To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structura...To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control, multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.展开更多
Dynamic characteristic is presented by identifying the model and the dynamic parameters of a precise long stroke linear motor （PLSLM） with the air-bearing in optical lithography. The PLSLM is supported by air-bearin...Dynamic characteristic is presented by identifying the model and the dynamic parameters of a precise long stroke linear motor （PLSLM） with the air-bearing in optical lithography. The PLSLM is supported by air-bearing on the stator, and is driven by on-board two large linear motors in a cross-configuration. Firstly, a model of the PLSLM is established by finite element method （FEM）. Secondly, based on the model, the natural frequencies and model shapes are discusse＆ And the contribution of each active mode is evaluated by computing the modal participation factors （MPF）, which indicates the major vibration direction. Furthermore, by the experimental modal analysis, the experimental results are in agreement with simulation results, which it is sure that the FEM is reasonable. What＇s more, comparing with the effects on the frequency due to the air-bearing stiffness, the relations of the natural frequencies with the air-bearing stiffness are found. It is found that the frequency response curve is fluctuant with the air-bearing stiffness in each direction. Finally, it is conclusion that the natural frequency of the PLSLM is largely affected by the air-bearing stiffness variety. This research is contributed to the dynamic characteristics resulted from the air-beating stiffness. Further work will include better optimization on the dynamic parameter in the controller design through the control algorithm for the precise long stroke motor.展开更多
基金Project supported by the Aviation Science Foundation of China (No.2000CB080601) the National Defence Key Pre-research Project of the 'Tenth Five-Year-Plan' of China (No.2002BK080602)
文摘To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control, multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.
基金National Basic Research Program of China (973 Program,No.2003CB716206)National Natural Science Foundation of China (No.50605025)
文摘Dynamic characteristic is presented by identifying the model and the dynamic parameters of a precise long stroke linear motor （PLSLM） with the air-bearing in optical lithography. The PLSLM is supported by air-bearing on the stator, and is driven by on-board two large linear motors in a cross-configuration. Firstly, a model of the PLSLM is established by finite element method （FEM）. Secondly, based on the model, the natural frequencies and model shapes are discusse＆ And the contribution of each active mode is evaluated by computing the modal participation factors （MPF）, which indicates the major vibration direction. Furthermore, by the experimental modal analysis, the experimental results are in agreement with simulation results, which it is sure that the FEM is reasonable. What＇s more, comparing with the effects on the frequency due to the air-bearing stiffness, the relations of the natural frequencies with the air-bearing stiffness are found. It is found that the frequency response curve is fluctuant with the air-bearing stiffness in each direction. Finally, it is conclusion that the natural frequency of the PLSLM is largely affected by the air-bearing stiffness variety. This research is contributed to the dynamic characteristics resulted from the air-beating stiffness. Further work will include better optimization on the dynamic parameter in the controller design through the control algorithm for the precise long stroke motor.
