Advanced Estimation Techniques of Road Surface Condition and Their Experimental Evaluation using Test Electric Vehicle UOT March I and II

Transcription

1 Avance Estimation Techniques of Roa Surface Conition an Their Experimental Evaluation using Test Electric Vehicle UOT March I an II Kimihisa Furukaa Department of Electrical Engineering The University of Tokyo Ce-503, Komaba, Meguro, Tokyo Japan Tel: , Fax: , furukaa@horilab.iis.u-tokyo.ac.jp Yoichi Hori Institute of Inustrial Science The University of Tokyo Ce-501, Komaba, Meguro, Tokyo Japan Tel: , Fax: , hori@iis.u-tokyo.ac.jp, y.hori@ieee.org Abstract In this paper, avance techniques of roa surface conition estimation for electric vehicles (EVs) are reporte. Information on riving-force transmitte from the tire to the roa is inispensable for the estimation of roa surface conition in eciing a vehicle s state of motion. In our laboratory, various roa surface conition estimation techniques have been propose base on riving-force observer. This observer utilize one of the excellent features of EVs, i.e., motor torque can be knon easily an precisely from motor current. First, the principle of the riving-force observer is explaine. Next, to kins of the roa surface conition estimation techniques are introuce. One is µ an λ estimation techniques an µ - λ curve information. The other is base on vibration characteristics ithout vehicle velocity. Finally, applications of these estimation techniques are shon an confirme experimentally using the test EVs UOT March I an II. Keyors: Electric Vehicle, Wheel Hub Motor, Traction Control, Roa Surface Conition Estimation, Driving-Force, Slip Ratio, Frictional Coefficient 1 Introuction In these ays, Electric Vehicles (EVs) attract attention as one of environment-frienly technologies. Hoever, researches on motion control for EVs are not so ell evelope, although it can utilize the most remarkable merit of electric motor [1][2][3][4]. We have pointe out the folloing three avantages of EVs: 1. Motor torque can be knon easily an precisely from motor current. 2. Motor torque generation is very quick an accurate. 3. Motor can be installe in each heel. Figure 1: Our hanmae Experimental EV UOT March II

2 In our laboratory, many researches to utilize these merits of EVs are performe an verifie by the experimental EVs UOT (University of Tokyo) March I an II. UOT March II can be use for to-imensional motion control experiment (Figure 1). A heel hub motor is installe in each heel, an the torque of each heel can be controlle ith full inepenence [2][3][5]. In this paper, roa surface conition estimation techniques are introuce using the avantage of 1 [6]. The roa surface conition estimation is an important technique for active safety systems. In past researches, it is ell knon that riving-force beteen tire an roa has significant information. For Internal Combustion Vehicles (ICVs), irect estimation is impossible using riving-force information because observation of generate engine torque is ifficult. On the contrary, in the case of EVs, the estimation using riving-force observer is possible because it is easy to monitor generate motor torque. Next, the roa surface conition estimation techniques an their experimental results ith UOT March I are shon. Section 2 escribes frictional characteristics beteen tire an roa. In section 3, the riving-force observer, hich is utilizing the avantage of EVs, is introuce. In section 4, to kins of roa surface conition estimation techniques are introuce. First, µ an estimation techniques base on characteristics of µ - λ curve are introuce in 4.1. Secon, a novel estimation technique base on the vibratory characteristics is propose an investigate in 4.2. This technique utilizes only riving force an heel velocity ithout chassis velocity. In section 5, applications of the roa surface conition estimation techniques are shon. 2 Frictional characteristics beteen tire an roa In this section, frictional characteristics beteen tire an roa are shon hich are the funamental concepts of the roa surface conition estimation [7][8]. Driving-force is generate by velocity ifference beteen vehicle an heel, i.e., the slip velocity. Vehicle behavior is ecie by riving-force F shon in Figure 2. As shon in (1) riving-force is given by using frictional coefficient µ an normal force N. F = µ ( λ) N (1) Frictional coefficient µ is the function of slip ratio λ shon in Figure 2, an this curve is calle µ - λ curve. Slip ratio is given by using chassis velocity V an heel velocity V as (2). V V λ = max( VV, ) The performance of riving-force is affecte by the relationship beteen µ an λ, hich has non-linear characteristics ith value µ (hereinafter referre to as frictional coefficient). The slip ratio λ (hereinafter referre to as imal slip ratio) here frictional coefficient has µ is usually from 0.05 to 0.2. λ (2) (a) Driving force beteen tire an roa in one heel moel (b) Characteristics of µ - λ curve Figure 2: The schematic of one heel moel an the characteristic illustration of µ - λ curve

