Dynamic performance by mathematical modeling and trajectory tracking control in an FPGA-based architecture for an XYZ Cartesian system

Abstract This paper presents a novel methodology for analyzing, modeling, and experimental validating a dynamical model for a three-degree-of-freedom (3DoF) cartesian robot. The mathematical model is developed from a lumped parameter analysis of this study’s XYZ Cartesian system design. The Lagrangian equation of motion is applied to represent the dynamic behavior of the variables of the complete system. The control law improves performance by improving the dynamical model and the position error. Control algorithms for the Cartesian system are studied, with the best-fit controller consisting of a hyperbolic tangent, which is analyzed and simulated using MATLAB to study the system response. The controller is also implemented in a FPGA architecture to control the mechanism, and the results are compared with the simulation of the dynamical model with the control to verify performance, giving an 88% similitude between both the experimental and the simulated data. The error between the desired position and the real position is also obtained, giving the error in a rank between 1 and $$-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>-</mml:mo> </mml:math> 2 mm in the position of each axis. The comparison of the experimental and simulated results demonstrates a diminished position error and a higher precision performance, which validated the method used to obtain the equations.