Modeling And Tracking Control Of Compliant Micro-Motion Stage Supporting Nano-Scanning

Ultra-precision scientific instruments,such as scanning probe microscopes and laser scanning confocal microscopes,are the foundational techniques for explorations of mi-crocosmic world,which play an irreplaceable role in almost branches of nanoscience and nanotechnology.With the increasing requirements of detection precision in the filed of nanotechnology,these instruments are heavily relying on the high-precision scanning of piezoelectric driven compliant micro-motion stages.Different from the nano-positioning technology addressing the static performance including repeated posi-tioning precision,the nano-scanning technology focuses on the dynamical performance including high precision tracking of particular trajectories/contours and transient re-sponses with large workspaces and high speeds.In a word,the motion mode and servo mechanism of nano-scanning applications have posed significant challenge to the struc-ture design,precise modeling and high-precision tracking control of piezoelectric driven compliant micro-motion stages.To address these challenges,this dissertation presents a comprehensive modeling of compliant mechanisms,precise tracking control strategies and experimental evalua-tions for a compliant mirco-motion stage driven by piezoelectric actuators.In particular,this dissertation first studies the static modeling methods of bridge-type amplification mechanisms and compound parallelogram guiding mechanisms on the base of defor-mation mechanism analysis.With this,a precise mathematical model of the bridge-based-compliant micro motion stage is established for the purpose of structure design,parameter optimizations,performance analysis and motion control.We further explore the applications of the internal model principle on the nano-servo control.In particular,a parallel internal model based control structure and repetitive controller with consid-erations of actuator saturations are developed to improve the tracking performance of compliant micro-motion stages.The main research contents and achievements are listed as follows.Firstly,we presents a load-based analysis method for bridge-type amplifiers by in-corporating the effect of external loads(such as compliant guiding mechanisms),and establishes a theoretical model to reflect the effect of external loads on the input/output displacement amplification ratios.On this basis,we further investigate the Timoshenko Beam Constraint Modeling(TBCM)method for the corner-filleted flexure hinges(s-tubby beams)adopted in the bridge-type amplifiers to address the load-stiffening effect.Accordingly,a load-stiffening-based kinetostatic modeling method for bridge-type am-plifiers is developed,such that the deflection behaviors and displacement outputs are well predicted.Secondly,considering the nonlinear effects of center-shifting and load-stiffening,we propose a modified pseudo-rigid-body(MPRB)modeling approach for beam flexures.Based on the results of the beam constraint model(BCM),the fixed-free beam flex-ure is modeled by a rigid link connected with an extension spring by a torsion spring.Meanwhile,the characteristic parameters of the proposed MPRB model are no longer constant values,but affected by the applied general tip load,especially the axial force.The developed MPRB modeling method is then applied to the modeling of fixed-guided beams.Accordingly,an accurate model of the compound parallelogram mechanisms is established to predict the performance characteristics such as deformation capability,as well as stiffness variation.Thirdly,we apply the proposed modeling methods for bridge-type mechanisms and guiding mechanisms to the modeling of an XY bridge-based micro-motion stage,and establishes an accurate mathematical model to predict the nonlinear stiffness perfor-mance.Moreover,based on the electrical property of the piezoelectric actuators and voltage amplifiers,as well as the mechanical property of the compliant mechanisms,a general electromechanical model is proposed to characterize dynamic behaviors of the piezoelectric driven micro-motion stage,which is approximated as a third linear models and identified by experiments.Fourthly,a parallel internal model based control structure is investigated for the piezoelectric driven micro-motion stage for the purpose of high precise trajectory track-ing.In particular,the dynamical model of the autonomous system generating exogenous signals is immersed into the internal model units such that the asymptotic tracking is guaranteed.Further considering the effects of actuator saturations on the system stabili-ty and tracking performance,an anti-windup compensator is designed on top the parallel internal model control structure.In the presence of actuator saturations,the anti-windup compensators are activated to adjust the controller outputs and system outputs to elimi-nate the adverse effect of saturation nonlinearities on the system performance.Lastly,for the purpose of particular triangular wave signal tracking in nano-scanning,we propose a repetitive control-based anticipatory anti-windup tracking control struc-ture in this dissertation,which allows the periodical signals tracking in the presence of actuator saturations.The anticipatory anti-windup compensators are driven by the difference between the anticipatory controller output and the actuator saturation limits,such that the anti-windup mechanisms take effects to compensate the controller output and system output before the actuator saturation actually occurs.With this,the tran-sient performance of the system is improved when actuator saturation is triggered and finished.The stability and tracking performance is also guaranteed in the presence of saturations by the proposed repetitive anticipatory anti-windup tracking structure.