A study of dynamics performance improvement by rear right and left independent drive system

20080444 AVEC '08 - 044 A study of dynamics performance improvement by rear right and left independent drive system Takashi Sugano, Hitoshi Fukuba and Takamasa Suetomi Mazda Motor Corporation 3-1, Shinchi, Fuchu-cho, Aki-gun, Hiroshima, 730-8670, JAPAN Phone: +81 82 252 5011 Fax: +81 82 252 5342 E-mail: sugano.t@mazda.co.jp In this paper, a motion control of a rear right and left independent electric motor drive vehicle was researched There is making to instability when acceleration turns as a problem considered in a rear wheel drive vehicle In this research, a control method that especially dealt with this problem was examined, and the performance of independent drive system was evaluated by a simulation Moreover, the effects for driver were confirmed with a driving simulator The effectiveness of the system was confirmed from these results Topics / Direct Yaw-moment, electrical vehicle, driving simulator INTRODUCTION Cars will be driven by electric motor from the viewpoints of environmental conservation and lower-fuel consumption in the near future In electric drive systems, decentralized arrangement of the drive unit is possible Herewith, a driving force distribution system, which needs a complex mechanism, now, will be realized with comparative ease so far In addition, a Direct Yaw moment Control (DYC) with a fast response and accurate driving torque by the motor will be possible and expected to enlarge vehicle dynamics performance The research that uses the tire force to its maximum has been done by the combination of the driving/braking torque and the independent steer, and the improvement of the limit performance is suggested[1][2] Moreover, the research to which the dynamics performance is improved by the thing combined with DYC and other systems, for instance, Active Front Steer (AFS) and Active Rear Steer (ARS) is done[3] In this paper, a study of the improvement of driving operation and the dynamics performance by a simple rear right-left independent driving vehicle is conducted The precondition is to think about more realizable system by avoiding the complication of a mechanism On rear drive system, there is a possibility that the vehicle characteristic becomes unstable due to the slip angle – lateral force gradient decrease when the vehicle has accelerated The gradient is named ‘local Cp’ in this paper And, it is not evaluated enough how the DYC effects on driver’s maneuver Furthermore, It is proposed to keep the stability of the DYC vehicle by limiting yaw rate from acceleration/deceleration and friction between tire and road[4] But, the local Cp reduction is not minded in the paper For conventional vehicle, research that a driver operation and vehicle motion on cornering with acceleration was conducted and it was proposed that the combination of driving/braking and steering was important to effectively uses tire force[5] First of all, stabilization logic on acceleration in turn situations is designed and the improvement of the vehicle dynamics by DYC is validated by the simulation for a certain vehicle Next, the influence on the driver is evaluated with a driving simulator As a result, it is confirmed that driver's unnecessary steering decreased since the stability of the vehicle is increased CONFIGURE OF VEHICLE In this report, a vehicle system that equipped right and left independent motor on rear axle was considered The configure of vehicle system is shown in fig.1 On this configuration, yaw moment caused by difference of driving force between right and left tires affects vehicle turning motion in addition to driving force to move forward motion Hence, this yaw moment control expected to improve a cornering stability and a steering response f V f V lf Center of Gravity Electric Motors M FXL FXR lf lr lt M lr FXL FXR f Velocity Slip Angle Yaw Rate Length from C.G to front tire Length from C.G to rear tire Tread Yaw Moment Driving force on left side Driving force on right side Steering Angle lt Fig Target vehicle model 258 AVEC '08 CONTROL SYSTEM DESIGN 3.1 Requirement for Controller The characteristics of vehicle dynamics are possible to become unstable when turning motion with high driving force is generated on Rear Wheel Drive (RWD) vehicle It is thought that the cause of this problem is decreasing local Cp The phenomenon is shown in fig The Cf is the sum of local Cp of the front tires and the Cr is same for rear tires A Stable B Unstable if steering wheel angle is fixed The feedback controller is a simple proportional and integral (PI) controller The control gain is designed based on theoretical 2-DOF vehicle model and motor systems The motor system is assumed as a first order delay model that includes characteristics of transfer of driving torque 