a function of vehicle spee, steering wheel angle, an other variables [3]. Unoubtely, the greatest benefit of SBW is its active steering capability, that is, the ability to change the river s steering input to improve maneuverability or stability. herefore, the research institutes an automotive inustry pay consierable attention to the potential benefits of SBW systems, particularly for improving vehicle hanling behavior. Over the last two ecaes, a number of stuies have been carrie out on control of vehicle hanling an stability using SBW architecture. Yih [4] aresse some of the issues associate with control of a steer-by-wire system. A general steering control strategy was evelope to emphasize the avantages of fee forwar. he controller was implemente on a test vehicle that was converte to steer-by-wire. Kazemi an Janbakhsh [1] propose a nonlinear aaptive sliing moe control that aims to improve vehicle hanling through a Steer-By-Wire system. heir results confirme that the propose aaptive robust controller not only improves vehicle hanling performance but also reuces the chattering problem in the presence of uncertainties in tire cornering stiffness. Qiu et al. [5] built a simulation moel of SBW, incluing steering motor moel, steering executive system moel, vehicle moel an Fiala tire moel. Base on the Linear Active Disturbance Rejection Control (LADRC) technique, a kin of control algorithm on steer angle of vehicle SBW was esigne. Marumo et al. [6] iscusse the control effects of the SBW system for motorcycles on the lane-keeping performance by examining computer simulation with a rier-vehicle system which consiste of a simplifie vehicle moel, a rier control moel an the controller of the SBW system. avoosi et al. [7] evelope a 4DOF simplifie moel for steering system using vehicle parameters for stanar maneuvers in ry an wet roa conitions. hey use the harware in the loop metho to prove the controller ability in realistic conitions. hey showe the effectiveness of NAOC on vehicle hanling an reveal that the propose controller can significantly improve vehicle hanling uring severe maneuvers. In this paper, a 4DOF moel with nonlinear tire an SBW subsystem is presente using harware in the loop metho. Since some space variables cannot be measure, an estimator is use to extract the measurable variables from the simulate moel an convert them to the require variables of the controller. hese variables are transmitte to the controller an then it aopts itself with new conitions an applies the best moification on the steering. he Simulink MALAB software is use for vehicle moeling.. Vehicle ynamic moeling he Lagrangian metho was use to extract the vehicle lateral motion equations. he propose moel is a 4DOF moel incluing roll angle, longituinal spee, lateral spee, roll rate. Accoring to Fig. 1, Eq. (1) was obtaine as follows [8-10]: m(u - rv - hjr - hrj) = F + F - F xf xr yf m(v + ru + hj - hr j) = F + F + F yf yr xf I r +(I q - I )j - mh (u - rv)j = z z r xz af - bf + af + M yf yr xf Z (I + mh )j + mh (v + ru)+(i q - I )r - x z r xz (mh + I - I )r j +(c + c )j y z jf jr +(k + k - mgh)j=0 jf jr (1) 770 Vol. 1, August 014

3 he longituinal forces of front an rear tires are ignore ue to the negligible variation of them uring the maneuvers. he vertical forces on the front an rear axle are assume to be equal because of the system asymmetry an no longituinal acceleration an therefore, the effect of their variations on the lateral force is not taken into account. he transverse forces of front an rear axle s tires have important effect on the lateral behavior of the vehicle. he transverse an longituinal forces on the left an right han sie tires are assume to be equal. he values of resultant amper an stiffness coefficients of suspension system are consiere for the rear an front axles. he applie steering angle will be on the steere tires hea. he angle of both tires is assume to be equal. F y= D sin[c arctan{ba - E(Ba - arctan(ba))}] where: C B= Fa CD D=mF z =F y,peak F C = c sin(arctan( z Fa 1 )) c (4) where, B, D, C, E are stiffness, peak an shape coefficients, respectively an c 1, c are the maximum lateral stiffness an loa at maximum lateral stiffness, respectively. In Eq. (4), is the slip angle of tire an is separately calculate for each axle. f r v ar f ( ) u v br r ( ) u (5) In the case that the rear axle is steering, the steering input term is not equal to zero for the rear axle, otherwise it is equal to zero. Eq. (6) expresses a liner relationship between lateral force an slip angle [11]. F y i (6) Cii Figure1. he vehicle s 4DOF moel [11]. Fig.. epicts the calculate force from Eqs. (4) an (6) for both axles of the teste vehicle. m(u - rv) = F xf + Fxr - F yf m(v + ru) = F yf + F yr + F xf Izr= af yf -bf yr +af xf +M Z () After simplification an elimination of longituinal spee, a DOF moel is obtaine (Eq. (3)) [9-11]. m(v + ru) = F yf + F yr Izr= af yf -bf yr +M Z (3) In Eqs. (1), () an (3), the lateral force is obtaine through well-known nonlinear Magic formula moel, from Pacejka [11]. Figure. he comparison of linear an nonlinear moel for the teste vehicle. Journal of Applie Research an echnology 771

