Robust Active suspension Control Strategy to Improve Ride Comfort of Vehicles

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Chad Hubbard
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1 Robust Active suspension Contol Stategy to Impove Ride Comfot of Vehicles ( ) ( ) ( ) Yasutaa Tsuchida, Kyushu Institute of Technology, Tobata, Kitayushu-shi Qiang Wang, Kyushu Institute of Technology Masahio Oya, Kyushu Institute of Technology In this pape, a new obust active suspension contol scheme is developed so that ide comfot at any specified location becomes best. To achieve this end, a combined ideal vehicle is designed so that ide comfot at a specified location becomes best by using only one design paamete. To achieve the good popety stated above in eal vehicles, a obust tacing contolle is poposed. It is shown by numeical simulations that ide comfot at a specified location can be easily impoved and good obustness fo font and ea suspension stiffness, damping ate and tie sping stiffness is confimed Key Wods: Automobile, Ride Comfot, Ideal Model, Robust Tacing Contol 1. C C.G. P (1) (11) (1)-(11) f f u l m m uf u uf w u uf w f (1) Fig. 1 Two wheels model. l = l p. A x s (t) ẋ s 1 θ(t) A3 Hx (t) O n I n n n Hẋ (t) n n 1 A4 ẍ (t) = M 1 d(t) H 1 ẅ(t) ẍ u (t) = K u x u (t) Mu 1 (H T ) 1 d(t) ẅ(t) x (t) = H 1 [ f (t) w f (t), (t) w (t)] T (1) x u (t) = [ uf (t) w f (t), u (t) w (t)] T 3. d(t) = H T ( Cẋ s (t) Kx s (t) + u(t)) x s(t) = Hx (t) x u(t), w(t) = [w f (t), w (t)] T u(t) = [u f (t), u (t)] T, M =(Th T ) 1 diag[m, i c ]T 1 h M u = diag[m uf, m u ], K = diag[ f, ] C = diag[c f, c ], K [ u = Mu 1 diag[ ] uf, [ u ] ] 1 a 1 T h = I Dh, H =, D = 1 a () c a h a A1 q(t) = [ f (t), (t)] T l y(l, t) = [ l (t), θ(t)] T ( l (t) l ) d(t) y(l, t) = (I + Dl)M 1 d(t) [No. 7-] (7.11.4, ) c f -78-

2 Table 1 Notation of vehicle model C, CG cente and cente of gavity of vehicle body cg, θ vetical displacement at CG and pitching f, vetical displacement of vehicle body at positions on font and ea wheel axle uf, u vetical displacement of font and ea unspung mass w f, w vetical displacement of oad distubance added to font and ea wheel v longitudinal speed of vehicle m, i c spung mass and moment of inetia of vehicle body a half of vehicle body length h, l distances fom C to CG and fom C to P m uf, m u font and ea unspung mass f, font and ea suspension stiffness c f, c font and ea suspension damping ate uf, u font and ea tie sping stiffness u f, u font and ea wheel active contol foce l l p =.8 l p =.8 p [m] l p = l[m] 1 C l 1 1 (a) Combined vehicle (b) elation between l and l p Fig. Chaacteistic of combined ideal model. [m].4. Table Nominal values of paametes m 781 g i c 99 gm h.4 m a 1.38 m f 716 N/m 94 N/m c f 4 Ns/m c Ns/m m uf 69 g m u 96 g uf 9 N/m u N/m (a) (1) l p d(t) = M(I + Dl) 1 y(l, t) l p = ±.8m x(t) = [x T (t), x T u (t), ẋ T (t), ẋ T u (t), d T (t)] T l p ẋ(t) = Ax(t) + Bu x (t) D w ẅ(t) l p A = Γ + BF D w = [,, (H 1 ) T, I, ] T l (b) (b) (3) B = [,,,, H] T l p u x(t) = u(t) + u(t) 4 l p =.8m 3 I l =.8m I Γ = M 1 l (t) Θ(t) K u Mu 1 (H T ) 1 (4) x uf (t), x u (t) x sf (t), x s F =[ KH, CK u + K, (C + K)H, C + K, F ] 4(a) (b) F = C(HM 1 + Mu 1 (H T ) 1 ) (H T ) 1 (3) 6% x m(t) = [x T m(t), x T um(t), ẋ T m(t), ẋ T um(t), d T m(t)] T 4(c)-(f) Fig. 3 [m] Load distubance. (1) l p (l = l p ) (a) l -781-

