Lateral Handling Improvement with Dynamic Curvature Control for an Independent Rear Wheel Drive EV

Transcription

1 Pae WEVJ7-038 EVS8 KINTEX Korea May Lateral Handlin Improvement with Dynamic Curvature Control or an Independent Rear Wheel Drive EV Youn-Jin Jan 1 Min-Youn Lee In-Soo Suh 3 Kwan Hee Nam 4 1 Research Enineer Hyundai Motor Korea younjin530@naver.com PhD Student KAIST Korea lihton@kaist.ac.kr 3 Proessor KAIST Korea insoo.suh@kaist.ac.kr (correspondin author) 4 Proessor POSTECH Korea kwnam@postech.ac.kr Abstract The interated lonitudinal and lateral dynamic motion control is important or our wheel independent drive (4WID) electric vehicles. Under critical drivin conditions direct yaw moment control (DYC) has been proved as eective or vehicle handlin stability and maneuverability by implementin optimized torque distribution o each wheel especially with independent wheel drive electric vehicles. The intended vehicle path upon driver steerin input is heavily dependin on the instantaneous vehicle speed body side slip and yaw rate o a vehicle which can directly aect the steerin eort o driver. In this paper we propose a dynamic curvature controller (DCC) by applyin a newly-deined parameter the dynamic curvature o the path derived rom vehicle dynamic state variables; yaw rate side slip anle and speed o a vehicle. The proposed controller combined with DYC and wheel lonitudinal slip control is to utilize the dynamic curvature as a taret control parameter or a eedback avoidin estimatin the vehicle side-slip anle. The eectiveness o the proposed controller in view o stability and improved handlin has been validated with numerical simulations and a series o eperiments durin cornerin enain a disturbance torque driven by two rear independent in-wheel motors o a 4WD micro electric vehicle. Keywords: direct yaw-moment control dynamic curvature stability handlin 1 Introduction Vehicle lateral dynamic control techniques such as direct yaw-moment control (DYC) and active ront- and rear-wheel steerin can improve the lateral dynamic perormances by directly reulatin yaw rate and tire slip anles and thus lateral tire orces and/or by eneratin speed dierentials or torque distributions which are important in vehicle stability and maneuverability control under critical drivin circumstances such as aressive cornerin or near-limit drivin perormance conditions [1]. The undamental DYC adopts the yaw moment observer by estimatin the yaw rate which is diicult to be measured. Usin the yaw moment observer the controller compensates the disturbance applied to the EV to keep the vehicle ollow the reerence trajectory. When the yaw rate is not the same as the desired yaw rate or cornerin the yaw moment observer inds the dierences between actual and desired value o yaw rate. The perspective o DYC control is to provide a eedback o the dierence o yaw rate or desired cornerin reardless o disturbances. EVS8 International Electric Vehicle Symposium and Ehibition 1