4 By substituting Eqs. (5) an (6) into Eq. (3), the two egrees of freeom moel is obtaine as following, m( v ru) C I r ac z f f f C bc r r It can be rewritten in state space form as: X AX BU ED v a X, U A 11 r i a 1 C f B ac m f I z 3. Design of optimal controller f (7) (8) As iscusse earlier, improve steering an esire stability are two important aspects of optimal steering of vehicle. he DOF moel is taken into account an since the objective is to achieve the esire value for variation of roll angle therefore the tracking control metho was selecte. So, the Performance Inex for the optimal steering of vehicle is efines as [1], (9) where, R an Q are weight matrices. he minimization of Performance Inex was performe in orer to optimize steering behavior of vehicle. By esire choosing of weight factors (Eq. (6)) an proper esign of control law, the favorable value of roll angle variations an optimal steering were obtaine an the ynamical constraints of vehicle were met. he Hamilton s function was obtaine from Eq. (9). r r a 1 a C C ac bc f r f r a, a u 11 mu 1 mu ac bc a C b C f r f r a, a 1 I u I u zz zz t 1 f U(t) R(t)U(t)+ X(t) - X (t) J= t t 0 Q(t) X(t) - X (t) 1 H( u) U RU P ( AX B ) c (10) he state equations are written an accoring to the constraints an bounary conitions, the algebraic nonlinear system of equations is obtaine. he time relate to the transient part of the system answer is very short, thus this system is stuie in stable conitions. Eq. (11) presents the result. A ( A (11) he above system of equations is analytically solve an the optimal control law is attaine. (1) he esire steering uring turning an stanar maneuvers (like Lane change) is not achieve with zero roll angle, but in orer to esign of controller for DOF moel assuming that vehicle is moving with constant longituinal spee uring a turn with constant raius of R, the esire value of is efine as [13], (13) In fact, the esire value of system state is etermine through Eq. (14). 3.1 Estimator 1 ( X X ) Q( X X ) K Q KA KBR 1 B K 0 KBR 1 B ) S B QX c R 1 B ( KX S c r X u es ( a b)(1 k u ) us 0 r ) 0 (14) Since some of the system states cannot be measure an they are effective in etermination of controller output, these variables shoul be extracte. Hence there is a nee to an estimator in a control system. In this paper, the lateral an 77 Vol. 1, August 014