3.3 Acceleration Control The high accuracy of acceleration control will be designed using advantage of motor drive[7][8] But, a simple feed forward logic, the driving force is calculated proportional to acceleration pedal, and wheel inertia compensator is implemented in this research The rear wheels don't put out lateral force to correspond to force where the front wheels are generated Cr on A Lateral Force Cf 3.4 Traction Control (TRC) Traction control logic is implemented and it is used with DYC In this logic, driving force is limited as equation (1) Note that FX_CMD is target driving force; FZ is tire load; FY lateral force; and is friction coefficient The ‘*’ means each wheel The inputs, FZ, FY and , should be estimation value But in this paper, the true values are used Cr on B Slip Angle Fig Degradation of local Cp caused by Driving Force FX _ CMD* If rear local Cp is excessive decreasing, rear tires can not generate anti yaw moment that corresponds to an increase of yaw moment that the front tires generate when the slip angle increases As a result, yaw moment that increases slip angle will remain, and yaw moment will be increased in the self-excitation Therefore, there is a possibility of making the vehicle unstable even if there is margin in the tire availability Because the problem is the balance of front and rear local Cp A system that improves stability on acceleration in turn was constructed by controlling this phenomenon The over-view of control system is shown in fig K FB Driving Force Driving Force on stability limit Vehicle Fx FB Controller Fx Tire force Tire load Acceleration Controller DYC Moment Throttle Pedal (1) Lateral Force Yaw rate K FF Min Velocity Target Model Target Yaw rate Kx FY * 3.5 Driving Force Limitation Logic (DFL) The rear local Cp deceleration on acceleration in turn is prevented by this logic One of a direct solution in this problem is to deaden driving force However, it is necessary to maintain the turn ability by making the best use of DYC in the viewpoint of safety Consequently, as shown in fig.4, the control method is that driving force of both tires is similarly decreased to keep the difference of driving force Direct Yaw Moment Controller FF Controller In addition, even if driving torque for one side is limited, the DYC moment is fulfilled by reducing the other hand f Steering Angle FZ * Slip Angle Traction Control Motor &Driver Traction Control Maximum Driving Force Estimator Target Rear Cp Fig Strategy to compensate stability Tire Load Slip Angle [Stability of turning motion] There is a well known 2-DOF model to study vehicle turning motion on steady velocity analytically It is shown as equation (2) and (3) Note that m is vehicle mass and the other symbols are same as fig.1 and fig.2 mV & C f Cr l f C f l r Cr V (2) 2C f f Cp Limit Estimator Acceleration Force Limitation Logic Fig Overview of Control System 3.2 Direct Yaw Moment Control A target model following feedforward and feedback controllers are designed Same type of control system has researched well heretofore The target model is a first order delay that assumes steering wheel angle to be input And the yaw gain was changed depending on the velocity It is set based on base vehicle Therefore, target yaw rate is increasing on acceleration in turn even IZ & l f C f lr Cr 2 lf Cf V l r Cr (3) 2l f C f f The condition of stability of this model is obtained 259 AVEC '08 as equation (4) by evaluating the characteristic equation by Routh stability criterion, etc[8] It leads to assuring stability by enlarging Cr more than a value of right hand of equation (4) The Cr calculated by equation (4) is used as reference Cp in this logic mV l f C f Cr (4) 2C f lr l f mV 2l r [Tire Force and Local Cp] In this paper, Brush Model, that is a well known physical tire model[9], is applied to estimate driving force on the Cp of stability limit The equations of tire force on driving side are shown as follows: For s > : 1 FX K s s s FZ cos (5) s s FY K s s decrease local Cp when large slip angle It is mismatch sensuously And, it is unsuitable for convergence calculation because of having local solution So, the equation (11) is approximated as equation (11)’ An example of figure is shown in the left hand of fig.5 It is shown that the local Cp is increasing on very large slip angle In this logic, it is assumed as Because such a large angle is all skid area even if slip ratio equal to zero And this approximated local Cp is calculated smaller than original local Cp So, it is considered safe side error Cp To increase Local Cp, Slip ratio is increased in this area s , Fz tan Ks 3 Fz (11)’ s s tan Local Cp is assumed as Because, this area is all skid even if slip ratio equal to zero Slip ratio Direction where slip ratio increases Direction of slip ratio increasing Direction of slip ratio