2 Pae WEVJ7-039 Numerous control methods applyin DYC have been proposed and veriied in vehicle lateral dynamic perormance improvement to assist drivers in enhancin cornerin and straiht-line stability on slippery roads and in unavorable road conditions []. For micro electric vehicles (MEVs) with in-wheel motor application an electric dierential system is widely used [3]. Combined with independently controlled our inwheel motored vehicles the stability o electric vehicles (EVs) especially can be improved by controllin the drivin/brakin orces rom enerated speed dierential between let and riht wheels thus the yaw moment is controlled to minimize the side slip anle at a vehicle center o ravity (c..) [3]. Recently numerous studies are reported to improve the vehicle stability and maneuverability by applyin body slip anle uzzy observer parameter uncertainties or robust yaw moment control [4] slidin mode control [5] and comprehensive uniied approach or vehicle ull-state estimation [6]. However due to the diiculties on estimatin the side slip anle or lateral velocity o the vehicle current production vehicles are not equipped to measure the side slip anle directly. Thus the side slip anles are estimated or vehicle control purposes or lateral dynamic stability and steerby-wire or brake-by-wire system development which require ull vehicle dynamic state eedback [7]. Common techniques or estimatin side slip anle are interatin on-board inertial sensors or usin a physical model as an observer. While these approach have applied to actual vehicle dynamics control both has some undamental errors such as accumulated sensor errors and unrealistic measurements rom road rade or bank anle etc. while estimatin with a physical vehicle model can be sensitive to chanes in the vehicle parameters and inaccuracy on slippery road suraces etc. We propose a new parameter called as a dynamic curvature to be applied as a main control taret parameter. By introducin the dynamic curvature as a main control parameter in the proposed dynamic curvature control (DCC) system it will eliminate the necessity o measurin the vehicle side slip anle which can be a unique approach rom conventional DYC systems. In this case the measured dynamic curvature can be obtained rom an on-board IMU (inertial motion unit) while the reerence dynamic curvature is set as the curvature o the vehicle path o the neutral steerin case. An IMU is the basic on-board equipment or proposed DCC system. The dynamic curvature can be measured relatively easily compared with estimatin the vehicle sideslip anle which will be described in this paper. Vehicle Lateral Dynamics or DCC durin Cornerin Fi. 1. The bicycle model o the vehicle.1 Lateral Dynamics durin Cornerin As shown in Fi.1 the lateral motion dynamics o a vehicle can be simpliied as a bicycle model with two derees o reedom by nelectin the orce dierences between let and riht wheels [8]. From the model the equations o lateral motion can be derived as: d mv ( r ) (1) dt d I Mz Mt Md () dt where r and are the lateral orces o ront and rear tires respectively β is the vehicle side slip anle at the vehicle center o ravity (c.. or CG) γ is the yaw rate M z is the motor torque moment rom dierential orce Mt is the torque moment rom the lateral orce o tire M d is a disturbance torque moment and I is the yaw moment o inertia o the vehicle. For simplicity o analysis and veriication the lonitudinal slip o tires or rollover motions are not included in this paper. It is also assumed that the lateral orce on the tire is enerally proportional to tire slip anle or small slip anles [8]. Side slip anles o each tire are approimated with the side slip anle o vehicle body. Usin the above equations the lateral dynamics o side slip anle and yaw rate can be derived as ollows [8]: Av ( ) Bv ( ) u (3) EVS8 International Electric Vehicle Symposium and Ehibition

3 Pae WEVJ7-040 u M z ( C Cr) ( lc lrcr) 1 mv mv Av ( ) ( lc lc r r) ( lc lc r r) I Iv C 0 mv Bv ( ) lc 1 I I It ollows rom (3) that the transer unctions o steerin anle and state variables are obtained such that () s b 1s bo () s s as 1 a (4) () s 1s 0 () s s as 1 a (5) () s m 1s m0 M () s s as a (6) z where b1 lc C mv 1 lc 4lLCC ( v ) r r b0 I miv 1 4LCCr 0( v) I miv m 1 I 4LC C ( C r Cr ) 0( v) m0( v) miv miv ( C Cr) C a1 mv Iv and 4L CC r ( lc lc r r) a. miv I α α r : tire slip anle at ront and rear β: body side slip anle at vehicle c.. β β r : tire side slip anle at ront and rear δ: steerin anle input by driver : velocity vector at vehicle c.. v : lonitudinal velocity m: mass o the vehicle l l r : distances between the vehicle c.. and ront or rear wheel ale L: wheelbase o the vehicle (=l + l r ) 1 C C r : stiness at rear and ront tire With the simpliied -d.o.. model the lateral dynamic equations can be described with two state variables and two inputs. Speciically the yaw rate γ and side slip anle β can be controlled by steerin anle δ and motor torque moment Mz. The objective o a DYC in eneral is to maintain vehicle stability via reulatin the vehicle yaw rate. It is emphasized here that the dierential torque o two rear motors is utilized or DYC aside rom steerin anle chane. It is believed that the dierential torque makes the vehicle s cornerin eort more less than relyin just on side slip anle o the ront wheel. Sub-headins are numbered as above. Subsections are numbered sequentially.. Dynamic Control or Neutral Steerin Vehicle handlin conditions durin cornerin will be dierent dependin on vehicle speeds and dierence in tire stiness etc. They are classiied as under-steerin neutral steerin and oversteerin as shown in Fi.. A normal vehicle tends to be under-steerin makin the radius o curvature larer i it is accelerated with a constant steerin anle. The side slip anle in case o understeerin is illustrated in Fi.3. The vehicle dynamic motions durin a neutral steerin can be described rom (3) by lettin v a constant v c. Av ( c) Bv ( c) u (7) u M z where v c is a constant lonitudinal velocity δ is a steerin anle or neutral steerin and the variables with indicate the variables while the vehicle is under neutral steerin or a constant radius. (a) (b) Fi.. Vehicle dynamic motions durin cornerin (a) Vehicle handlin conditions (b) Side slip anle durin under-steerin EVS8 International Electric Vehicle Symposium and Ehibition 3

