ADAPTIVE BERNSTEIN POLYNOMIAL BASED TRACKING CONTROL FOR CARTESIAN POSITIONING MECHANISMS IN 3D PRINTING MOTION STAGES

Öz

Accurate motion tracking is a key requirement in three-dimensional printing systems, where deviations of the planar positioning stage directly degrade the accuracy of the deposited path. This study proposes an adaptive Bernstein polynomial based nonlinear tracking controller for a class of two axis Cartesian positioning mechanisms whose axis dynamics are uncertain and contain unmodeled effects. The design exploits the finite duration of a printing motion by representing the lumped uncertainty that appears in the error dynamics as a normalized time signal along the trajectory, rather than requiring its explicit model. The Bernstein coefficients are updated online from the tracking error, yielding a compact approximation structure tailored to finite horizon printing trajectories. The controller is supported by a Lyapunov based stability analysis, which proves uniform ultimate boundedness of the closed loop error signals and relates the resulting bound to the feedback gain, the approximation residual, and the leakage term. Simulations on a CoreXY printing mechanism illustrate the tracking performance and the online uncertainty compensation of the proposed scheme under a demanding disturbance comprising ripple and external effects. A comparison with a nonadaptive baseline further demonstrates that the proposed adaptive structure reduces the cumulative tracking error while maintaining the same cumulative control effort. The proposed scheme uses only axis level position and velocity measurements together with a fixed number of adaptive coefficients, and it requires no model identification stage, so it is suitable for implementation in an embedded motion controller.

Anahtar Kelimeler

• Cartesian Positioning Mechanism
• Bernstein Polynomials
• Nonlinear Adaptive Control
• Trajectory Tracking
• Lyapunov Methods
• 3D Printing.

Kaynakça

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