tailieunhanh - Mechatronic Systems, Simulation, Modeling and Control Part 6

Tham khảo tài liệu 'mechatronic systems, simulation, modeling and control part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 164 Mechatronic Systems Simulation Modelling and Control Fig. 11. Time evolution of the estimated parameters p1 and p2. The dotted lines represent the limited values of variation. Time s Time s Time s Time s Nonlinear Adaptive Model Following Control for a 3-DOF Model Helicopter 165 Fig. 12. Time evolution of the estimated parameters from p3 to P10. The dotted lines represent the limited values of variation. The model equations with model uncertainties and external disturbances Parameter identification algorithm Although the use of the integral form of the dynamics has improved the tracking performance of both the outputs e and 9 tracking errors still remain. On the basis that these errors are caused by model uncertainties and external disturbances for example motor dynamics or friction other than viscous friction we add the additional terms fe fg and fị into equation 4 to represent model uncertainties and external disturbances. Generally the additional terms should be given as for instance fe t cf t 46 where Ci is a constant and fi is a known function of time. For simplicity however here we assume these additional terms are constant because tracking errors in the experimental results approximately remain constant in Fig. 10. Then the system dynamics are expressed as W1 k -e k ĨĨqi k w2 k - 9 k Ĩ2 1-2k w3 k - ị k gq3 k 47 48 166 Mechatronic Systems Simulation Modelling and Control where 1 T P11 T 2 zĩ P12 T 3 d P13 T q1 k T k 1 q2 k T k 1T q3 k 3 k 1T P11 fe ỉ P12 fe Je P13 fy ỉ It is worth noting that all the parameters Pi i 1 . 13 of the equations are constant. Then the integral form of the dynamics is obtained as well as the previous subsection as where Zi k Tqt k i 1 2 3 49 q1 k T k q15 k T q2 k 2 k q25 k T q3 k 3 k q33 k T q15 k T Ẹ 1 l k- n-1 i l- n-1 T2 n - 1 2 q25 k T2 n - 1 2 q33 k T2 n - 1 2 Hence defining the estimated parameter vectors corresponding to the vectors 1 2 3 as 1 k 2 k 3 k the estimate model for expression 49 is given by T. . . . .

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