3 [m/s ] [ad/s ] w u x Vehicle x ~ = x x m x ~ = x x u ( ) u um ( 6) (a) l 1 1 (b) Θ Fig. T T + ω ω B G α P Configuation of poposed contol system. 1 1 [m] (c) x uf 1 1 [m] (d) x u () Λ α = diag[α 1, α ] Λ β = diag[β 1, β ] α i β i s L L 1 µ(t) = d(t) H T M u L 1 [s(si + Λ α) 1 Λ β L[ x u(t)]] (6) (t) = x (t) M 1 H T M u L 1 [(si + Λ α) 1 Λ β L[ x u(t)]] (6) A u (s) = (si + Λ α )(s I + K u ) + Λ β s x u(t) 1 Fig. 4 (e) x sf 1 (b) x s Tansient esponses in combined ideal model. L[ x u (t)] = A u (s) 1 (si + Λ α )L[ u (t)] A u(s) 1 (si +Λ α)mu 1 (H T ) 1 L[µ(t)] (7) u(t)= (t) Kux um Mu 1 (H T ) 1 1 MM dm(t) (8) K u = K u K u, M = M M (7) µ(t) x u(t) x u(t) (t) o (t) (6) d(t) x (t) x (t) (t) = [(M (t)) T, (M (t)) T, µ T (t)] T (t) () 3. (t) (t) x (t) = x (t) x m (t) x u (t) = x u (t) x um (t) () d(t) = d(t) MM 1 (t) = A (t) + B (u x(t) + ω 1(t) + (t)) (9) d m (t) ω 1(t) = F x(t) (H T ) 1 MM 1 d m(t) + M uλ β d(t) y(l, t) = (I +Dl)M 1 d(t) = (K u x u(t) + M 1 (I + Dl)M 1 u (H T ) 1 d1(t) d m (t) M + L 1 [s(si + Λ α) 1 Λ αl[ x u(t)]]) l y(l, t) (t) = F x(t) + MuΛ β Kux u(t) l (I + Dl)M 1 d m (t) I x (t) x u (t) A = I, B = F = F F, d1(t) = d(t) d m(t) (9) (t) ω (t) H T (1) -78-

4 (a) l p = (b) l p =.8,.8 Fig. 6 Maximum vetical acceleation in the closed loop system in case of m add = g,6g, 1g. Fig (a) l p = (b) l p =.8,.8 Maximum vetical acceleation fo changes of K u. Fig (a) l p = (b) l p =.8,.8 Maximum vetical acceleation fo changes of K, C. Θ 7 (t) = Θ T ω (t) (11) K C (K = } Θ T = [ F, Mu Λ β Ku ] K,.8K, 1, K, C = C,.8C, 1.C) (1) ω (t) = [x T (t), x T u (t)] T 7 K C u x (t) = G (t) ω 1 (t) αω T (t)ω (t)b T P (t) (13) 8 K u (K u = K u,.8k u, 1.K u ) (8) u(t) α 8 G 1dB Â = A B G (14) P Â T P + P Â = I 6 (1) (13) 9 K u (K u = 1 (13) K u,.8k u, 1.K u ) l p =.8m 3 (t) l =.8m (t) ρ l (t) Θ(t) (16) α x uf (t), x u (t) ρ α x sf (t), x s(t) 9(a) ( ) 1 α 9(c) (d) (t) (8) u (t) 4. v = 1 1/36m/s, Λ α = diag[4, 4], Λ β = diag[6, 6] α = 6 l p l p =.8,,.8m (m add =, 6, 1g) (8) u (t) (b) (e) (f) -783-

5 [m/s ] 1 1 (a) l 1 1 [m] (c) x uf 1 Fig. 9 (e) x sf.. [ad/s ] 1 1 (b) Θ 1 1 [m] (d) x u 1 (b) x s Tansient esponses in closeed loop system. [9] A G Thompson and C E M Peace Diect Computation of the Pefomance Index fo an Optimally 1mm K contolled Active Suspension with Peview Applied C l p to a Half-Ca Model Vehicle System dynamics 3- (1) [1] A G Thompson and B R Davis RMS Values of foce Stoe and Tie Deflection in a Half-Ca Model with Peview Contolled Active Suspension Vehicle system Dynamics 39 (3) 4-3 l p [11] A G Thompson and C E M Peace RMS Values fo Foce Stoe and Deflection in a Quate-Ca Model Active Suspension with Peview Vehicle System Dynamics 39 (3) 7-7 [1] Masahio Oya Hioshi Haada and Yoshiai Aai. An Active Suspension Contolle Achieving the Best Ride Comfot at Any Specified Location on A Vehicle Jounal of System Design and Dynamics (7) 4-6 [13] H Kwaenaa and R Sivan Linea Optimal Contol Systems John Wiley & Sons (197) l p [1] D Hovat Suvey of Advanced Suspension Developments and Related Optimal Contol Applications Automatica 33-1 (1997) [] H Dai Zhang and W Zhang Robust Pefomance Analysis of Active Suspension with Model Uncetainty Using Stuctued Singula Value µ Appoach Vegicle System Dynamics Supplement 8 (1998) [3] Y J Tsao and R Chen Foce contol of Active Suspnesion Design with a Half Ca Model by Using Genetic Algoithms Poceedings of Intenational Symposium on Advanced Vehicle Contol (1998) [4] M M Elmadany and Z S Abduljabba Linea Quadatic Gaussian Contol of a Quate-Ca Suspension Vehicle System Dynamics 3 (1999) [] I J Fialhao and G J Balas Design of Nonlinea Contolles fo Active Vehicle suspnesions Using Paamete-Vaying Contol Systems Vehicle System Dynamics 33 () [6] S Ienaga F L Lewis J Campos and L Davis Active Suspension Contol of Gound Vehicle Based on a Full-Vehicle model poceedings of the Ameican Contol Confeence () [7] A G Thompson and B R Davis RMS Values fo Contol Foce Suspension Stoe and Type Deflection in an Active Suspension Vehicle System Dynamics 34 () [8] A G Thompson and C E M Peace Pefomance Index fo a Peview Active Suspension Applied to a Quate-Ca Model Vehicle System Dynamics 3 (1)

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