4 Pae WEVJ Curvature Determination and Dynamic Curvature or Control 3.1 Curvature o Vehicle Drivin Path There are many ways to measure the curvature durin vehicle motion. Firstly the curvature can be derived rom the dynamic steady state model with the ollowin assumptions that the sum o the lateral orces at ront and rear tires is the same as the centriual orce and that the torque moment by the lateral orce is zero. When the vehicle drives ollowin a curve with a constant radius the curvature should be equal to [8]: 1 R lc r r lc L mv CCL r (8) where the steerin anle and lonitudinal speed can be measured by on-board sensors in a vehicle. However a drawback o this approach is that the tire stiness and are not readily available so they need to be estimated by other methods. Also there can be possible errors because this curvature ormula is derived rom the steady state model. 3. A Dynamic Curvature In this work we introduce a dynamic curvature variable as a main control parameter within a DYC system. When the radius o vehicle cornerin path is R the instantaneous curvature o the vehicle drivin path can be epressed as introduced by Okajima et al. in [9]: k. (9) v The variable can be considered as a measure o the instantaneous dynamic curvature o vehicle path so we name it here as a dynamic curvature. Note that is conveniently measured in practice since yaw rate is directly available rom a yaw rate sensor and time-derivative o the side slip anle can be calculated rom an on-board IMU sensor. The dynamic curvature is a characteristic variable o vehicle dynamics durin cornerin. Let a total lateral vehicle movement anle deined t by d. 0 4 Proposed Dynamic Curvature Control (DCC) System 4.1 Proposed DCC Control with Reerence Neutral Steerin The control alorithm and resultant perormances o the direct yaw moment control method based on the yaw moment observer have been presented in [1-6]. The typical DYC alorithm utilizes the yaw rate as a eedback variable to stabilize the vehicle lateral dynamic motion. Note that the typical DYC s ocus on reulatin the yaw rate so that they may ail to obtain neutral steerin trajectory when the lateral tire slip conditions are not even or chanin. More speciically DYC controls the yaw rate only the vehicle maneuverability or the dynamic curvature control is not directly relected durin steerin motion. In this work the dynamic curvature is a taret variable to be controlled instead o yaw rate. It should be emphasized that the side slip anle chane bein a major inluential element to determine a circular motion is included in the dynamic curvature. Thereore the DCC enables the vehicle to track a neutral trajectory better than DYC. Note that the lateral acceleration which is equal to directly obtainable rom an IMU sensor. Thereore the dynamics curvature is measured as. (10) Note that the DCC is advantaeous in implementation since the dynamic curvature is relatively easily measured or eedback control without monitorin or estimatin the side slip anle separately. Fi. 3 shows the proposed DCC block diaram based on measured dynamics curvature which will be described in below. A steerin reerence value is applied as a command value. ks () k () s T PI M z 1M z r T l p 1 M z T r l p T r T l EV v Fi. 3. Block diaram o the proposed DCC control alorithm A y A v y k EVS8 International Electric Vehicle Symposium and Ehibition 4

