The University of Tokyo, Institute of Industrial Science (Information & System Division, Electrical Control System Engeneering) Ce-501, Komaba,

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1 The University of Tokyo, Institute of Industril Science (Informtion & System Division, Electricl Control System Engeneering) Ce-5, 4-6- Komb, Meguro-ku,Tokyo Jpn Phone: , Fx: E-Mil: [] A. ms,, ms, B.,,,,, C.,, [3] 8 [4],,,, ABS TCS,,,,,,,.2,, 2, 3, µ µ,,, 4,, 5 µ,, µ 6,, 6

µ,,,, 3, DC Wounded Motor Current Sensor motor velocity (8ppr) ccelertion commnd PC98 note motor current output commnd Qudrnt Chopper Counter Bord A/D, D/A converters Bttery rer tire velocity (2ppr)

2 µ,,,, 3, DC Wounded Motor Current Sensor motor velocity (8ppr) ccelertion commnd PC98 note motor current output commnd Qudrnt Chopper Counter Bord A/D, D/A converters Bttery rer tire velocity (2ppr) ,,, 2,,,, Conversion Bse Nissn Mrch (Micr) size [mm] weight [kg](btteries included) Motor Advnced D.C. Motors, Inc. type DC series wound rted power 9[kW](hr.), 32[kW](5min.) size/weight φ 232,length 397[mm], 65[kg] Controller Curtis Instruments, Inc. type MOSFET PWM Chopper opertion frequency 5[kHz] rted voltge/current 2[V]/4[A] Bttery Jpn Storge Bttery Co.,Ltd. GTX-3E4L type led cid voltge/cpcity 2[V]/92[Ah](5hr.) weight 27.5[kg] CPU PC98NS/T(i386SL, 2MHz) weight 3.2[kg] A/D nd D/A converters 2bit, 8ch/2bit, 2ch 2, [5][4][5], 4 F d F s, 2 F d, F s µ, N () F d = µ(λ)n () 2., 5 λ, 2

3 F d 4. N F s 3, λ opt, 6, V w >V [2][6],, V M w M V w F m N F d 5., V, V w (2) λ = V w V mx(v,v w ) (2) 2, 2, µ mx,, µ mx µ mx λ opt,,.5.2 λ λ opt, λ >λ opt, λ, λ = F s = µ(λ)n =,, µ-λ 6. 6, dv w M w = F m F d (3) dt M dv dt = F d (4), M w, F m, F d, M, (3), (4), F m F d F d = M w M dv w dv (5), V w >V, (2) dv w dv = V w V = λ (6) (5), () µ ( ) µ = F M w m M + M w M N + M w + M w M M λ (7), F m λ, F m /N, +M w /M, 3

4 (c) F m µ 4. Friction Coefficient µ B A C (b) () D E I Fd KN KN Q r Q J Js Jns ω Jn λ r ˆFd 7. 8., µ-λ,, 2, 7 (),(b),(c), F m () (b) (c) µ-λ, () (b) (c) (b) () A B E D A 2 (b) (c) (c) (b) E D,, λ opt,,, 4, µ (), F d N, [][][2],,,, DC, AC (3), (8) F d = dω (T J r dt ) (8), r, T, J, ω, F m = T/r, M w = J/r 2 (8), 8 ˆF d, 8 K, N, J n,,,,, 8 Q Low Pss Filter (LPF) 4.2, M (9) F d = M dv dt (9) 4

5 5 4 Current(A) Driving Force(N) 3 2 Velocities(m/s) Time(s) () Driving Wheel Chssis Time(s) (b) 9. Driving Force(N) Observed Reference Time(s).,, () {.5I 2 I<2 T =.252I.4 () I>2 9 Q, () Low Pss Filter Q = ( + τs) 2 (), τ =.5[s].2.4., 3[s], 9(b), 9(b),, 5 µ Friction Coefficient dµ dλ µ 2 µ-λ µ,, µ [7][8], µ 2 5. µ µ (2) 5

