Abstract
In this paper, an adaptive backstepping control (ABC) method for a plane-type 3-DOF ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</i> ,θ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> ) precision positioning table is proposed. First, according to the dynamics of a mechanical mass-spring system, we establish mathematical equations that contain linear viscous frictions and varied elasticities with cross-coupling effects due to mechanical bending. In system identification, the real-coded genetic algorithm (RGA) method is employed to find the optimized parameters, and the dynamic responses of numerical simulations and experimental results are compared. On the basis of the state-space model, the ABC is proposed to track trajectories and impose on the dynamic performance, robustness of parameter variations, and trajectory-tracking errors. The comparisons between numerical simulations and experimental results illustrate the validity of the proposed ABC method for practical applications in contour tracking and also show the performances in reducing the cross-coupling effects.
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