Modeling And Control Technology Of Piezoelectrically Driven Micropositioning Stage

With human beings exploring the microworld, micro/nanopositioning technology was developed quickly in the past years. Piezoelectrically driven actuators are the presently common used micro/nanopositioning devices, and they make use of the piezoelectric effect or the electrostrictive effect to realize micrometer even nanometer level accurate positioning, which has played the very important role in accurate positioning domain.Piezoelectrically driven micropositioning stage (piezo-stage) is one of the typical piezoelectrically driven actuator which is widely used in scanning probe microscopy. Its interior usually uses combined integration machine design structure of piezoelectric stack and flexible hinge, which enabling piezo-stage has high position resolution and stability.This article carries on modelling and control technology research to piezo-stage which is now applied widespread. The research results have general significance which has guaranteed the piezo-stage's fast dynamical positioning accuracy and may extend application to the present common multiform piezo-stage's control system design. The main achievements can be summed up as follows:1. An experimental micro/nanopositioning system has been built based on Tritor100 piezo-stage.2. The dynamic hysteresis model structure equation which can simultaneously manifest the piezo-stage's dynamic characteristic and hysteresis characteristic has been established, and the identification ways of the hysteresis partial parameters and the dyniamic partial parameters of the dyniamic hysteresis model structure equation were given. Moreover, the dynamic hysteresis model structure equation can easily be combined with each kind of existing analysis hysteresis model to show many kinds of different forms. Furthermore, the dynamic hysteresis model based on PI hysterersis was established. Experimental research indicated that the model precision of dynamic hysteresis model based on PI hysterersis was high and not influenced by the piezo-stage's positioning rate, which has provided model foundation for piezo-stage's control system design.3. The piezo-stage's feedforward and compound control strategy were designed based on the dynamic hysteresis model. The piezo-stage's feedforward controller can be easily achieved through inversing the dynamic hysteresis model. Moreover, This feedforward open-loop controller is easy and feasible, and does not need extra position sensor, so it is one kind of economical choice when the positioning accuracy request is not in the very harsh situation. However, the piezo-stage's open-loop controller' performance is decided by the mathematical model precision, and easy to receive each kind of disturbance to cause the pointing accuracy to drop. Therefore, to make up the open-loop controller's insufficiency, the neuron PID adaptive feedback loop controller was designed to constitute the piezo-stage's compound control strategy. The piezo-stage's compound control strategy unify the merits of feed forward control and neuron PID adaptive control: on one hand, the suppementary of feedback control makes up the modeling error, enhances the system's adaptability; on the other hand, the feed-forward control enhances system's rapidity.4. The piezo-stage's hysteresis compensation control strategy was designed based on the dynamic hysteresis model. First the piezo-stage's hysteresis characteristic should be compensated using the static hysteresis model and the linear controller can be design easily. However, the hysteresis compensation always has certain residual in addition with other uncertainty influence, which make hysteresis compensation system not a simple linear system but a parameter time-variable system (or be regarded as one kind of perturbation system). Thus, in order to enhance the control system's performance, this article used two kind of control algorithms to realize this kind of linear feedback controller's design: One kind is self-tuning PID controller design, the other kind is sliding mode controller design. These two kinds of feedback controller design have gained the satisfactory progress. 5. For further enrich piezo-stage modeling and control system design methods, the piezo-stage's artificial neural networks online identification model and the artificial neural networks controller have been designed. The artificial neural networks can identify one-to-one or many-to-one mapping relation nonlinear functions, and can not identify many-to-many mapping relation nonlinear functions. The piezo-stage has the hysteresis characteristic, and its input and output manifests complex many-to-many mappping relation, therefore, in order to realize the artificial neural networks indentification of the piezo-stage, the double Sigmoid activation function which is proposed by Liu Xiangdong was selected to construct piezo-stage's artificial neural networks online identification model. In the same time, the neural network identification model's weight, threshold value and the activation function threshold value correlation formula has been inferred. The experiments indicated that the model precision was high, and can be online dynamic alignment. Based on this neural network model, a neural network PID controller was designed, and the performance of the control system was satisfied.