increasing Fig An example of local Cp and approximated it [Limitation of Driving Force] Now, it thinks about the following expression concerning yaw moment Note that WM is proper value of weight value; M is yaw moment at a certain sL and sR LM WM M REF M ( sL , s R ) (14) The example of plotting this equation is shown in fig.6 LM becomes when target yaw moment is filled, and it is identified as a line in sL-sR space Same as LM, LCP is thought as equation (15) As same as LM, LCP becomes when the target is filled LCP WCP Cr REF Cr ( sL , s R ) (15) Note that Cr is combined local Cp at a certain sL and sR In these expressions, sL and sR that wants to be obtained where LCP should be minimized on the condition of LM equal to zero In other word, there is possibility that LCP doesn't become zero in the restraint condition of LM equal to zero In this logic, find a proper yaw moment is more important rather than finding minimum For looking the figure of LM carefully, a direction to minimize LM becomes vertical to the line of LM equal to as it approaches the line And the shape is expected simple like fig So, moving direction on convergence calculation is considered to separate LM from LCP At first, a direction to minimize LM value (vector A) is calculated on a certain pair of sL and sR Next, a direction for LCP (vector B) is calculated Then, the vector C is defined as the vector B restricted the vertical direction of the vector A The moving direction on convergence calculation is defined to use the vector A and the vector C as shown in fig But in the case of not becoming LCP equal to zero in LM equal to 0, sL and 2 Slip ratio Opposite direction to increase Local Cp, unlike the left area (8) K s tan (9),(10) Ks The expression of local Cp is obtained from equation (6) by partial differential in the slip angle It is shown as follows: K s Kss Cp cos s (11) s cos Fz cos K tan (6) 1 s s Note that FX is longitudinal force; FY is lateral force; FZ is tire load; Ks is driving stiffness; K is cornering stiffness; s is length of adhesion area of ground plane; is slipping direction of ground plane The s is represented as equation (7), (8) and cos and sin are approximated as equation (9), (10) Ks (7) s Fz s2 cos Ks s s Fz FZ sin K Ks K sin Note that Cp is local Cp of certain tire Using described above, target yaw moment and target local Cp that is combined two tires are expressed as follows: lt M REF FX ( FZL , L , sL ) FX ( FZR , R , s R ) (12) Cr REF C p ( FZL , L , s L ) C p ( FZR, R , s R ) (13) Note that MREF is the target yaw moment that is defined by DYC and it is generated by difference of driving force; CrREF is the target rear local Cp to satisfy a stability condition It is calculated by equation (4) with some additional margin Equations (12) are expressions to relate yaw moment to cornering force But, they are functions of slip ratio, not of driving force Furthermore, it is difficult to resolve analytically So, at first, a target slip ratio is solved by numerical approach And then, a driving force is calculated with equation (5) And now, an example of figure of equation (11) is shown as the right hand of fig.5 In this figure, the direction of slip ratio to increase local Cp is changed with slip angle A larger slip ratio is required to 260 AVEC '08 sR will be calculated as excessive large value To begin with, the purpose of this logic is to limit a driving force on safe value, not to find out the optimal value So, the limited slip ratio is searched in only adhesion area that means that  s is greater than By the way, the slip angle , tire load FZ and tire-road friction parameter are required in this logic And, cornering stiffness K and driving stiffness Ks are required, too Heretofore, the research to estimate these parameters has been done [10][11][12] In this paper, the controller uses true values of these parameters Table Vehicle System Parameters Mass Yaw moment of inertia Length from C.G to front wheel Length from C.G to rear wheel Length of Tread Cornering Power of front(nominal) Cornering Power of rear(nominal) Motor output Motor max torque(for one motor) 1360kg 1500kgm2 1.13m 1.20m 1.49m 33800N/rad 38700N/rad 60kW 1200Nm 1400 Wheel Torque (Nm) 1200 LM = 1000 800 600 400 200 0 a vector A 50 100 150 200 Velocity(km/h) Fig Vehicle Speed to Tire Torque Direction of Slope 35 Stability limit Capability of Yaw Rate change 30 25 Motor ability limit 20 The convergence point Yaw Rate(deg/s) Fig Example of LM Line of LM = 10 Nominal Yaw Rate vector A : a direction toward LM equal to vector B : a direction toward LCP equal to vector C : restricted Vector B to vertical The direction to find the convergence point 15 40 60 80 100 120 140 160 -5 Stability limit direction of vector A -10 Motor ability limit sR -15 Velocity(km/h) vector C Fig Example of Capability of yaw rate