5 longituinal spee states which are require for etermination of inputs to the optimal controller are extracte by simple estimation metho. In orer to estimate u an v by using longituinal acceleration sensors, the acceleration of roll rate is obtaine through following estimator [14-15]: t uˆ 0 r v ˆ m (15) where, a xm, a ym an r m are measure values of longituinal acceleration, lateral acceleration an roll rate, respectively. û an vˆ are the estimate values of longituinal an lateral spee. 3. Moeling by HIL r a m uˆ a xm 0 vˆ ym Due to the lack of experimental facilities for testing of a real vehicle equippe with the consiere controller, the HIL metho is use for the moeling as shown in Fig. 3. In this paper, an ECU is esigne an manufacture using Atmega16 microcontroller from AVR family. It is connecte to a computer through serial port. he vehicle moel is simulate in the computer an the output values of the system are transmitte to the ECU through the serial port as moel sensors outputs. he ECU circuit acting as controller, by receiving information from the system creates the moifie steering angle by using linear optimal control metho an estimation of lateral spee. his moifie steering angle is returne to the simulate system as an input an forms a close control loop. he Simulink MALAB is use for the simulation an CoeVision is use for the coing of microprocessor. Figure 3. Harware loop an its components. 4. Results an iscussion 4.1 Moel valiation he Jeep Cherokee vehicle was selecte for the moeling. able 1 shows the relate parameters for this vehicle. he results accesse from Ref. [16] were relate to a J-urn test. he test conitions were as following: the steering input was J-urn type an the maximum steering angle was 310 egree applie to the simulation moel. he vehicle s longituinal spee at the onset of test was equal to 73.86Km/h. Fig. 4 shows the steering angle in both simulation an real test conitions. Parameter Symbol Value Unit Vehicle total mass m 1988 Kg Vehicle yaw moment of inertia I z Kgm Distance from CG to the front axle a 1.15 m Distance from CG to the rear axle b 1.43 m Front tire cornering stiffness Rear tire cornering stiffness C f N/ra C r N/ra able 1. Vehicle parameters [1]. Actually, the input of this test was extracte accoring to the Unite States National Highway raffic Safety Aministration's (NHSA) Vehicle Research an est Center (VRC). he steering input was applie with 0.5 sec elay in the real test, thus the real moel outputs have time elay as same as this value. he results obtaine show that the nonlinear 4DOFmoel gives the same lateral acceleration as the measure one (Fig. 5). Fig. 6 illustrates that the roll angle has reache to the maximum of 6 egree in the real test which is compatible with simulation results. After valiating the nonlinear moel, the compatibility of twoegrees of freeom moel to the more complete moel shoul be evaluate. he stanar sinusoial test was use for simulation an esigning of the controller. he test spee was 80 Km/h or. m/s. he steering amplitue of tires was 3 egrees an the variation frequencies were 0.5 Hz. Journal of Applie Research an echnology 773

6 (a) Figure 4. he steering input to the simulation moel uring the a) J-urn test, b) simulation. (b) (a) 774 Vol. 1, August 014

7 Figure 5. a) lateral acceleration of the real test [14]; b) simulate lateral acceleration. (b) (a) (b) Figure 6. he roll angle: a) real test; b) simulation. Journal of Applie Research an echnology 775

8 4. Controller esign Firstly the weight coefficients for the optimal esign of controller shoul be selecte an then the ratios of Q to R an Q to Q 11 were selecte an evaluate. he simulation results inicate that the best choice for final controller esign was achieve from Eq. (16). 0.1 Q 0 R (16) hen, since the longituinal spee exists within the coefficients matrix, it shoul be evaluate that how the three control coefficients (K 1, K, S ) vary with the longituinal spee. Fig. 7 shows the variation of coefficients versus longituinal spee. As can be seen in Figs. 7, 8 an 9 the variations of control coefficients versus longituinal spee can be ignore or it can be approximate by a thir orer equation using curve fitting methos. In this paper, just the variation of K 1 is taken into account an the effects of the other two parameters are isregare. (a) -0.0 Control gain VS Vx K Vx (Km/h) (b) 776 Vol. 1, August 014

9 -9.45 Control gain VS Vx K Vx (Km/h) (c) Figure 7. a) he variation of S versus longituinal spee; b) he variation of K1 versus longituinal spee; c) he variation of K versus longituinal spee. he results show that the optimal controller with estimator can effectively make the vehicle stable in snowy roa conitions an prevents it from any accient. hen, the controller was exite from simulation moe an the output values of harware controller were inputte to the system instea of it. his harware controller gets the same simulate controller inputs through RS3 cable an after processing, returns it to the simulate ynamical system. he harware in the loop simulation inicates that the consiere harware can immeiately calculate the control metho an apply it to the vehicle. 5. Conclusions In this paper a new nonlinear 4DOF moel was propose to optimal control of SBW system by using harware in the loop metho. A nonlinear 4DOF moel was evelope; then it was simplifie to a DOF moel with reasonable assumptions to esign observer an optimal controllers. he obtaine results inicate that the utilization of harware in the loop metho for controlling of a SBW system can favorably stable the vehicle in critical conitions an suen maneuvers on the roas with low friction. In aition, simulations emonstrate that the propose controller can consierably improve vehicle hanling uring a severe maneuver. Journal of Applie Research an echnology 777

