Control Of Piezoceramic Actuated Micro/Nanopositioning Stages With Hysteresis Compensation

Along with the rapid development of nanoscience and nanotechnology, piezoceramic actuated micro/nanopositioning stages are becoming a promising technique in many precision manufacturing equipments. However, piezoceramic actuators suffer from the inherent hysteresis effect because of loss phenomena taking place inside piezo-ceramic materials. The hysteresis effect exhibits complex nonlinear characteristics, which usually introduces undesirable inaccuracies or oscillations and even instability. Interest in studying piezoceramic actuated micro/nanopositioning stages with actuator hysteresis is also motivated by the fact that they are complex dynamic systems with un-known non-smooth nonlinearities for which traditional model-based control methods are insufficient and thus require the comprehensive dynamic model of the controlled stage. Development of control techniques to mitigate the effects of hysteresis is a quite challenging task and recently attracts significant attentions.To address such challenges, this dissertation presents a comprehensive model-ing, controller design and experimental evaluation for piezoceramic actuated micro/-nanopositioning stages with unknown hysteresis nonlinearity. With the emerging ap-plications of smart material based actuated systems, the results of the dissertation will enrich the theory and methodology of hysteresis compensation and control, and ad-vance the state of nanomanufacturing in both theoretic and practical aspects. The main research contents and achievements are listed as follows.A modified Prandtl-Ishlinskii(P-I) hysteresis model with a nonlinear input func-tion is developed to describe the symmetric as well as asymmetric hysteresis loops on the basis of the classical P-I hysteresis model. The essential wiping-out and con-gruency properties for the validity of the developed hysteresis model are addressed. With the modified P-I model, a new real-time inverse hysteresis compensation method is proposed. Different from the commonly design procedures for inverse hysteresis compensation, the proposed method directly utilizes the modified P-I model to cap-ture the inverse hysteresis effect of the piezoelectric actuators. Then, the identified hysteresis model is cascaded in the feedforward path for direct inverse hysteresis can-celation. Experimental results on a piezoceramic actuated positioning stage verify the effectiveness of the feedforward controller along with the modified P-I model.A general electromechanical model is proposed to characterize dynamic behaviors of the piezoceramic actuated micro/nanopositioning stage, including nonlinear elec-tric behavior, voltage-charge hysteresis, piezoelectric effect, and frequency response of the stage. To identify the parameters of the general model, the adopted approach is to express the general model into a third-order linear plant preceded by an input hys-teresis nonlinearity. Then, the linear parameters and the hysteresis term can be iden-tified separately. To validate the proposed model, the modified P-I model is adopted as an illustration to describe the hysteresis nonlinearity, which is also confirmed by experimental results.A robust adaptive control approach is developed for a reduced dynamic model of the piezoceramic actuated stage with unknown parameters and hysteresis nonlinearity. In-stead of constructing the inverse of the hysteresis model to cancel the hysteresis effect, the hysteresis decomposition approach is adopted in the control scheme to express the hysteresis effect as an approximate linear relationship with unknown but bounded nonlinear term. In the developed robust adaptive approach, a sliding mode controller is designed to remedy the unknown hysteresis nonlinearity and disturbances, while a discontinue projection-based adaptive control law is utilized to handle the parameters uncertainties of the dynamic plant. The global stability of the chosen control laws is established by the Lyapunov function method. Experimental tests on a prototype plat-form with different motion trajectories are conducted to validate the feasibility and effectiveness of the proposed robust control approach.With the estimated inverse hysteresis compensation, a robust adaptive controller is developed for a class of nonlinear systems with unknown asymmetric input backlash. Considering the characteristics of the asymmetric backlash nonlinearity, an analytical expression of the estimated inverse compensation error for asymmetric backlash is ob- tained, which can be expressed as a parametrizable part with a bounded unparametriz-able disturbance. With the analytical expression of the inverse compensation error, a corresponding controller is designed by using the robust adaptive control approach. The proposed controller ensures the boundedness of the closed-loop signals, and yields desired tracking precision. The simulation results demonstrate significantly enhanced tracking performance when the estimated inverse of the asymmetric Backlash model is considered in the closed-loop control system.