Research On Key Modeling And Controling For Multi-Dimensional Ultra-Precision Positioning System

Precision positioning is a key technology in ultra precision machining technology, electronics assembly production line, integrated circuit device manufacturing, bioengineering and nanotechnology, etc. With the arrival of the industrial era 4.0, nano-scale positioning technology has become a hot research topic.It is known that piezoelectric(PZT) actuators, and shape memory alloy (SMA) actu ators, etc are usually used in nano-positioning systems, In micro displacement control sy stems, piezoceramic actuator has the merits such as small in size, high resolution displac ement, and fast response, etc. Therefore, the use of piezoelectric ceramic as a displace ment actuator is one of the major directions in nanotechnology research. Nevertheless, t he piezoelectric actuators have seriously hysteresis characteristic which is a non-smooth function with multi-valued mapping. This feature will not only reduce the control accura cy of the system, but also make the input signal amplitude associated phase shift and h armonic distortion. Hysteresis will weaken the performance of closed-loop feedback syst em and even cause system instability. Hysteresis characteristics seriously constrains the a pplications of piezoelectric actuators. In order to reduce the adverse effects caused by h ysteresis in piezoelectric ceramics, many research researchers have focused on the resear ch of modeling and compensation of hysteresis in piezoceramic actuators. The well kno wn Duhem hysteresis model with the form of differential equations is a useful tool for describing hysteresis behavior in piezocermic actuators. Compared with the Preisach mod el, the obvious advantage of the Duhem model is that it has a definite function express ion. Note that the Duhem model consists of a parameter and two functions, i.e. f (·) and g (·). The Duhem model has the capability of representing the hysteresis characteris tics of piezoelectric ceramics. Because it is a dynamic model, its output is associated w ith the frequency of the input signal. It is identical with the dynamic characteristics of smart materials in actual hysteresis nonlinearity. By adjusting parameter α and two fun ctions f (·) and g (·), The Duhem model can accurately describe the hysteresis behavior. However, it is difficult to select the parameters and functions in Duhem model. This i s also the bottleneck in the application of Duhem model.According to Weierstrass theorem, a theorem is composed in this dissertation that uses polynomials to construct the functions f (·) and g (·) in Duhem model and selects a different polynomial orders according to the requirements of model accuracy, which successfully resolves the difficult problem in Duhem model function construction. Furthermore, by using recursive least squares method, the parameters of Duhem model are on-line identified and the identification results are used to obtain hysteresis inverse model, which may avoid the complexity of the model inversion process and realize the adaptive inverse compensation control to the piezoactuator. The experiments have been implemented on a three-dimensional piezoelectric ceramic actuators, and the experimental results have shown that the algorithm is valid and correct.Since the precision displacement system is in series connection of the hysteresis and the linear component, hysteresis output cannot be directly measured, which leads to great difficult for system identification.Based on the model analysis in this thesis, a two-step identification method is proposed. In step 1, the parameters of linear part were firstly identified by step response. Then, in step 2, the inverse function of was designed by mixed fast tracking differentiator, and then connected it to the output of the system to form the hysteresis observer. The hysteresis output was estimated by the hysteresis observer. By using the input signal and the estimated signal, the Duhem model parameters were identified by on-line recursive least squares method. Thus, the model parameters of the system can be successfully identified. Then, the corresponding inverse compensation and feedback control technology were used to achieve precise control to the one-dimensional piezoelectric ultra-precision platform. Experimental results demonstrate the effectiveness of the proposed method.In the multi-dimensional ultra-precision positioning system, there exists not only the serious nonlinear hysteresis phenomenon, but also the coupling phenomenon between axes. The coupling phenomenon will seriously affect the accuracy of the system and will cause inconvenient for the controller design.Due to the complexity of multi-dimensional coupling mechanism, it is difficult to establish a model by the first principles method. However, neural networks can be applied to establish a system model. As one-dimensional control system has serious hysteresis, multidimensional control system must also present a serious hysteresis. Hysteresis is a multi-valued mapping. Theory and practice have proved that the traditional neural network method can only approximate one-to-one mapping or multi-valued mapping. It is unavailable to multi-valued nonlinear mapping just like hysteresis. This multi-valued mapping of hysteresis between input and output makes the neural network be greatly restricted in the establishment of the hysteresis model, Therefore, if we can find a way to transform the relationship between the input and output of hysteresis into one-to-one mapping or many-to-one mapping, vast areas of space will be opened up for applying the neural network in this fieldIn this dissertation, the basic principle for constructing sub-hysteretic operator was proposed according to the properties of hysteresis. By this principle, one can conveniently construct a proper hysteretic operator. The operator can transform the multi-valued mapping into one-to-one mapping, and thus it solves the problem that neural networks can not be used to establish hysteresis model before. In this dissertation, a new dynamic hysteresis operator was also designed by the proposed method, In order to select the optimal parameters, the genetic algorithm (GA) was used to optimize the parameters of the hysteretic operator. In addition, hysteresis model and inverse hysteresis model were established for multi-dimensional piezoelectric actuators by use of the hysteresis operator. By employing both hysteresis model and inverse hysteresis model and by employing the equivalent transformation, the coupling between the outputs of the multi-dimension system can be measured. Thus it satisfies the conditions of design of feed-forward compensators. With the application of feed-forward compensation, the axes coupling problem is solved, and thus the decoupling control is achieved for multidimensional systems.In summarize, in this dissertation, the hysteresis characteristics of the piezoelectric ceramics is successfully described by using Duhem model, based on polynomial approximation theory and identification method. A two-step identification method is also proposed in this paper. Thus, the model of the positioning system wt piezoactuators can be identified. The inverse compensator and the controller are also designed based on the obtained system model. The experimental results have shown that the proposed algorithm is effective. Based on the bevaior of one dimensional positioning system and the hysteresis characteristics with strong coupling, a dynamic hysteresis operator is designed to construct the expanded the input space for transforming the multi-valued mapping of hysteresis to a one-to-one mapping... Then, the model and inverse model of the coupling system are established by use of neural network. With the model and inverse model, the corresponding decoupling controller is designed to achieve a decoupling control for multi-dimensional ultra-precision systems. Experimental results have proved that the validity of the proposed method. It also shows that the proposed method has practical potential for applications in precision positioning systems.