10 References [1] Kazemi, R., Janbakhsh, A.A. Nonlinear aaptive sliing moe control for vehicle hanling improvement via steer-by-wire. International Journal of Automotive echnology, Vol. 11, No. 3, pp , 010. [] Renon-Mancha, J.M., Sanahuja, G., Castillo, P., Lozano, R. A new experimental groun vehicle with hybri control an hybri vision sensor. Journal of Applie Research an echnology, 8 (3): 310-3, 010. [15] Bayani, M. Designing Vehicle Stabilizer Controller Estimator. Master s thesis, Mechanic Engineering Department, K. N. oosi University of echnology, (in Persian) 007. [16]_NHSA. A Comprehensive Evaluation of est Maneuver hat May Inclue On-Roa, Untrippe, Light Vehicle Rollover. echnical Report, National Highway raffic Safety Aministration, 00. [3] Yao, Y. Vehicle Steer-by-Wire System Control. SAE technical paper series, , 006. [4]_Yih, P. Steer-by-wire: implications for vehicle hanling an safety. PhD hesis, Stanfor University, 005. [5] Qiu, X., Yu, M., Zhang, Z., Ruan, J. Research on steering control an simulation of vehicle Steer-by- Wire system. 7th International Conference on MEMS, NANO an Smart Systems, ICMENS 011; Kuala Lumpur; 011. [6] Marumo, Y.a, Katagiri, N. Control effects of steer-bywire system for motorcycles on lane-keeping performance. Vehicle System Dynamics, Vol. 49, No. 8, 011, pp [7] avoosi, V., Kazemi, R., Oveisi, A. Nonlinear aaptive optimal control for vehicle hanling improvement through steer-by-wire system. Journal of Central South University, 014 1: [8] [Salaami, M.K., Guenther, D.A., an Heyinger, G.J.: Vehicle Dynamics Moeling for the National Avance Driving Simulator of a 1997 Jeep Cherokee. SAE Paper No [9] Rajmani, R. Vehicle ynamic an control. Springer, 006. [10] Wong, J.Y. heory of Groun Vehicles, John Wiley & Sons, Inc, 001. [11]_Pacejka, H.B. yre an Vehicle Dynamics. Butterworth Heinemann, 00. [1].Kirk, E. Optimal control theory an introuction. Prentice-hall, INC, [13]-Esmailzaeh, E., Gooarzi, A., Vossoughi, G.R. Optimal yaw moment control law for improve vehicle hanling. Int. J. Mechatronics, Vol , pp [14] Slotine, J.J., Li, W. Applie Nonlinear Control. 1st e., Prentice Hall International Inc, Vol. 1, August 014

11 Appenix 4 sinusoial manoeuvre mu= Dynamicl Aaptive Optimal Controller Vy (m/s) time (s) (a) 3 sinusoial manoeuvre mu=0.3 Dynamic Aaptive Optimal Controller 1 Ay (m/s ) time (s) (b) 30 0 Sinusoial Manoeuver mu=0.3 Vx=80Km/h Dynamic Aaptive Optimal Controller Steering wheel angle (eg) ime (s) (c) Journal of Applie Research an echnology 779

12 10 5 sinusoial manoeuvre mu=0.3 Dynamic Aaptive Optimal Controller 0 r (eg/s) time (s) () 3 sinusoial manoeuvre mu=0.3 Y (m) 1 0 Dynamic Aaptive Optimal Controller X (m) (e) Figure 8. he sinusoial maneuver test in snowy roa; comparison of vehicle with an without controller. (a) (b) 780 Vol. 1, August 014

13 (c) () (e) Figure 9. a) comparison of the applie steering by the river an HIL controller; b) comparison of the roll rate an HIL controller; c) lateral acceleration in HIL controller; ) lateral spee in HIL controller; e) he vehicle path with an without harware controller. Journal of Applie Research an echnology 781