Nonlinear finite element modelling and adaptive sliding mode control of piezoelectric tube actuator

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Nonlinear finite element modelling and adaptive sliding mode control of piezoelectric tube actuator

 

Author: Chung, Sui-hong
Title: Nonlinear finite element modelling and adaptive sliding mode control of piezoelectric tube actuator
Degree: M.Phil.
Year: 2011
Subject: Hong Kong Polytechnic University -- Dissertations
Piezoelectric devices -- Mathematical models.
Actuators -- Mathematical models
Finite element method -- Mathematics
Adaptive control systems -- Mathematical models
Department: Dept. of Mechanical Engineering
Pages: xxv, 215 leaves : ill. (some col.) ; 31 cm.
InnoPac Record: http://library.polyu.edu.hk/record=b2441568
URI: http://theses.lib.polyu.edu.hk/handle/200/6096
Abstract: The piezoelectric tube actuator is a compact device, which realizes three dimensional nano-scale scanning on the sample in Atomic Force Microscope (AFM). However, nonlinearities, including creep and hysteresis, together with coupling effect significantly limit the accuracy of AFM. The main goal of this research is to design a controller to minimize the tracking error due to coupling effect, creep and hysteresis, and also increase the stability for the piezoelectric tube actuator with electrode dislocation. An accurate model of piezoelectric tube actuator which can fully describe the dynamic properties and nonlinear phenomena is a pre-requisite for model-based controller design. The first objective is to develop a reduced order nonlinear finite element (FE) model for controller design and computer simulation. The key point for developing a nonlinear model is to implement Prandtl-Ishlinskii hysteresis operators and Kelvin-Voigt creep operators into constitutive equations. The order of the nonlinear FE model in state space form is reduced by the balanced model truncation via Schur method in order that the model is feasible for controller design and computer simulation. The working operation of the piezoelectric tube actuator is simulated in such a way that the cantilever is desired to scan the sample surface in a raster pattern. The simulation results of the open loop nonlinear system reveal that coupling effect, creep and hysteresis can lead to significant tracking errors. Simulations on the closed loop nonlinear system with electrode dislocation using the proportional-integral (PI) controller and the output feedback controller (OFC) show that creep cannot be compensated and the tracking errors in Y direction diverge. The second objective is to develop an adaptive sliding mode controller (ASMC) for the piezoelectric tube actuator. The piezoelectric tube actuator is characterized as a multiple-input-multiple-output (MIMO) nonlinear time-varying system. The design of controller is based on the reduced order nonlinear FE model. A continuous-time dynamic model assists the design process such that part of hysteresis can be extracted as known design information. The remaining part of hysteresis together with coupling effect and creep are considered as uncertainties. Walcott Zak observer is adopted to estimate the unmeasurable states. Lyapunov criterion is stated to guarantee the theoretical stability of the closed loop system. Adaptive scheme is used to search for the unknown controller gains. The simulation of the piezoelectric tube actuator using the ASMC is performed. It shows that the ASMC can reduce more tracking error due to adverse effects and is relatively more stable than the PI controller and the OFC. The performance of the ASMC with the same settings is further investigated in piezoelectric tube actuator with different creep properties and hysteresis properties in addition to electrode dislocation. The results are evident that the proposed ASMC can tolerate certain changes of nonlinearity properties. The ASMC is the best candidate for AFM among the controllers investigated in this research.

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