Modeling And Control Of Piezo-Positioning Stages

Along with the development of nanoscience and nanotechnology, microscopic imaging and micro/nano manipulation at the nanometer scale are the research sub-jects of great concern. The micro/nano positioning stages actuated by piezoelectric actuators are the key components in the micro/nano manipulation. However, the mi-cro/nano positioning stages suffer from the inherent hysteresis, creep nonlinearity in the piezoelectric actuators and vibration effect in the mechanical structure. These ef-fects can cause undesirable system performance, even instability. This thesis focuses on the modeling and control for the hysteresis nonlinearity and other effects in the micro/nano positioning stages. The main contents and contributions are as follows.1. The static hysteresis model is investigated to describe hysteresis nonlinearity in piezoelectric actuators. A parabolic model is developed according to the motion rules of hysteresis curves when the piezoelectric actuator operated away from the saturation voltage. And a memory operator is proposed to compensate for the modeling error caused by the nonlocal memory property.It is observed that all hysteresis curves are alike and converge to a converging point. Mathematical transformation is adopted to obtain the other hysteresis curves based on two dominated curves. Dominant curves are determined and expressed as continuous functions, and the other hysteresis curves are modeled using two dominant curves through nonlinear transformation of coordinate axis. In the event of memory saturation, the upper converging point needs to be updated. The experimental results show that the proposed model is very useful.2.A rate-dependent hysteresis model is developed to capture the rate-dependent hysteresis characteristic. A rate-dependent Prandtl-Ishlinskii model is developed to characterize the time-dependent hysteresis in the piezoelectric actuators. This model employs the dynamic threshold and weighting values. And the rate-dependent hys-teresis phenomenon is analyzed after hysteresis data processing. The main reason of rate-dependent hysteresis can be attributed to output delay in the process of data ac-quisition. Delaying one or several sample periods for the input voltage, the width of the hysteresis loops remains unchanged. That is, the hysteresis is rate-independent.3. The iterative learning control method is studied to form hysteresis compen-sating feedforward input. The convergence of P-type iterative learning algorithm is achieved on the whole desired trajectory when the operator satisfies the property of incremental strictly increasing. The Prandtl-Ishlinskii model is utilized to capture the nonlinear behavior in piezoelectric actuators. The play operator and the Prandtl-Ishlinskii model are both incremental strictly increasing if the initial state of play op-erator equals zero. At last, the feedforward input is obtained according to the iterative learning algorithm. The effectiveness of the iterative learning control is verified by the the simulation and experimental results.4. An adaptive inverse controller based on Prandtl-Ishlinskii model is designed. The discrete Prandtl-Ishlinskii model is used to describe the hysteresis nonlinear in the piezoelectric actuators. The adaptive projection algorithm is utilized to identify the weighting values. An adaptive inverse controller is used to track the piezoelectric actuator considering that PI model has its analytical inverse.The weighting values of the PI model are identified by using the adaptive projection algorithm, and then the weighting values and threshold values of the PI inverse model are calculated online. Experimental results show that the adaptive inverse controller leads to major improve-ments of system performance.5. The hysteresis nonlinearity and the vibration effect are both considered on the fast tracking control of the piezo-positioning stages. In low-frequency operations, the vibration effect of piezoelectric actuatorS could be safely neglected due to the high stiffness of piezoceramic materials. The KP hysteresis model could be identified. Then the approximate KP inversion is introduced to cancel the hysteresis effects. An adaptive backstepping control scheme is developed to find the feedback control and the parameter update law. The proposed controller ensures the uniformly ultimate boundedness of the closed-loop system. Simulation results show the effectiveness of the proposed scheme.Finally, some open issues and the future works on micro/nano positioning stages are discussed.