5 Pae WEVJ Simulation and Test Results 5.1 Simulation Results speciication o the test track can be eplained with the vehicle trajectory as shown in Fi. 5. The vehicle as described in [10] o which speciications are shown in Table 1 is driven alon the line in Fi. 5 (a). An EV with two sets o independent motors at rear wheels is accelerated rom 18 km/h to 30 km/h or 0 seconds or a simulation purpose. The velocity o the reerence model is chosen as v c = 10 km/h. Initial position o the vehicle is set as the coordinate o (0 0) or plottin purpose. For the simulation and eperimental purpose the disturbance torque is applied at the ront let tire. The disturbance torque moment applied rom 7.5 second to 1.5 second with a value o 50 Nm at the ront let tire which simulates the vehicle velocity is abruptly chanin durin the cornerin possibly caused by stron wind and road riction dierence between let and riht etc. By usin the reerence law the reerence dynamic curvature is determined to keep the vehicle s desired trajectory with a constant speed as shown in Fi. 4 (a). We can see that the vehicle s radius o curvature with the proposed control ollows the reerence trajectory i.e. the neutral steerin case while the radius o the vehicle path without the control becomes larer as the vehicle velocity is increased as shown in Fi. 4 (b). (a) (b) Fi. 4. Simulation results: (a) the dynamic curvature k (b) the vehicle trajectory 5. Test Results Fi.9 shows the eperimental environment such as the test track the micro electric vehicle with two rear wheel independent control drivin test scene and the on-board GPS receiver. The Fi. 5. Eperimental environment: (a) test track or drivin test (b) subject vehicle or testin with two independent motor control at rear wheels The actually enaed steerin anle input and torque input durin this eperiment are shown in Fi. 5. Fi. 6 shows the measured vehicle trajectory with the dynamic curvature controller turned on. Dierently rom no curvature control case the trajectory keeps the constant curvature as i the vehicle maneuvers under neutral steerin. As the lonitudinal speed increases the lateral acceleration increases also due to the centriual orces durin cornerin. But the dynamic curvature controller provides a eedback sinal o the lateral acceleration to stay at the constant curvature radius. 6 Conclusion The direct yaw rate control (DYC) system introducin newly deined parameter o the dynamic curvature k which is called in dynamic curvature control (DCC) system is proposed and veriied the eectiveness with the simulation and a series o eperiment in this paper. The instantaneous dynamic curvature can be obtained rom the measured lateral acceleration and lonitudinal speed by an on-board IMU easily. The measurable dynamic curvature k is utilized as a eedback parameter durin vehicle cornerin motion especially when the speed o the vehicle is varied emphasizin the dynamic handlin as well as the vehicle dynamic stability. The dynamic curvature o the vehicle path with the control system maintained the constant radius o curvature as the reerence model o neutral steerin durin the cornerin even with the disturbance enaed which proved the eectiveness o vehicle handlin as well as the dynamic stability. EVS8 International Electric Vehicle Symposium and Ehibition 5

6 Pae WEVJ7-043 (a) System Dynamics Vol. 46 Supplement pp [3] H. Okjima S. Yonaha N. Matunaa and S. Kawaji Direct Yaw-Moment Control Method or Electric Vehicles to Follow the Desired Path by Driver Proceedins o SICE Annual conerence pp (b) [4] H. Du N. Zhan and G. Don Stabilizin Vehicle Lateral Dynamics with Considerations o Parameter Uncertainties and Control Saturation throuh Robust Yaw Control IEEE Trans. Veh. Tech. Vol. 59 no. 5 June 010. [5] H. Zhou and Z. Liu Vehicle Yaw Stability- Control System Desin Based on Slidin Mode and Backsteppin Control Approach IEEE Trans. Veh. Tech. Vol. 59 n0.7 September 010. Fi. 6. Vehicle control input durin the eperiment when the controller is turned on: (a) steerin anle (b) torque at rear wheels [6] W. Cho J. Choi C. Kim S. Choi and K. Yi Uniied Chassis Control or the Improvement o Aility Maneuverability and Lateral Stability IEEE Trans. Veh. Tech. Vol. 61 no. 3 March 01. [7] O. Mokhiamar and M. Abe Active Wheel Steerin and Yaw Moment Cotnrol Combination to Maimize Stability as well as Vehicle Responsiveness durin Quick Lane Chane or Active Vehicle Handlin Saety Proc. Instn. Mech. Enrs. Vol. 16 Part D: J. Automobile Enineerin pp [8] R. Rajamani Vehicle Dynamics and Control Spriner 01.J.J. Romm The hype about Hydroen ISBN Washinton Island Press 005. [9] H. Okajima S.Yonaha N. Matsunaa and S. Kawaji Direct Yaw-Moment Control Method or Electric Vehicles to Follow the Desired Path by Driver in Proceedins o SICE Annual conerence pp Fi. 7. Eperimental results when the controller is turned on: measured vehicle trajectory [10] I. Suh K. Hwan M. Lee and J. Kim In-wheel motor application in a 4WD electric vehicle with oldable body concept IEEE Int. Electric Machines & Drives Con. pp May 013. Reerences [1] D. Li S. Du and F. Yu Interated Vehicle Chassis Control based on Direct Yaw Moment Active Steerin and Active Stabiliser Vehicle System Dynamics Vol. 46 Supplement pp [] P. Raksincharoensak T. Mizushima and M. Naai Direct Yaw Moment Control System Based on Driver Behavior Reconition Vehicle EVS8 International Electric Vehicle Symposium and Ehibition 6