6 .5, (3) (6).45.4 λ(t) = α µ(t) β α = C µ(t)+c 2 (6) Texture mesure gmm s.2.5. s s s ii i i i i g g g g g g i (6) λ µ (6) β/α α, β, /α (6) slip slope k 3. µ ()sphlt, (s)snow, (i)ice, (g)grvel α = dµ dλ = dµ(t)/dt dλ(t)/dt (2) (3) µ(t) =αλ(t)+β (3) F. Gustfsson (3), [7], µ, λ = µ 3 λ = µ, λ = µ, λ = µ 3, µ α, ω v, r (4), (5),, (5) Vr e = ω v/r (4) γ =4Vr(e) (5) 3, γ α γ >.27 γ <.27, α>3 γ <.27, α<3, γ, α, µ Estimted slip slope Time [s] 4. µ 5.2 µ (8),, 2 µ µ,,, µ µ (7), (8) µ [][][2][3] A = dµ dλ = dµ/dt dλ/dt dµ dt = Adλ dt (7) (8),, κ, (9) (2) (2) y[k] =ˆθ T [k]φ[k] (9) P [k ]φ[k] ˆθ[k] =ˆθ[k ] +φ T [k]p [k ]φ[k] (ˆθ[k ]φ[k] y[k]) (2) 6

7 P [k] = [P [k ] κ P [k ]φ[k]φt [k]p [k ] ] (2) +φ T [k]p [k ]φ[k], κ γ =trp [k], κ (22) κ = +γ φ[k] 2 (22), (8) (9) (23) (25) µ φ[k] = dλ dt (23) y[k] = dµ dt (24) ˆθ[k] =Â (25),,.6, γ (22), φ[k],,,, µ 5 6() κ =.98, (b) γ =. 6(), t = 2[ms], 5(),,, λ µ,, 6(b) (), dλ/dt = κ = () Estimted Vlue of A 2 Forgetting Fctor.98" Driving Force[N] 5 Driving Force (b) Estimted Vlue of A () (κ =.98) gmm= (b) (γ =.) µ () 7

8 Driving Force[N] Estimted Vlue of A Estimted Vlue of A Slip rtio () Driving Force (b) Forgetting Fctor= () (κ =.98) gmm= (b) (γ =.) 8. µ,, dλ/dt, κ< 9,,, Forgetting Fctor gmm= (γ =.),,,, 2,, κ γ, 6 µ 6. λ = µ µ mx µ mx, [9][] [] 6.., 2 2 2, 22,, p l, p m (26), F z w (27) p =4p m l ( l ) (26) 8

9 N = 2 3 p mwl (27) 23, σ (), k x (28), σ (s) µ mx, (29) µ mx p Sliding Are Adhesive Are l σ () = k x λ (28) σ (s) = µ mx p (29) 23. = (3) Rod Friction Coefficient Ground Contct Are Adhesive Are Sliding Are σ () = σ (s) (3) (28), (29) (3), S n (3) S n = l = C sλ 3µ mx N (3), C s, (32) 2. C s = 2 wk xl 2 (32) T F d l Adhesive Are Sliding Are 2. p p m w l 22. =,, F d (33) F d = = l σ wd σ () wd + l σ (s) wd = C s λl 2 n + µ mx N( 3l 2 n +2l 3 n) =3µ mx NS n ( S n + S2 n 3 ) (33), (3) S n, F d (34) F d = µn = C s λ (C sλ) 2 3µ mx N + (C sλ) 3 27(µ mx N) 2 (34) (34) µ mx N 2,, µ mx N (35) µ mx N = 3(C sλ) 2 + 3(C s λ) 3 (4F d C s λ) 8(C s λ F d ) (35) (35), F d, λ, C s 9

10 ,,, (32) C s, C s C s 2,, (36), λ = C s C s = df d dλ (36) λ=, 5 µ,,, S n = (3), (37) C s = 3µ mxn λ opt (37) 2 C s 6..2,, (35) µ-λ, [] 5.2 µ,,,,, y[k] =ˆθ T [k]φ[k], (38) (4), 5.2 (2), (2) y[k] =3(C s λ) 2 + 3(C s λ) 3 (4F d C s λ) (38) ˆθ[k] =µ x W (39) φ[k] = 8(C s λ F d ) (4) λ (4) φ[k],, λ, φ[k],, Driving Force(N) () (b) 24. Driving Force(N) Mx Driving Force

11 , C s,, (37), (4) C s =7 4 [kn] (4),,,, C s, (4) Vehicle Direction Driving Force(N) Driving Force Mx sphlt () wetplte -.2 sphlt wet plte 6[m] x[m] Wet Plte Asphlt (b) 28. Driving Force(N) Driving Force Mx 2 3 () (b) , 2[s], γ = 25, Low Pss Filter 4.2 (), τ =.4[s],,,, µ, 26,,, 27 27, [s],.6[s], 2[N],,.6[s],

12 , 2[N],,, 26 3[m] 28 27,,, , r (42) r = ˆF d µ mx N (42) (42) ˆF d µ mx N (42),, r, r 6..3, ,, (),,, LED Driving Force(N) Adhesion Rte Mx Driving Force sphlt wet plte () sphlt wet plte (b) λ opt, µ A Â,,,,, [4][5] µ-λ µ-λ λ opt µ, 3 A, A 2 µ, 2

