Modeling And Control For Ultra-precision MIMO Motion System With Flexible Structures

For lithography wafer stage,control bandwidth is the critical factor for the throughput and overlay accuracy,and nowadays the flexible structure dynamics have become the bottleneck to achieve excellent control bandwidth.Therefore,it is valuable both on theory and engineering application to study the modeling and control of multi-input multi-output(MIMO)motion system with flexible structures for ultra-precision wafer stage.With the object of suppressing the flexible modes as well as solving the contradiction between the flexible structure dynamics and the control bandwidth,this thesis focuses on the study of modeling,control,comprehensive properties analysis and optimization for the MIMO motion system with flexible structures.Considering the wafer stage as the control plant,this thesis firstly conducts the state space modeling for the MIMO motion system with flexible structure.Through theoretical modeling method,this thesis proposes a modal decoupling state space model,which realizes the modal states control for certain mechatronics system with fixed quantity of drivers and measuring sensors.This state space model is obtained by experimental modeling under closed-loop frequency domain identification and time domain identification,respectively.The frequency domain identification uses the general parameters fitting method to achieve the transfer function matrix model with the same denominator,and utilizes the singular value decomposition technology and the modal superposition method to obtain the state space model.The time domain identification uses the closed-loop subspace method with modal analysis to obtain the modal state space model directly.Research result shows that the proposed model is controllable and observable to satisfy the requirement of flexible structure dynamics control.Based on the modal state space model,a full-state feedback control strategy is proposed for MIMO system with flexible structures.Specifically,a Kalman filter is developed to online estimate the mode state variables as real-time state feedback.An error state space model with integral effect is proposed to eliminate the closed-loop system static errors.More importantly,the state feedback gain matrix is designed by the MIMO poles assignment method,which realizes the mode control purposes.On the other hand,in order to solve the flexible model perturbation and high-frequency model perturbation problems,the robust control of MIMO motion system with flexible structures is studied in this thesis.Firstly,a structured uncertainty state space model is studied to avoid modeling conservativeness and achieve less order.Secondly,the weight function matrixes are proposed by loop-shaping design method,which simplifies the model analysis and the controller design.Thirdly,? analysis and synthesis method is employed to reduce the conservativeness of controller design.The controllability and observability criterions are put forward for the comprehensive performance analysis and optimization of MIMO motion system with flexible structures.In order to realize the modeling optimization,the optimal input design is employed,which is designed by asymptotic covariance minimization to improve the identification accuracy.The stability criteria of state feedback control is put forward,and the analysis methods of robustness and stability are studied to improve the performance of closed-loop system under controllable,observable and stable conditions.The proposed modeling and control methods are applied to a developed ultra-precision wafer stage,and the results validate the practical effectiveness and availability of the proposed methods.