Long Stroke Motion Characteristics Analysis And Control Research Of Compliant Leaf Spring-Based Planar Micro-Motion Stage

With the rapid development of the nanotechnology,the ultra-precision scientific instruments,such as scanning probe microscope,micro/nano additive manufacturing system,etc.,have been widely used in semiconductor engineering,MEMS,optoelectronic communication,biomedicine,precision manufacturing and other fields showing great scientific value,economic value and social value.The compliant micro/nano manipulating system with high motion accuracy has gradually become the key generic technology in the above fields and the research focus in the related high-tech industries and interdisciplinary areas.At the same time,in order to meet the increasingly diverse and complex technical needs,it needs to develop the micro/nano manipulating system with wider range of motion(millimeter scale)and higher accuracy.To address these challenges,this paper takes the long stroke compliant parallel planar micro-motion stage as the research object.Firstly,based on the compliant leaf spring element elastic deformation and boundary constraint coupling,the accurate modeling method of the compliant mechanism(guiding mechanism)is deeply studied,and a mechanical model to accurately describe the stress stiffening effect of the mechanism is also established.Furthermore,the configuration design of the compliant micro-motion stage is proposed and the related performances are tested and analyzed.Then,the planar displacement measurement method based on the laser interferometer is improved,which effectively suppresses the measurement error caused by parasitic rotational motion and coupling effect of cross-axis forces.The prososed method provides a basis for the displacement measurement in the process of multi-axis parallel planar motion control of the micro-motion stage.Finally,the control algorithm for the nanometer planar motion is explored,which effectively compensates the problem of the cross-axis coupling and stress stiffening effect,and realizes the high precision planar motion control.The main research contents and achievements are listed as follows.Firstly,on the basis of the Euler-Bernoulli beam theory,starting from the compliant element represented by a single compliant leaf spring,and considering the axial/transverse/bending moment loads and the deformation relations in each direction,an explicit kinostatics expression describing the stress stiffening effect of the elastic component is obtained.The displacement-load model of the parallelogram guiding mechanism is obtained by considering the boundary conditions of the compliant leaf spring element.The compound parallelogram guiding mechanism with symmetric boundary constraints is taken as an example for thermal-stiffness coupling analysis,and an error analytical model which could accurately describe the variable stiffness behavior of the mechanism under different thermal loading conditions is obtained.Considering the complex structure and boundary constraints caused by the intermediate rigid stages of the double parallelogram guiding mechanism,the kinostatic modeling of such structure is developed.Secondly,a 4-PRP type parallel stage configuration with kinematics decoupling is proposed for the design of a high-precision planar compliant micro-motion stage with millimeter stroke.On the basis of the completion of the experimental setup system,the forward and reverse input-output characteristics,working space,step and harmony response and other characteristics of the compliant stage are tested,and the hysteresis phenomenon under the condition of uniform/non-uniform speed,cross-axis coupling rate and natural frequency of the stage are analyzed.Thirdly,based on the theory of compliant leaf spring component/mechanism and the configuration characteristics of the compliant stage,the mechanical model and analysis of the proposed stage are carried out.According to the structure and function division of the stage,the static model of the flexure bearing and guiding mechanism are developed respectively,and the overall static model of the stage is obtained by using the stiffness matrix combination method.Then,based on the dynamic stiffness matrix,vibration analysis of flexible body and modal analysis theory,the dynamic analysis of the basic structural elements of the compliant stage are carried out respectively.The dynamic model of the whole stage is finally obtained through the dynamic stiffness matrix combination method,which provides the model foundation for the control algorithm research in the following paper.Fourthly,for the displacement measurement error in the process of the compliant micro-motion stage(millimeter level)planar dynamic moving,we integrate the optical rectangular prism light path reflection principle and the optical path difference of laser beam interference,and improve the laser beam reflection path.It can implement the separation of linear displacement and angle displacement of the micro-motion stage,and ensure the displacement measurement accuracy.Finally,considering the variable stiffness problem caused by the cross-axis coupling and stress stiffening during the multi-axis cooperative planar motion control of the compliant micro-motion stage,we design a discrete adaptive extended state observer(AESO)with exponential forgetting factor based on the Kalman-type observer structure.At the same time,the synergetic control theory(SCT)and the observer structure are combined to realize the micro/nano multi-axis motion control,and the convergence conditions of the AESO and the robust stability of the closed-loop system are proved theoretically.The proposed control algorithm is implemented on the experimental setup system compared with the existing methods(such as PID,ADRC and H?),and the results show that the proposed algorithm has significant advantages.