Motion Control Of Piezo-actuated XY Nanopositioning Stages For High-speed Raster Scanning

Piezo-actuated nanopositioning stages have been widely applied in precision equipments.In particular,they are the critical components in AFMs.With the rapid development of nanoscience and nanotechnology,high-speed AFM imaging has been increasingly demanded.The current pivot of the high-speed AFM is to ensure the high-speed and high-precision motion of the piezo-actuated nanopositioning stage in the XY plane.However,the low resonance frequency of the nanopositioning stage is a major impediment to achieving high-speed operation.The existing compliant mechanisms with high stiffness often sacrifice the travel range.In addition,the lightly damped resonance mode of the mechanical structure would result in the low-gain margin issue,which restricts the improvement of control bandwidth.The piezoelectric actuators suffer from inherent hysteresis nonlinearity,which will be coupled with the vibrational dynamics of the stage in the high frequencies to affect the tracking performance.The cross-coupling effect between the X-and Y-axis is also a main factor degrading the tracking accuracy during raster scanning.To address these issues,the dissertation presents the mechanical design of highbandwidth piezo-actuated XY nanopositioning stage,the compensation of hysteresis nonlinearity,the suppression of lightly damped resonance mode,and the control of cross-coupling.It is aimed at achieving high-speed raster scanning of the piezoactuated nanopositioning stage,which will lay a foundation for the high-speed AFM.The main research contents and achievements are listed as follows.A piezo-actuated high-bandwidth XY nanopositioning stage is designed.To completely decouple the motion between two axes,the flexure modules are distributed symmetrically around the end-effector.Based on the Castigliano's second theorem,the static and dynamic models of the stage are established.Then,with the constraints of maximum travel range and stress,the dimensions of the stage are optimized to maximize the first resonance frequency.After that,finite element analysis is utilized to validate the design.A prototype of the stage is finally fabricated and the experimental platform are established for the performance test of the developed stage.Experimental results demonstrate that the developed stage has high resonance frequencies,a relatively large travel range,and nearly decoupled performance between two axes.It is theoretically analyzed that for periodic reference input the hysteresis nonlinearity can be decomposed as a bounded periodic disturbance over a linear system.Then,a modified repetitive control strategy is proposed to handle the hysteresis nonlinearity by rejecting the periodic disturbance.In this sense,the constructions of the hysteresis model and its inversion are avoided.The modified repetitive control strategy can also compensate for the tracking errors caused by the system vibration dynamics,and thus address the coupling issue of the hysteresis nonlinearity and the vibration dynamics under high-speed trajectory.In addition,the modified repetitive control alleviates the nonperiodic disturbance amplification problem of conventional repetitive control.Experimental results validate that the proposed control strategy can effectively compensate for the hysteresis nonlinearity and vibration dynamics and improve the tracking performance of the nanopositioning stage under high-speed triangular trajectory.It is experimentally found that,with triangular reference input,the hysteresis nonlinearity mainly affects the system at the odd harmonics of the input signal.In this sense,an odd-harmonic repetitive control strategy is proposed to handle the hysteresis nonlinearity,with the hysteresis treated as the odd-harmonic periodic disturbance.Therefore,it avoids the modeling and inverting of the complex hysteresis nonlinearity.Another benefit of the developed odd-harmonic repetitive control strategy is that it can also account for the tracking errors caused by the vibration dynamics.Compared with the conventional repetitive control,the odd-harmonic repetitive control strategy reduces the data memory occupation to a half,which is beneficial for real-time implementation.Experimental results show that,the nanopositioning stage with the developed control strategy achieves high-precision and high-speed tracking of triangular trajectories.A new damping control scheme is proposed for piezo-actuated nanopositioning stages with recursive delayed position feedback,based on which a high-bandwidth control strategy with two feedback loops is presented.The recursive delayed position feedback controller is utilized to attenuate the resonant mode of the nanopositioning stage in the inner feedback loop,which results in a neutral-type time-delay system.To realize the pole placement of this system,a new numerical integration method is proposed to determine the rightmost pole and select the controller parameters with optimization algorithm.Then,a high-gain proportional-integral controller is designed in the outer loop to minimize the tracking errors caused by the hysteresis nonlinearity,modeling uncertainties and disturbances.Experimental results demonstrate that the proposed controller effectively improves the control bandwidth and also shows robustness to variation in system resonance frequency.A cross-coupling compensation approach based on modified repetitive control is proposed to account for the X-to-Y coupling-caused tracking error during raster scanning of nanopositioning stages.It is experimentally found that the X-to-Y coupling-caused motion can be regarded as the periodic output disturbance of Y-axis.Hence,when X-axis is tracking triangular trajectory and meanwhile the input to Y-axis is 0,modified repetitive control is employed for Y-axis to derive the control signal for crosscoupling compensation.Then,during raster scanning,the derived control signal in the first step can be applied to Y-axis as a feedforward controller to alleviate the X-to-Y coupling-caused tracking error.The proposed approach avoids the frequency response identification and modeling of the cross-coupling,which is ease of implementation.Experimental results show that,with the proposed approach,the X-to-Y couplingcaused tracking errors are reduced effectively and the raster scanning performance of the nanopositioning stage is significantly improved.