3 In ahesion state: λ λ, vehicle is in stable because the conition beteen tire an roa is in ahesive. In ski state: λ > λ, the heel is accelerate an big spin occurs. The roa surface conition estimation is use for the purpose of holing vehicle motion stable. In other ors, it estimates the stability limit beteen ahesion an ski states hen the vehicle is in ahesion. 3 Driving-force observer The information of frictional coefficient µ is inispensable for roa surface conition estimation. As it as shon in (1), frictional coefficient is obtaine by riving-force F an normal force N. Hoever it is impossible to observe irectly riving-force generate beteen tire an roa, therefore observer is neee to estimate riving-force. In this section, the principle of riving-force observer is briefly explaine [9]. In electric motor, generate torque can be monitore precisely an easily, therefore it is possible for EVs to estimate riving-force ith high precision. In the case of EVs, motor current an heel velocity, hich are neee to calculate generate torque, can be measure. Actually, armature current in a DC motor or torque current in an AC motor is use. The ynamic equations about a riving heel an a chassis, (3), are erive from one heel vehicle moel shon in Figure 3, V V M = Fm F, M = F (3) t t here, M is heel inertia converte to mass, F m is motor torque converte to force, F is riving-force an M is vehicle boy mass. The ynamic equation of riving heel shon in (3) is use to erive riving-force as (4), 1 ω F = ( T J ) (4) r t here, r is raius of heel, T is motor torque, J is heel inertia an ω is angular velocity of riving heel. These values are relate ith F, M, an V respectively as follos. m 2 Fm = Tr /, M = Jr /, an V = rω (5) Base on (4), the block iagram of the riving-force observer is shon in Figure. 4. The figure is for a shunt DC motor case, F ˆ, K, N, an J n are the estimate riving-force, the torque coefficient, the gear ratio of transmission, an the nominal value of heel inertia respectively. This is calle riving-force observer, though this structure is the same as isturbance observer often use in mechatronics. The observer uses first orer erivative of ω, hich inuces higher frequency noise from ifferential operation. Therefore, lo pass filters Q are neee. Figure 3. The schematic of one heel vehicle moel Figure 4. Block iagram of the riving-force observer

4 4 Roa surface conition estimation using riving-force observer The roa surface conition estimation base on the riving-force observer is one of the merits of EVs. In this section, the roa surface conition estimation techniques for EVs are introuce Estimation techniques using µ - λ relation µ estimation base on tire brush moel The tire moel propose by Dr. Yamazaki says that the value of µ λ (hereinafter referre to as µ graient) inclues the information of frictional coefficient µ [10]. Therefore, the value of µ can be estimate by the ata of riving-force, heel velocity, chassis velocity an typical characteristics of µ - λ curve. This technique is very useful to prevent big skiing [6]. First, a physical analysis about the frictional characteristics beteen tire an roa is given. On tire trea, ahesive an sliing areas are mixe. The proportion of to areas is change by the slip ratio as shon in Figure 5(a). This phenomenon is analyze base on the brush moel (see Figure 5(b)). The istribution of groun contact pressure in tire trea is assume as parabolic shape shon in Figure 5(c). Groun contact pressure p is given as (6) using maximum groun contact pressure p m, an groun contact length, l. p= 4 p (1 ) (6) l l m Normal force of tire trea, N, is given by (7) using groun contact ith. 2 N = pl (7) 3 m In ahesive area, friction stress σ ( a) is ecie by shearing stress an use longituinal spring constant of ( ) trea rubber for each unit area. In sliing area, friction stress σ s is ecie by frictional coefficient µ. They are given by (8). σ ( a) k x = λ, σ = µ (8) ( s) p The friction stresses take the same value at the bounary beteen ahesive an sliing areas represente by = a, ( a) ( s) σa = σa. (9) Driving-force F is given by (10), (a) Variation of ahesive an sliing areas (b) Tire brush moel (c) Distribution of groun pressure Figure 5: Physical configurations of tire trea