13 , µ-λ, µ mx µ mx, 6., µ mx,, λ µ, ASPHALT, GRAVEL, SNOW, ICE 4, µ mx, 4, µ λ 3, ASPHALT = ^ λ µ λ µ Â λ, 4 λ opt, ˆλ opt (43), K A K I ASPHALT ICE, ˆλ opta ˆλ opti λ = Smll µ ICE SNOW GRAVEL ASPHALT m 35. λ =Middle-Smll, Middle-Big, Big µ ˆλ opt = K Aˆλ opta +K GˆλoptG +K S ˆλoptS +K I ˆλoptI K A + K G + K S + K I (43) λ 33, µ λ =MS MB B µ 34 35, λ =SS µ-λ 36. L 3

14 Â, µ A λ λ opt. λ Â (44) L, 36, 3 L λ opt /λ 2 L = log Â (44) 2. L λ opt /λ Rod Conditon L(=log Â) PB PS ZO NS NB ASPHALT GRAVEL SNOW ICE , Â, λ opt, (45) ˆλ opt if A = Negtive then ˆλ opt [k+] =.9ˆλ opt [k](45), , 37 λ opt λ, 38 λ opt, ˆλ opt ˆλ opt ,, µ-λ (46) Mgic-Formul 39. µ = C sin(d rctn(eλ)) (46) 3, λ opt µ mx 5 µ-λ 4, 5[s], λ. < Â<.5, λ µ Low Pss Filter 4. µ-λ 4

15 4 43 4, 42, 2[s] λ λ opt, λ opt 43 2[s], 42, 43 44, 45 [s] F d,, [s] 4. A A A B B A,,,

16 ABS,,.6.4 Adhesion.2 A Skid B Adhesion Time[s] () Grdient of F d -F m curve g Theoreticl F d / Fm for dhesive wheel. Experiment Skid Simultion Time [s] (b) 46. C [] Y.Hori, Future Vehicle driven by Electricity nd Control -Reserch on 4 Wheel Motored UOT Mrch II, Proc. of AMC 22, invited pper, pp.-4, Mribor, Sloveni, 22. [2] Y.Hori, Y.Toyod nd Y.Tsuruok, Trction Control of Electric Vehicle -Bsic Experimentl Results using the Test EV UOT Electric Mrch, IEEE Trns. on Industry Applictions, 34, 5, pp.3-38, 998. [3] S. Ski, H. Sdo nd Y. Hori, Motion Control in n Electric Vehicle with Four Independently Driven In-Wheel Motors, IEEE Trns. on Mechtronics, 4,, pp.9-6, 999. [4] H. Shimizu, K. Kwkmi, Y. Kkizki, S. Mtsugur nd M. Ohnishi, KAZ The super electric vehicle, Proc. of EVS8, Berlin, 2. [5], ABS,, 995. [6],,,, D, Vol.8-D, No., pp [7] F. Gustfsson, Slip-bsed Tire-Rod Friction Estimtion, IFAC Automtic, Vol. 33, No. 6, pp.87-99, 997. [8] M. Sugi, H. Ymguchi, M. Miyshit, T. Umeno nd K. Asno, New Control Technique for Mximizing Breking Force on Antilock Breking System, Proc. AVEC 98, pp , 998. [9],,, Vol. 5, No., pp.58-62, 997. [],,,,, Vol.2, pp.87-9, 999. [],,,, 5, pp.45-46, 999. [2] H. Sdo, S. Ski nd Y. Hori, Rod Condition Estimtion for Trction Control in Electric Vehicle, in Proc. of the 999 IEEE Interntionl Symposium on Industril Electronics, Bled. Sloveni, 99TH8465,Vol.2, pp , 999. [3],,,, 4, pp.93-94, 998. [4],,,,, D, Vol.2-D, No.4, pp , 2. [5],,,,,, pp.43-44, 999. [6],,,, D, Vol.2-D, No.2, pp , 2. 6

.. F x) = x ft)dt ), fx) : PDF : probbility density function) F x) : CDF : cumultive distribution function F x) x.2 ) T = µ p), T : ) p : x p p = F x

.. F x) = x ft)dt ), fx) : PDF : probbility density function) F x) : CDF : cumultive distribution function F x) x.2 ) T = µ p), T : ) p : x p p = F x 203 7......................................2................................................3.....................................4 L.................................... 2.5.................................