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Optimization algorithms for the multimodal nonseparable problems

English Abstract

In the field of micro/nano technology, piezo-driven flexure-based micro-gripper and positioning mechanism with high positioning precision and large workspace are really desirable for the realization of high-performance micro/nano scale operation. In order to meet this requirement, several novel large-stroke compliant micro grippers and positioning mechanisms are developed and presented in this thesis: Firstly, two kinds of novel compliant micro-grippers, one is the X- and Y-directions motion and other is single direction, are presented. The amplifiers with bridge-type magnification and Scott-Russell amplification are applied for overcoming the drawback of small output displacement coming from piezoelectric actuator (PZT). Besides, the established models for the mechanical performance evaluation of the grippers in terms of kinematics and dynamics are verified by the finite element analysis (FEA). After a series of dimension optimizations carried out through simulated annealing algorithm (SAA) and particle swarm optimization (PSO) algorithm, a least square optimization method (LSOM) is employed for estimating the parameters of the hysteresis model. The simulation results demonstrate that the first natural frequency of the 2- degree-of-freedom (DOF) micro-gripper is 260.25Hz and the amplification ratio is 4.83. Other micro-gripper owns the natural frequency with 815.77Hz and amplification ratio for 8.06 under the size W × L = 30mm × 60mm. Secondly, two novel nanopositioning platforms with 2-DOF and 3-DOF are proposed based on flexible beam theory and lever principle. The mechanical kinematics modeling is conducted by using the Pseudo-Rigid-Body (PRB) method,also, the lever deformation modeling is carried out, as well as the dimension optimizations and the mechanism performance validations which are conducted by using the genetic algorithm (GA) and the finite-element-analysis method. After a series of modelings and optimizations for the sake of large workspace, small cross-coupling, and precision tracking, the simulation results indicate that the 2-DOF nanopositioning stage obtains the natural frequency of 354.21Hz with the cross-coupling error within 0.1% under the workspace 215.50µm × 215.50µm, and other 3-DOF micromanipulator achieves ii the first natural frequency of 54.56Hz with the cross-coupling within 1.82% under the workspace 404.98µm × 404.98µm × 235.64µm. Additionally, the concept of ‘Transfer coefficient’ for the 3-DOF compliant mechanism has been firstly proposed. The transfer efficiencies of the 3-DOF mechanism have been calculated with the values η1 = 0.85 in X and Y directions, and η2 = 0.99 in Z direction, respectively. Finally, the proposed mechanisms are fabricated by using Wire Electrical Discharge Machining (WEDM). After a series of hysteresis model and inverse model carried out to eliminate the hysteresis effect, the adaptive backstepping sliding mode control (ABSMC), robust tracking control, and the backstepping dynamic surface control are used in evaluating the tracking performances of the proposed mechanism-s. Especially, considering the outside disturbance uncertainty, adaptive backstepping sliding mode control has been firstly used in the piezo-driven flexure-based micromanipulator in this thesis. A number of tracking experiments with different trajectory signals are carried out, the results indicate that the proposed mechanism obtains the excellent tracking performance within the presented control laws of three controllers. The tracking errors of all experiments are within 2.5%. All the results uniformly validate that the design, analysis, optimization, and control of proposed mechanisms are effective and reliability for further applications.

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Zhang, Geng


Faculty of Science and Technology


Department of Electromechanical Engineering




Mathematical optimization



Li, Yang Min

Yang, Zhi Xin

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