change by DYC (Nominal vehicle is turning on 0.3(g).) Line of LCP = vector B 4.2 Methodology The control logic is evaluated by a computer simulation The simulation was conducted using veDYNA that is a product of TESIS Corporation And the benefit for driver by DYC system is checked using a motion-base driving simulator [Cases for computer simulation] We conducted several case including follows But, a result of following (1) is described in this paper (1) Turn in Acceleration In this case, driving force limitation logic is checked in this case (2) Disturbance reduction performance A simple DYC logic that follows a yaw rate target is checked in this case And, an influence of drive shaft elasticity to control performance is checked [Cases for Driving Simulator] We conducted several case including follows using a driving simulator shown in Fig 10[13] The driving simulator has a single-seat cabin, which can move meters in lateral direction with 0.8 g, 160 degrees in vector A sL Fig Schematic of direction to find the optimized point VERIFICATION AND EVALUATION 4.1 Target Vehicle The main parameters of the target vehicle system are shown in table 1.The speed torque diagram of the motor is shown in fig.8 The ability of the motor is limited under this line An example of the vehicle performance is shown in fig.9 A capability of yaw rate change is in this range when the vehicle is turning on 0.3g of lateral acceleration The reason why the capability decreases in high-speed area is not only the motor ability but also aerodynamics drag However, the figure shows that the vehicle has sufficient ability from low to middle speed 261 AVEC '08 yaw rotation and 40 degrees in roll and pitch rotations by electrical motors to provide motion sensation to the driver and gives him/her a frontal view, an engine sound, and a steering control feel (3) Straight -ahead driving in crosswind disturbance How the disturbance reduction control performance worked effectively was confirmed (4) Lane change feeling The influence on driver's operation by the target yaw rate following In this paper, the result of (3) above is described instability since slip angle continues to increase The vehicle of DYC and TRC is turning outer line And the maximum slip angle is a little large The vehicle of DYC, TRC and DFL is turning center line It is looks like stable since slip angle is only 2.6 degree A B C Fig.10 Driving Simulator 4.3 Simulation Result Simulations that steering wheel angle was held as constant and vehicle turned in acceleration were conducted The case of that steering wheel angle is 40 degree and road friction factor is 0.5 are shown in fig 11 to 13 In this case, acceleration pedal was opened 20% at first, and then, it was opened 40% D Fig 12 Result of vehicle state Force Limit(Controller) Slip angle is being settled But maximum DYC and TRC slip angle is large (9.1deg) E DYC+TRC+DFL (Vehicle Output) DYC+TRC (Vehicle Output) DYC Only Inner wheel is spinning out and slip angle is increasing Acceleration pedal is opened from 20% to 40% at this point Long Forces are limited by TRC DYC, TRC and DFL Long Forces are limiting by DFL after this time The stable state is maintained Front (DYC+TRC+AFL) * The represented angle values are slip angle in the moment Rear (DYC+TRC) Rear (DYC+TRC+AFL) Rear Limit Fig 11 vehicle trajectories on acceleration in turn Vehicle trajectories are shown in fig.11 It is represented the result of 20 sec The DYC only vehicle is turning inner line and slow, because the inner wheel is spinning out soon after acceleration force changed So, only driving force of outer side is remained It cause less driving force and generates uncontrolled yaw moment And then, the yaw moment will make F Fig 13 Longitudinal force and Estimated local Cp The yaw rate, lateral acceleration and vehicle speed are shown in fig 12 The inner wheel of DYC only vehicle is spinning out after point A So, driving force is 262 AVEC '08 not able to be generated enough, and the slope of velocity is moderate incline The DYC, TRC and DFL vehicle is able to be following the reference yaw rate well as shown at pointed as B The DYC and TRC vehicle is following, too But on the peak region of yaw rate and lateral acceleration, pointed as area C, it looks like unstable It is considered that DYC system isn’t able to generate enough additional force and the vehicle characteristics become unstable Therefore, the vehicle motion is unstable-ish and it is not able to keep the speed as pointed on D The longitudinal force of rear axle and estimated local Cp is shown in fig.13 DYC and TRC vehicle and DYC, TRC and DFL vehicle are generating the same forces at first But, after the time pointed on D, the driving force is restricted on DYC, TRC and DFL vehicle The result by this control, local Cp becomes lower than stable limit on DYC