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Mechatronic Systems, Simulation, Modeling and Control 2012 Part 4

Tham khảo tài liệu 'mechatronic systems, simulation, modeling and control 2012 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 134 Mechatronic Systems Simulation Modelling and Control ặ 2 p h - H- ac e. c fa ỉpỹ-2 py h -H - ac e js k 2 pz - as e i 1 2 3 i 1 2 3 i 1 2 3 H 2 a c XX c fa py h-H s ei - pzc ei j l2 2 a c X px c X py h-H s e2 -pzc e2 Je3 2 a c X px c X pv h-H j s X -pzc e3 j dr2 _ dr3 ãẽ7 ãẽ dTL dTL ddx de3 drx _ dr2 dfk de Once we have the derivatives above they are substituted into equation 44 and the Lagrangian multipliers are calculated. Thus for j 1 2 3. 2 1 px h-H a c ei x 2 p h-H a c e2 cp px h-H a c e3 cp mp 3mbjpx-ppx 2p1 py h-H a c ei si i Ị. Ả2 y h-H a c e2 s 2 j Ấ3 py h-H a cX sX J mp 3mb ịpy -ppy 2 21 pz-as ei Ấ2 pz-as e2 23 pZ-as e3 mp 3mb pz g m 3mb -ppz 50 Note that Fpx Fpy and Fpz are the components Qj j 1 2 3 of an external force that is applied on the mobile platform. Once that the Lagrange multipliers are calculated the 45 is solved where j 4 5 6 and for the actuator torques rck Qk 3 k 1 2 3 . Tc1 maa 2 1 mba 2 ei ma mb gac ei -2 aẰ1 pxc 1 pys 1 h-H s ei -pzc e Tc 2 maa 2 1 mba 2 e2 ma mb gac e2 -2 aẢ2 pxc 2 pys 2 h - H s e2 -pzc Tc3 maa 2 1 mba 2 e3 ma mb gac N-2 aẰ3 pxc 3 pys 3 h - H j s e3 -pzc 51 New visual Servoing control strategies in tracking tasks using a PKM 135 Fig. 7. Basic architecture of the control system of the Robotenis platform. The results above are used in real time to control each joint independently. The joint controller is based in a classical computed-torque controller plus a PD controller Santibanez and Kelly 2001 . The objective of the computed-torque controller is to Feedback a signal that cancels the effects of gravity friction the manipulator inertia tensor and Coriolis and centrifugal force see in Fig. 7. 3.4 Trajectory planner The structure of the visual controller of the Robotenis system is called dynamic positionbased on a look-and-move structure Corke 1993 . The above structure is formed of two intertwined control loops the first is faster and makes use of joints feedback the second is external to the first one and makes use