5 F = l 0 0 σ a l ( a) ( s) a (10) = σ + σ 2 3 ( Csλ) ( Csλ) = Csλ + 3µ N 27( µ N) 2 here, riving stiffness C s, hich is the riving-force for unit slip ratio at λ = 0, is given by (11). 1 2 Cs = kxl (11) 2 The solution of the maximum riving-force, µ N, from (10) is obtaine as (12). µ N = 2 3 3( Csλ) + 3( Csλ) (4 F C ) 18( C λ F ) s sλ As measure signals contain much noise, µ estimation is ifficult if (12) is irectly applie. To ientify linear characteristics represente by (13), algorithm of aaptive ientification (recursive least-squares (RLS) metho) is applie, T yk [ ] = ˆ θ [ k] φ[ k] (13) here, yk [ ], φ [ k] an θ[ k] take the forms of (14). 2 3 yk [ ] = 3( Csλ) + 3( Csλ) (4 F C s λ), ˆ[ θ k ] = µ N, an φ[ k] = 18( Csλ F ) (14) In the case of Fixe Trace (FT) metho, trace gain γ = trp[ k] is fixe. Especially, in the 1st imension FT metho, forgetting factor κ is given by (15), 1 κ =. (15) γ φ[ k] In comparison ith RLS, FT metho uses variable forgetting factor κ because trace gain γ = const. as (15). In other ors, hen φ [ k] is big an ˆ θ can be ientifie ith goo precision, ˆ θ is upate in a short time. Whereas, hen φ [ k] is small an not of rich information, θˆ is selom upate. (12) To confirm the valiity of the introuce technique, roa surface conition is estimate in off-line calculation using the ata measure by the experimental EV UOT March I. The experimental ata in ry asphalt roa an the estimation result of maximum riving-force are shon in Figure 6. In this experiment, the vehicle is accelerate at 2 sec. Hence, slip ratio gros bigger immeiately by urgent acceleration. Figure 6: Experimental ata on asphalt roa an result of the µ estimation

6 λ estimation base on geometric similarity of µ - λ curve To estimate the imal slip ratio, λ, e use the information of µ, λ an µ graient. Hoever, this information contains much noise an error, too, stable estimation is ifficult in search algorithm such as graient metho. In this section, as a robust imal slip ratio estimation Fuzzy inference is introuce [8]. One of the characteristics of the µ - λ curve, imal slip ratio λ has strong relation ith µ graient A1 2 (see Figure 7, an A represent µ graient). This geometrical characteristic can be applie to estimation. This characteristic is prove in λ µ - λ curves hich have same µ. We o not nee so accurate µ value. Then, e nee similarity information of µ ith four kins of stanar roa surface conitions, ASPHALT, GRAVEL, SNOW an ICE, hich are isplaye in Figure 8. Using µ an λ values, egrees of similarity to the stanar roa surface conitions are obtaine numerically by Fuzzy inference. λ In imal slip ratio estimation, e nee to kins of algorithms. The first algorithm is to obtain roa surface conition similarities ith four kins of stanar roa surface conitions, escribe as above. The secon algorithm is estimation to the stanar roa surface conitions ith Fuzzy inference. This estimation uses estimate µ graient: Â, an λ base on geometrical characteristics. The block iagram of the imal slip ratio estimator is shon in Fig. 9. Using information from these algorithms, ˆ λ is obtaine by (16). Estimate imal slip ratios to each stanar roa, ˆ λ,,, A ˆ λ G ˆ λ S an ˆ λ I are eighte by K A, KG, KS, an K I respectively, hich are roa surface conition similarities ith stanar roa surface conitions. K ˆ ˆ ˆ ˆ Aλ + K A Gλ + K G Sλ + K S IλI ˆ λ = (16) KA + KG + KS + KI The estimate result by this technique ill be shon in 5.2. Figure 7: Geometrical characteristics of µ - λ curves Figure 8: The schematic about the classification of roa surface conitions Figure 9: Block iagram of imal slip ratio estimator