and TRC vehicle But, local Cp of DYC, TRC and DFL vehicle doesn’t become lower than the limit as pointed on F disturbance In the driving simulator, it was confirmed that DYC was possible to reduce driver’s operation and stabilize vehicle motion Therefore, the target vehicle system was confirmed to improve the performance sufficiently and to affect well for driver’s operation REFERENCES [1] O.Nishihara, H.Kumamoto,“Minimax Optimizations of Tire Workload Expoiting Complementarities between Independent Steering and Traction/Braking Force Distributions”, Proc of AVEC ’06, 2006 [2] E.Ono,Y Hattori,Y.Muragishi,“Estimation of Tire Friction Circle and Vehicle Dynamics Integrated Control for Four-wheel Distributed Steering and Four-wheel Distributed Traction/Braking Systems”, R&D Review of Toyota CRDL vol.40, No 4, 2005 [3] M.Shino,P.Raksincharoensak,M.Nagai, “Vehicle Handling and Stability Control by Integrated Control of Direct Yaw Moment and Active Steering”, Proc of AVEC ’02, 2002 [4] R.Chumsamutr, T.Fujioka “Improvement of Electric Vehicle’s Cornering Performance by Direct Yaw Moment Control”, Proc of AVEC 2000, 2000 [5] M.Yamakado, M.Abe,”Understanding and Evaluation of Driver and Vehicle Dynamic Characteristics base upon Jerk Information – An Investigation of Longitudinal and Lateral Integrated Control –“, JSAE Annual Congress, No.11-07, 2007 (in Japanese) [6] Y.Hori, “Future Vehicle Driven by Electricity and Control- Research on Four-Wheel-Motored “UOT Electric March II””, IEEE Transactions on Industrial Electronics, Vol 51, No 5, pp.954-962, 2004 [7] K.Fujii, H.Fujimoto, “Slip Ratio Estimation and Control based on Driving Resistance estimation without Vehicle Speed Detection for Electric Vehicle”, The 7th SICE Control Division Conference, CD-ROM(6 pages), 2007 (in Japanese) [8] E Ono “Bifurcation in Vehicle Dynamics and Robust Front Wheel Steering Congrol”, IEEE Trans On Control Syst Technol., 6-3(1998), pp412-420 [9] M.Abe “Vehicle Dynamics and Control”, Sankaido Publishing Co.,Ltd.,1992 (in Japanese) [10] T Kanou, H.Fujimoto “Yaw-rate Control Based on Slip-ratio Control With Driving Stiffness Identification for Electric Vehicle”, The 8th SICE Control Division Conference,Vol.SY004/04/08/0000 -06414,2008 (in Japanese) [11] N.Takahashi, H.Fujimoto “Consideration on Yaw Rate Control for Electric Vehicle Based on Cornering Stiffness and Body Slip Angle Estimation’, Technical Meeting on Industrial Instrumentation and Control, IEE Japan, Vol IIC-06-04, pp.17-22, 2006 (in Japanese) [12] Y.Shiozawa, M.Yokote, M.Nawano, H.Mouri “Development of Technique for Estimating Unstable Behavior of Vehicle’, JSAE Annual Congress, No.104-6, 2006 (in Japanese) [13]T.Suetomi et al., The Driving Simulator with Large Amplitude Motion System, SAE Paper 910113,1991 4.4 Driving Simulator Result A bias and random disturbance of crosswind was occurred when a vehicle moving straight-ahead The result of this test is shown as fig.14 It shows steering wheel angle on the frequency domain Even when the vehicle is driven straight, the driver is always steering a low frequency of about 0.1Hz The DYC compensation was not effective for this frequency But, reducing large operation angle of steering wheel was confirmed on frequency of 0.8 to 1.1Hz The, the total angle of steering wheel is reduced as fig 15 So, one of effect for driver of DYC is confirmed Steering Wheel Angle(deg) DYC Vehicle with RWD Base Vehicle(RWD) (Reference)DYC Vehicle with FWD Frequency(Hz) Fig 14 Steering wheel angle on frequency domain CONCLUSION A study of dynamics performance improvement by rear right and left independent drive system was conducted in this paper At first, a control system that prevents a possible cause of unstable was designed in addition to simple direct yaw control system And then, the performance of the system and effect on driver’s operation were carried out on computer simulation and driving simulator In the simulation, the possible turning performance was checked on the steady state turning And, control logic of preventing to become unstable was confirmed on the acceleration turn And then, the response of the motor that influences the performance of the DYC was confirmed by inflicting with a sidewind 263 ... M.Yamakado, M.Abe,”Understanding and Evaluation of Driver and Vehicle Dynamic Characteristics base upon Jerk Information – An Investigation of Longitudinal and Lateral Integrated Control –“, JSAE... peak region of yaw rate and lateral acceleration, pointed as area C, it looks like unstable It is considered that DYC system isn’t able to generate enough additional force and the vehicle characteristics... AVEC '08 as equation (4) by evaluating the characteristic equation by Routh stability criterion, etc[8] It leads to assuring stability by enlarging Cr more than a value of right hand of equation