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Manufacturing the Future 2012 Part 19

Tham khảo tài liệu 'manufacturing the future 2012 part 19', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | On Direct Adaptive Control for Uncertain Dynamical Systems - Synthesis and. 891 4.4 Discrete-time Active Suspension System We use the quarter car model as the mathematical description of the suspension system given by Laila 2003 r 1 T 0 01 T rn1 - 1 Tp 0 x k 1 p 1 0 0 p 1 2 1 T Ta 2 0 Tp - 1 L p 1 A k x k - 128 where d k 1 -10 0 k 0 Wsm 20rá 0 k 100 A k 1 0 k 100 0 0 0 1 00 11 0 k k 800 0 0 5 0 0 0 0 0 k 800 0 k 0.01sm 0.3k . x k x1 k x2 k x3 k x4 k T and x1 is tire defection x2 is unsprung mass velocity x3 is suspension deflection x4 is sprung mass velocity _. rad . . . _ _ . D 20 and p 10 are unknown parameters T 0.001 is sampling time sec d k is disturbance modeling the isolate bump with the bump height A 0.01m and A k is the perturbation on system dynamics. Next let Ac is asymptotically stable r 1 -1 0.75 1 1 r 0 1 0.75 0.3 -1 - 0.1 0 Ac 0 0 -0.1 - 0.5 B0 0 L - 0.1 0 0 0.1 _ L1J We apply the framework from Corollary 4.2 and choosing the design matrices 892 Manufacturing the Future Concepts Technologies Visions 2 0 0 0 1 0 0 0 0 10 0 0 4 0 0 Y 0.03 R 0 0 4 0 0 0 9 0 _ 0 0 0 1 _ 000 0.82 q 0.05 Tire Deflection 0.06 0.04 A 0.02 -0.02 0 0.5 1 1.5 UnspruTgmMaSsesc Velocity 2 2 2 0 0.5 1 Time sec 1.5 2 Figure 9 Tire defection and unsprung mass Velocity Suspension Deflection 0.4 0.2 p n 0 -0.2 -0.4 _ 0 0.5 1 1.5 2 Sprunc MasTVelocity 20 10 X 0 -10 -20 _ _ 0 0.5 1 1.5 2 Time sec Figure 10 Suspension deflection and mass velocity On Direct Adaptive Control for Uncertain Dynamical Systems - Synthesis and. 893 P satisfies the Lyapunov equation 121 . The simulation start with x 0 0.05 0 0.01 0 .To demonstrate the efficacy of the controller the states are perturbed to x 800 0 0 0.02 0.5 r at k 800 and the system parameters are changed to p 4 . The controller stabilizes the system in 2 sec under no information of the system changes either the perturbation of the states. Figure 9 depicts tire defection and unsprung mass velocity versus the time steps Figure 10 shows the .