7 4.2. Proposal of a novel estimation technique base on vibration characteristics The roa surface conition estimation techniques base on the information of slip ratio an riving-force ere escribe in the previous sections. These techniques nee chassis velocity to obtain slip ratio. The novel estimation technique propose in this section uses vibration characteristics beteen riving-force an heel velocity. It oes not nee chassis velocity. In the folloing, this estimation technique is introuce by using the experimental ata from UOT March I, an its effectiveness is confirme. The block iagram of the roa surface conition estimation is shon in Figure 11. In this estimation technique, a system transfer characteristic from heel velocity to riving-force is analyze by using the experimental ata. To analyze the roa conition change, Short Time Fourier Transform (STFT) is utilize. As is ell knon, the original Fourier Transform takes the form of (17). jω X( e ) = x( n) e n= jωn On the other han, STFT is given by (18). jω X ( e ) = x( n) ( n kn) e kn n= jωn When e nee to etect the change of the frequency spectrum accoring to time, the signal x( n ) ith the ino function ( n ) an limite length N is calculate by the Fourier transform. The signal x( n ) is cut out by the ino function ( n ) an this is the reason hy this calculation is calle Short Time Fourier Transform. The ino function is shifte along time axis. Above-mentione proceure is repeate to analyze the time epenent frequency spectrum. The concept of the signal processing is shon in Figure 11. By using STFT, the time shift of system transfer function can be observe. When the system input an output are assume to be x( n ) an yn ( ) respectively, the transfer function G( j ω) is given by (19), P ( jω) = G( jω) P (19) x xy here, the auto-correlation function x R xx an the cross-correlation function R ( m) = E{ x( n) x ( n+ m)}, R ( m) = E{ x( n) y ( n+ m)} xx xy R xy are efine by (20). Then, the poer spectrum ensity: Pˆ ( jω ), Pˆ ( jω ) an the transfer function: Gˆ ( j ω ) are obtaine as follos: ˆ ( ) ( ) j m Pxx jω = Rxx m e ω, ˆ ( ) ( ) Pxy jω = Rxy m e ω m= xx m= xy j m, an (17) (18) (20) ˆ ˆ P xy G ( j ω ) =. (21) Pˆ xx Figure 10: Block iagram of tire system ientification Figure 11: STFT analysis

8 These relations are applie to the experimental ata an the frequency spectrum of transfer function from heel velocity x( n) = V to riving-force yn ( ) = F is analyze. The experimental conition is shon in Figure 12. We use et iron plates as slippery roa surface. Water is scattere to reuce the friction coefficient. The front heels are on the et iron plate area beteen t = 1.3 sec. an 2. 0 sec. In the analysis, Hanning ino shon in Figure 13 is applie. The experimental ata an the result of the analysis are shon in Figures 14 an 15, respectively. As the result of this analysis, the transfer function gain on et plate is bigger than that on ry asphalt roa. This characteristic appears aroun 10Hz or less. Figure 12: Roa conition in experiment Figure 13: STFT analysis Figure 14: Experimental ata Figure 15: Result of STFT analysis

