Trajectory Tracking Control Method For Piezoelectric Micro-nanopositioning Stages

Piezoelectric micro-nanopositioning stages can generate deformation with the exciting signal of input voltage or current based on the converse piezoelectric effect,and they are the high-precision micropositioning driving mechanism which can ensure the micro-nanoscale resolution mechanical motion,making them have unparalleled virtue compared with the traditional motor driving mechanism.Due to their merits of small volume,quick response,low power consumption and high position resolution,piezoelectric micro-nanopositioning stages become promising in various emerging areas such as smart structure,precision machining,nanotechnology,micro electric engineering,precision optical system and bioengineering.Especially piezoelectric micro-nanopositioning stages have a brilliant function in nanopositioning equipment such as ultra-precision micro-nano manipulation,scanning probe microscope,and astronomical telescope.Nevertheless,the piezoelectric material exhibits the hysteresis nonlinearity that undeniably compromises the positioning accuracy of piezoelectric micro-nanopositioning stages,and even hinders their application in various branches.This thesis based on the piezoelectric micro-nanopositioning stage is aim to solve the complicated hysteresis nonlinearity problem by constructing the precise hysteresis model and designing the effective controller and achieve the excellent tracking performance with micro-nano scale precision,providing theoretical and methodological basis for further study,so as to facilitate and boost the industrial applications of new smart material actuators.The main research content of this thesis is as follows:Due to the indescribable and intricate hysteresis nonlinearity,the piezoelectric micro-nanopositioning stage is subject to the inevitably drawback in the tracking positioning.The modeling approach to capture the hysteresis effects is investigated IV firstly.This thesis develops the Bouc-Wen model and the bat-inspired optimization algorithm is adopted to identify the parameters of this model.Considering the structure of Bouc-Wen model,the feed-forward compensators based on the inverse multiply and step iterative methods are designed and implemented to the piezoelectric micro-nanopositioning stage,so that the problem of the unavailable inverse model is settled.Experimental results indicate that these two feed-forward open-loop control methods both can reduce the influence of hysteresis behavior on positioning precision,and achieve the desired tracking performance without using a displacement sensor to collect the feedback signals.The tracking performance of the feed-forward compensator is highly dependent on the precision of the hysteresis model and the disturbance rejection ability of the compensator is weak,take these problems into account,the close-loop integral sliding mode controller based on Bouc-Wen model is deduced.In order to compensate the model uncertainties and external perturbation part,the estimator part is added into the control system.Combining the advantages of the equal velocity reaching law and power reaching law,a modified sliding mode reaching law is designed to further enhance the control performance.And then the stability of the proposed control method is demonstrated via the Lyapunov theory.The triangular signals under different frequencies and amplitudes and complex harmonic signals are applied to the controller so as to verify the control performance.After a series of comparative experiments,it is intuitive that the proposed technique allows a precise positioning control of the piezoelectric micro-nanopositioning stage.The conventional sliding mode control has low convergence rate and serious chattering phenomenon,to deal with these problems,this thesis proposes a novel double-power reaching sliding mode control approach.The merits of the developed controller are that it possesses the strong robustness,reduces the controller conservative property,furthermore,the states can convergence to a fixed interval in finite-time,which can further improve the trajectory tracking performance.According to the Lyapunov stability theorem,convergence time and convergence region of this scheme can be strictly certified and acquired.The proposed controller shows a decent level of accuracy in the tracking task compared with the above modified sliding mode control scheme.Owing to the fact that the piezoelectric micro-nanopositioning stage has the characteristic of obvious rate-dependent property,however,the Bouc-Wen model is a static hysteresis model which is unable to reflect the inherent rate-dependent feature and will deteriorate the controller performance.Thus,a nonlinear autoregressive moving average with exogenous inputs(NARMAX)model is proposed,and it is identified online by the Pi-Sigma fuzzy neural network.The convergence of the proposed NARMAX model is analyzed availably in theory under the persistent excitation condition to guarantee the parameters can converge to the true values.To further make an improvement of the tracking precision,a self-adaption compensation controller is derived based on the NARMAX model.In order to testify the performance of the developed control scheme,experiments on trajectory tracking control of the piezoelectric micro-nanopositioning stage are conducted.Experimental results show that the trajectory tracking error is within 1?m.A rate-dependent hysteresis nonlinearity model based on KP operator is proposed to make it have the ability to accurately describe the hysteresis behavior under different frequencies.The neural network is employed to identify the dynamic density function online in view of the difficulty of identifying the density function of KP model using traditional ways.The convergence of parameters in the identification procedure of dynamic density function under the persistent excitation condition is proved theoretically,and the effectiveness of the rate-dependent KP model is guaranteed.For the sake of eliminating the hysteresis characteristics,a direct self-adaption compensation controller based on the KP compensation operator is designed innovatively.Experimental results show that in terms of the different reference signals,the direct self-adaption compensation control can achieve better trajectory tracking performance compared with the above proposed control methods.