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Tham khảo tài liệu 'motion control 2009 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Rolling Stability Control of In-wheel Motor Electric Vehicle Based on Disturbance Observer 167 Yawing motion I ywSY Fyfl Fyfr l f - Fyrl Fyrr l r O lf o lr 4 -2Cf fi VV r-Wf 2c r fi- V rK N Rolling motion Mshcrữy Irỉ C rộ Krộ-Msễhcr sin ộ ộ ộ wheel-lift-off 5a d Mshcray Ir 2ộ - Mh sin ộ M sg ỵcosộ ộ ệwheel-lift-off 5b Here these motion equations need to be expressed as state equations to design observer. Observer gain matrix however becomes 2 4 matrix if whole equations are combined. To reduce redundancy of designing gain matrix tire dynamics and rolling dynamics are separated. A matrix Art connects two state equations. From eq. 3 and eq. 4 state equation is expressed as Xt Atxt Btu 6 yt Ctxt Dtu- 7 It is noted that there is feedforward term in the transfer function from u to yt . Therefore to eliminate feedforward term and design stable observer xt vector is defined using differential torque and steering angle as the following equations where xt ay - c28 ay - c25 - b1 N - c1 r yt ay u n 1 At 0 1 _- a0 - ai _ B b 1 _aib1 b0 acc ajcj c0 _ Ct 1 0 Dt 0 c21 4cfcrl2 2 c flf - crlr 2M c flf crlj 2Iy c f cr a0 2 -------------- a1 ------------TYTTr------------ 0 MIyV2 Iy 1 MIyV 2 cf c 2 cflf - cl 4cfcJ 4cfcrlrl --- b1 J J c0 c1 2 M 1 MI V M 1 MI V . . . . . 2cf c0 c0 a0 c2 cj cj ajc2 c2 N From eq. 5a state space equation is xr ArXr Ar y 8 168 Motion Control yr CrXr 9 It should be noted that lateral acceleration dynamics expressed as eq. 6 is a linear time varying system depending on vehicle speed. The states are observable at various longitudinal speed except for a very low speed. In the following sections for repeatability reason experiment has been done under constant speed control. Observer gains are defined by pole assignment. These parameters are based on the experiment vehicle Capacitor-COMS1 developed in our research group. The method to evaluate the values of Cf Cr are referred to the paper Takahashi et al. 2006 . Since rolling dynamics was unknown model .