9 5 Application of the roa surface conition estimation 5.1. Inication of ahesion rate to river If the car tells the river "Our car has entere snoy roa", it must be a great help for vehicle safety. The µ estimation technique realizes this function [6]. The technique for µ estimation before entering ski state as propose in The ratio of present riving-force to estimate maximum riving-force can be use as the information of ahesion state beteen tire an roa. The ahesion rate r is efine as (22). F r = µ N (22) In (22), F an µ N are obtaine by the riving-force observer an frictional coefficient estimator respectively. Ahesion state beteen tire an roa can be quantitatively presente to river by shoing r. In the case that r is lo, the state of tire is kept in ahesive if heel is accelerate further more. Meanhile, in the case that r approaches 1, the possibility of skiing is high even if heel is accelerate a little. Driving-force an ahesion rate hen vehicle runs from ry asphalt roa to et iron plate suenly is shon in Figure 16. On ry asphalt roa, r is about 0. 5 an the vehicle is in safe state. While, on et iron plate, r is rapily up to about 0.8 shon in Fig. 16(b). It is possible to inform quantitatively ho easy to ski cause by suen change in roa surface conition even if the riving-force is kept almost constant as shon in Figure 16(a). (a) Estimate maximum riving-force (b) Inicate ahesion rate Figure 16: Estimation result of riving-force an ahesion rate hen roa surface conition changes Suenly 5.2. Optimal slip ratio control Slip ratio can be maintaine to commane value by strong feeback control. As riving-force is affecte by highly nonlinear frictional characteristics beteen tire an roa, real-time generation of imal slip ratio is necessary hile vehicle is moving (see 4.1.2).

10 Figure 17: Block iagram of slip ratio control Figure 18: Whole block iagram of the imum slip ratio control system The technique of imal slip ratio control, hich makes λ follo up changing in real-time ith roa surface conition, realizes the maximization of riving-force. To achieve this control, slip ratio control shon in Figure 17 is applie. λ, the estimate λ using the imal slip ratio estimator, is set up as the esire value for the slip ratio control. To obtain ˆ λ, the estimation algorithm base on Fuzzy inference is applie, introuce in The hole block iagram of the imal slip ratio control system is shon in Figure 18 [8]. Here, cruising simulation is performe using the estimation algorithm explaine in The approximate Magic-Formula shon in (23) is applie for µ - λ curve. µ = Csin( Darctan( Eλ)) (23) Five µ - λ curves hich have ifferent µ an λ are ecie by using the experimental ata from "UOT March I" for the simulation. These curves are shon in Figure 19. ˆ λ Figure 19: The schematic of µ - λ curves use in simulation

11 (a) Change from asphalt A to asphalt B (b) Change from asphalt B to asphalt A (c) Change of riving-force in case of (a) () Change of riving-force in case of (b) Figure 20: Simulation results at the changing roa surface conition Transient response of λ is simulate in the case that vehicle is in full acceleration an the frictional characteristic change at the moment of 5 sec. Dea-zone is set in 01. < Aˆ < 05., an Lo Pass Filter is inserte into λ an µ to uniform the elay of input signals to each estimator. Figures 20(a) an (b) are the estimation results hen the roa surface conition changes. It takes about 2 sec. to follo up in both case of Figs. 20(a) an (b). Change in the riving-force of Figures 20(a) an (b) cases is epicte in Figures 20(c) an (). The maximum riving-force is ell folloe ithin about 1 sec. This elay is alloable hen slippery roa, such as sno-covere roa, continues for a long time, although it is ifficult to estimate a small ater pool suenly appears uring cruising even on asphalt roa. 6 Conclusion In this paper, the roa surface conition estimation base on the riving force observer an some of its applications ere given. As the examples of roa conition estimation, µ estimation base on Yamazaki's brush moel of tire, λ estimation base on geometric similarity of µ - λ curves, an a novel estimation technique base on vibration characteristics ith Short Time Fourier Transform have been explaine. As the applications, the inication technique of the ahesion rate to river, an the imal slip ratio control ere given. These techniques can be realize firstly by using such avantages of electric motors that the motor torque can be knon easily from the motor current. In other ors, these avance estimation an control techniques are only available in EV. We believe that these remarkable avantages of EV ill open the ne fiel of control an estimation in the future electric vehicle.

12 7 References [1] Y. Hori, Recent Trens of Electric Vehicle Technology, Japan-China Bilateral Seminar on Transportation Research an Infrastructure Planning in 1998 (JC-TRIP 98), Beijing, [2] Y. Hori, Future Vehicle riven by Electricity an Control -Research on 4 Wheel Motore UOT March II, Proc. of AMC 2002, invite paper, pp.1-14, Maribor, Slovenia, [3] S. Sakai, H. Sao an Y. Hori, Motion Control in an Electric Vehicle ith Four Inepenently Driven In-Wheel Motors, IEEE Trans. on Mechatronics, Vol.4, No.1, pp.9-16, [4] H. Shimizu, K. Kaakami, Y. Kakizaki, S. Matsugaura an M. Ohnishi, KAZ The super electric vehicle, Proc. of EVS18, Berlin, [5] S. Sakai, T. Okano, C. H. Tai, T. Uchia an Y. Hori, 4 Wheel Motore Vehicle UOT Electric March II - Experimental EV for Novel Motion Control Stuies-, INTERMAC2001 Joint Technical Conference, Tokyo, [6] Y. Hori an K. Furukaa, Roa Surface Conition Estimation an Control utilizing Avantages of Electric Vehicle, 27th Technical Meeting of Control Technology Division, 2n Symposium of Aaptive an Learning Committee, SICE (Society of Instrumentation an Control Engineers), pp.1-16, 2002, in Japanese. [7] Y. Hori, Y. Toyoa an Y.Tsuruoka, Traction Control of Electric Vehicle -Basic Experimental Results using the Test EV UOT Electric March, IEEE Trans. on Inustry Applications, Vol.34, No.5, pp , [8] H. Kataoka, H. Sao, S. Sakai an Y. Hori, Optimal Slip Ratio Estimator for Traction Control System of Electric Vehicle base on Fuzzy Inference, The Transactions of The Institute of Electrical Engineers of Japan, Vol.120- D, No.4, pp , 2000, in Japanese. [9] H. Sao, S. Sakai an Y. Hori, Roa Conition Estimation for Traction Control in Electric Vehicle, in Proc. of the 1999 IEEE International Symposium on Inustrial Electronics, Ble. Slovenia, 99TH8465,Vol.2, pp , [10] S. Yamazaki, Evaluation of Friction Coefficient beteen Tire an Roa Surface uring Running, Journal of Automotive Engineers of Japan, Vol.51, No.11, pp.58-62, 1997, in Japanese. [11] K. Furukaa an Y. Hori, Recent Development of Roa Conition Estimation Techniques for Electric Vehicle an their Experimental Evaluation using the Test EV UOT March I an II, Proc. of IECON 2003, invite paper, Roanoke, Virginia, USA, 2003, to be presente. 8 Authors Furukaa Kimihisa, Master's egree caniate, University of Tokyo, as born in He receive B.C. egree in electrical engineering from Science University of Tokyo in 2002, an entere the master course in University of Tokyo. His research fiel covers poer electronics, an motion control of electric vehicles. He is a member of the Institute of Electrical Engineers of Japan. Yoichi Hori, receive the B.S., M.S. an Ph.D egrees in Electrical Engineering from the University of Tokyo in 1978, 1980 an 1983, respectively. In 1983, he joine the University of Tokyo, the Department of Electrical Engineering as a Research Associate. He later became an Assistant Professor, an Associate Professor, an in 2000 a Professor. In 2002, he move to the Institute of Inustrial Science, the University of Tokyo, as a Professor of Information & System Division, Electrical Control System Engineering. During , he as a Visiting Researcher at the University of California, Berkeley (UCB). His research fiels are control theory an its inustrial application to motion control, mechatronics, robotics, electric vehicle, etc. He is no the Vice Presient of IEE-Japan IAS.